{ "what": "The version seam of the TSavo bridge replay (certs/eth-tsavo-bridge.json, gaps), measured. TSavo's Bridge.ethIsFalse_of_claim takes as hypothesis OpenAI's challenge statement as TSavo's file states it (def Claim := ∀ k, 2 ≤ k → ClaimAt k), elaborated on Lean v4.33.1 with Anthropic's Mathlib 0df444a3; OpenAI proved exact_count_and_sat on Lean v4.34.1 with Mathlib d13f23b7 (certs/eth-kernel.json). The bytes are the same (the statement check); this record asks whether the ELABORATED statements are the same term, and so is every definition they can unfold to. It does not re-check any proof.", "campaign": "eth-refutation; the TSavo bridge lane, its version-seam gap; decided by tools/record-eth-seam.js from a GitHub-hosted run of .github/workflows/eth-seam.yml", "words": { "IDENTICAL": "Claim on Anthropic's side, ClaimAt unfolded once, is the same kernel term as exact_count_and_sat's statement on OpenAI's side, and every constant of the two closures is present on both sides as the same kernel term", "DIFFERENT": "anything else; every difference listed and classified (proof-internal, proof-reach, definitional), the verdict never softened by the classes" }, "kernelTerm": "the Expr structure: de Bruijn indices, constant names, universe levels with each parameter by its position, literals, projections; binder names, binder infos and metadata dropped (the kernel drops them). Surface: with them. Proof-erased: every subterm whose type is a proposition (Meta.isProof) replaced by one marker, and the closure taken over what remains", "closure": "from the root: definitions and opaques with their type and value; theorems with their statement only (proofs never followed); axioms and Quot with their type; inductives with their type, constructors, recursor, mutual block and, for a structure, its projection functions; constructors with their inductive; recursors with every rule's right-hand side. The proof-erased closure follows only what survives erasure, so it reaches no theorem", "statements": { "challenge": { "repository": "https://github.com/openai/math", "commit": "7ef5c0cc5ca4b0e072b7a050fca09ab24bc6fa3a", "path": "lean/ComparatorChallenges/SubexponentialSAT.lean", "sha256": "4183b2057cff350d66848215ff7167196dfc20e1891b598fdddea59077a76685", "module": "ComparatorChallenges.SubexponentialSAT", "root": "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "tsavo": { "repository": "https://github.com/TSavo/eth-bridge", "commit": "34f9ca204bed7fa6c595e56966773726e98dd3fd", "path": "bridge/Bridge/OpenAIStatement.lean", "sha256": "44ba68e759ec371685fdff9047ac5bf524347dd50961c0fdfe43cc049ba6abc1", "module": "Bridge.OpenAIStatement", "root": "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "unfolded": "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt" }, "bridgeHypothesis": { "theorem": "Bridge.ethIsFalse_of_claim", "module": "BridgeChallenge", "statement": "(∀ (h : OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim), MainResults.ETHIsFalse)", "hypothesis": "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "conclusion": "MainResults.ETHIsFalse", "ok": true } }, "sides": { "openai": { "project": "corpus/eth-refutation/bridge/openai (autoImplicit false, as OpenAI's lakefile) + the two statement modules", "toolchain": "leanprover/lean4:v4.34.1", "mathlib": "d13f23b723b8a846827a245b89c10fc7d3f11612", "exports": { "challenge": { "lean": "4.34.1", "githash": "5045d0056413266e57c625dcd7c365b10e377c52", "roots": [ "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" ], "rootModules": [ "ComparatorChallenges.SubexponentialSAT" ], "modulesImported": 11267, "closure": 2641, "erasedClosure": 2049, "nodes": 130487, "eraseErrors": 0, "ms": { "full": 43, "erased": 525, "write": 2354 }, "sha256": "dc2a3be04859836c336c5fff8f0bdd211d1aa0658ddaf5d8ea37d0cd3be20f78" }, "claim": { "lean": "4.34.1", "githash": "5045d0056413266e57c625dcd7c365b10e377c52", "roots": [ "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim" ], "rootModules": [ "Bridge.OpenAIStatement" ], "modulesImported": 11267, "closure": 2642, "erasedClosure": 2050, "nodes": 130504, "eraseErrors": 0, "ms": { "full": 48, "erased": 546, "write": 2362 }, "sha256": "39d5738952b382c8df1bad85287cf741bc240df37f91aa05532f6dab3c71ab23" } } }, "anthropic": { "project": "anthropics/formal-math@16a5ce41 eth/ with TSavo's bridge/ as eth-tsavo.yml sets it up (README block + the declared challenge-lib amendment) + the challenge module", "toolchain": "leanprover/lean4:v4.33.1", "mathlib": "0df444a360eaa60ab8c11dca51a86af692955474", "exports": { "challenge": { "lean": "4.33.1", "githash": "819816b2e0a3bf405af45ae5c7af2491d8f5bee6", "roots": [ "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" ], "rootModules": [ "ComparatorChallenges.SubexponentialSAT" ], "modulesImported": 11015, "closure": 2635, "erasedClosure": 2043, "nodes": 131377, "eraseErrors": 0, "ms": { "full": 43, "erased": 520, "write": 2241 }, "sha256": "5a19de424db0759eb290ee421aaf870b672ea651e6beec922b23c7cddf9d9f52" }, "claim": { "lean": "4.33.1", "githash": "819816b2e0a3bf405af45ae5c7af2491d8f5bee6", "roots": [ "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim" ], "rootModules": [ "Bridge.OpenAIStatement" ], "modulesImported": 11015, "closure": 2636, "erasedClosure": 2044, "nodes": 131394, "eraseErrors": 0, "ms": { "full": 44, "erased": 518, "write": 2216 }, "sha256": "290606d9ced120f45c31e3765cc38165ed6af83c77340e4bfdddb79bf636a575" }, "bridge": { "lean": "4.33.1", "githash": "819816b2e0a3bf405af45ae5c7af2491d8f5bee6", "roots": [], "rootModules": [], "modulesImported": 11017, "closure": 0, "erasedClosure": 0, "nodes": 0, "eraseErrors": 0, "ms": { "full": 0, "erased": 0, "write": 1 }, "sha256": "bbccc4fdde2ef463e87f50e9ed1f18a8fc09bb128d15088f3b1b61f5c5b0e225" } } } }, "verdict": "DIFFERENT", "why": "the two statements are the same kernel term (only a binder name differs: hk against an anonymous arrow binder), all 74 OAI constants of the challenge are the same kernel terms on both sides, but the closures are not: of 2585 common constants 308 differ, and 104 are present on one side only (305 definitional, 106 proof-reach, 1 proof-internal). Lean's kernel, reading each side's terms in the other environment, identifies 61 of the differing constants both ways and 199 one way. By cause (our reading, every one of the 412 differences): identified by the kernel both ways 61, in one closure only, identical in the other environment 1, the Monoid hierarchy's new shape in Mathlib 231, the moved files that construct ℝ, ℂ and NNReal 94, Lean core's Bool.and 2, a rename under the real power 10, NNReal's Nonneg 12, a proof-only binder order 1. 8 of the 151 constants the statement names directly differ: Monoid.toNPow, Real.instAdd, Real.instDivInvMonoid, Real.instLE, Real.instLT, Real.instMul, Real.instOne, Real.instZero. Modulo proofs: DIFFERENT", "moduloProofs": "DIFFERENT", "headline": { "compares": "Claim (TSavo's file, Anthropic's side, ClaimAt unfolded once) against exact_count_and_sat's statement (OpenAI's file, OpenAI's side); closures without Claim, ClaimAt and exact_count_and_sat", "statementTerm": { "kernelEqual": true, "surfaceEqual": false, "erasedEqual": true, "kernelDiff": null, "surfaceDiff": { "at": "∀ k body", "why": "binder name or info", "x": "(∀ (a._@._internal._hyg.#0 : (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) #0)), (Exists.{1} OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine (fun (machine : OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine) => (Exists.{1} (Fin (OAI.Algorithms.SubexponentialSAT.Computation.…", "y": "(∀ (hk : (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) #0)), (Exists.{1} OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine (fun (machine : OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine) => (Exists.{1} (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.tap…", "xIn": null, "yIn": null }, "nodes": [ 335, 335 ], "readAcross": { "openaiClaimReadInAnthropic": { "status": "same", "part": "statement" }, "anthropicClaimReadInOpenAI": { "status": "same", "part": "statement" }, "openaiChallengeReadInAnthropic": { "status": "same", "part": "type" }, "anthropicChallengeReadInOpenAI": { "status": "same", "part": "type" } } }, "closure": { "identical": false, "identicalModuloProofs": false, "surfaceIdentical": false, "constants": { "anthropic": { "full": 2634, "erased": 2042 }, "openai": { "full": 2640, "erased": 2048 }, "common": 2585 }, "presentOnly": { "anthropic": 49, "openai": 55 }, "kernelDiffer": 308, "surfaceOnly": 219, "erased": { "presentOnly": { "anthropic": 37, "openai": 43 }, "differ": 225 } }, "vocabulary": { "note": "the constants the statement is written in: the challenge's own OAI definitions, and every constant their types and values name directly (instances included)", "oaiDefinitions": 74, "oaiDiffering": [], "named": 151, "namedDiffering": [ { "name": "Monoid.toNPow", "class": "definitional", "group": "monoid-hierarchy", "kernel": "not identified" }, { "name": "Real.instAdd", "class": "definitional", "group": "moved-file", "kernel": "not identified" }, { "name": "Real.instDivInvMonoid", "class": "definitional", "group": "monoid-hierarchy", "kernel": "identified in OpenAI's environment only" }, { "name": "Real.instLE", "class": "definitional", "group": "moved-file", "kernel": "not identified" }, { "name": "Real.instLT", "class": "definitional", "group": "moved-file", "kernel": "not identified" }, { "name": "Real.instMul", "class": "definitional", "group": "moved-file", "kernel": "not identified" }, { "name": "Real.instOne", "class": "definitional", "group": "moved-file", "kernel": "not identified" }, { "name": "Real.instZero", "class": "definitional", "group": "moved-file", "kernel": "not identified" } ] }, "byClass": { "definitional": 305, "proof-reach": 106, "proof-internal": 1 }, "kernelAcrossSides": { "note": "each side's term read in the other environment (SeamCross): identified = same, same up to binder names, or definitionally equal there by Lean's kernel (theorem _ : foreign = local := Eq.refl accepted)", "not identified": 48, "identified both ways": 61, "identified in OpenAI's environment only": 198, "identified in Anthropic's environment only": 1, "one side only": 103, "one side only, identified in the other environment": 1 }, "groups": { "moved-file": { "reading": "The files that construct ℝ, ℂ and NNReal moved (Mathlib/Data/Real/Basic.lean → Mathlib/Basic/Real/Basic.lean, likewise Complex.Basic and NNReal.Defs). Private definitions (Real.add, Real.mul, Real.le, Real.inv', …) and the irreducible_def wrappers (Real.definition._@…, Real.wrapped._@…) carry their module in their names, so the same definitions appear under different names on the two sides, and the instances that use them (Real.instAdd, Real.instLE, …) name constants the other environment does not have.", "total": 94, "not identified": 10, "one side only": 84 }, "monoid-hierarchy": { "reading": "Mathlib's Monoid hierarchy changed shape between the two commits. In 0df444a3 (Anthropic's side) Monoid.mk takes a Semigroup and MulOneClass.mk a MulOne (AddMonoid, AddZeroClass likewise); in d13f23b7 (OpenAI's side) Monoid.mk takes One, Mul and mul_assoc directly and MulOneClass.mk takes One and Mul (Monoid.toMul, AddMonoid.toAdd, MulOneClass.toOne, … exist only there). The fields are the same propositions, but the structures carrying them are different inductive types, so every instance built with these constructors (on ℕ, ℚ, ℝ, ℂ, NNReal, Multiset: Real.commRing among them) and every statement projecting through them is a different term. Where Anthropic's term only projects (an instance path through Monoid.toSemigroup), it reads in d13f23b7 and the kernel identifies it there; where it builds a Monoid, it does not type-check there.", "total": 231, "not identified": 36, "identified in OpenAI's environment only": 186, "one side only": 9 }, "kernel-identified": { "reading": "The two terms differ, mostly in instance paths (which chain of parent projections reaches an instance: DivisionSemiring.toSemiring against CommSemiring.toSemiring from the same Field, in the Cauchy-sequence construction of ℝ), and Lean's kernel, reading each side's term in the other environment, finds them definitionally equal there, both ways.", "total": 61, "identified both ways": 61 }, "lean-core": { "reading": "Lean core: Bool.and is compiled through the matcher Bool.and.match_1 in v4.33.1 and directly by Bool.rec in v4.34.1; OpenAI's Bool.and, read in Anthropic's environment, is definitionally equal there.", "total": 2, "identified in Anthropic's environment only": 1, "one side only": 1 }, "renamed": { "reading": "A rename used by Real.sinOrderIso (so by Real.arcsin, Complex.arg, Complex.log, the real power): Equiv.setCongr and OrderIso.setCongr (0df444a3, universe parameters changed) against Set.equivOfEq and Set.orderIsoOfEq (d13f23b7).", "total": 10, "identified in OpenAI's environment only": 2, "one side only": 8 }, "nonneg": { "reading": "NNReal's carrier: d13f23b7 has a definition Nonneg for the subtype {x // 0 ≤ x} that the NNReal instances name; 0df444a3 writes the subtype directly.", "total": 12, "identified in OpenAI's environment only": 10, "not identified": 1, "one side only": 1 }, "binder-order": { "reading": "An auxiliary proof whose implicit binders {a} and [SemilatticeSup α] come in the other order; only proofs reach it.", "total": 1, "not identified": 1 }, "elsewhere-identified": { "reading": "Present in one closure only, but the constant exists in the other environment and the kernel identifies it there; the other side's terms simply reach the same instance by another path.", "total": 1, "one side only, identified in the other environment": 1 } }, "kernelDefeqAcrossSides": { "bothWays": 61, "notBothWays": 247, "byClass": { "definitional": { "bothWays": 37, "notBothWays": 188 }, "proof-reach": { "bothWays": 24, "notBothWays": 58 }, "proof-internal": { "bothWays": 0, "notBothWays": 1 } } }, "crossCounts": { "anthropicTermsReadInOpenAI": { "challenge": { "seconds": 7, "lean": "4.34.1", "counts": { "same-kernel": 64, "defeq": 259, "names-absent": 12, "absent": 44, "same": 2215, "not-defeq": 39, "shape": 2 } }, "claim": { "seconds": 6, "lean": "4.34.1", "counts": { "same-kernel": 64, "defeq": 259, "names-absent": 12, "absent": 44, "same": 2217, "not-defeq": 39, "shape": 2 } } }, "openaiTermsReadInAnthropic": { "challenge": { "seconds": 5, "lean": "4.33.1", "counts": { "same-kernel": 64, "defeq": 62, "names-absent": 222, "absent": 55, "same": 2214, "not-defeq": 24 } }, "claim": { "seconds": 6, "lean": "4.33.1", "counts": { "same-kernel": 64, "defeq": 62, "names-absent": 222, "absent": 55, "same": 2216, "not-defeq": 24 } } } }, "differences": [ { "name": "Real.instLT", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of LT.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.lt", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.lt", "xIn": "(LT.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.lt)", "yIn": "(LT.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.lt)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instLT (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instLT (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of LT.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.lt", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.lt", "xIn": "(LT.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.lt)", "yIn": "(LT.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.lt)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Basic.Real.Basic.#0.Real.lt" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Data.Real.Basic.#0.Real.lt" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "moved-file" }, { "name": "Real.instZero", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of Zero.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.zero", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.zero", "xIn": "(Zero.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.zero)", "yIn": "(Zero.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.zero)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instZero (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instZero (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of Zero.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.zero", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.zero", "xIn": "(Zero.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.zero)", "yIn": "(Zero.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.zero)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Basic.Real.Basic.#0.Real.zero" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Data.Real.Basic.#0.Real.zero" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "moved-file" }, { "name": "Real.instLE", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of LE.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.le", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.le", "xIn": "(LE.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.le)", "yIn": "(LE.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.le)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instLE (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instLE (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of LE.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.le", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.le", "xIn": "(LE.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.le)", "yIn": "(LE.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.le)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Basic.Real.Basic.#0.Real.le" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Data.Real.Basic.#0.Real.le" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "moved-file" }, { "name": "Real.instMul", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of Mul.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.mul", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.mul", "xIn": "(Mul.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.mul)", "yIn": "(Mul.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.mul)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instMul (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instMul (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of Mul.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.mul", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.mul", "xIn": "(Mul.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.mul)", "yIn": "(Mul.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.mul)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Basic.Real.Basic.#0.Real.mul" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Data.Real.Basic.#0.Real.mul" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "moved-file" }, { "name": "Monoid.toNPow", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M body › λ self body", "why": "different projections", "x": "(#0).Monoid#4", "y": "(#0).Monoid#5", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Monoid.toNPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Monoid.toNPow (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M body › λ self body", "why": "different projections", "x": "(#0).Monoid#4", "y": "(#0).Monoid#5", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n ⋯ = fun M [self : Monoid M] => self.5\nargument has type\n (M : Type u) → [self : Monoid M] → NPow M\nbut function has type\n (∀ (M : Type u) [self : Monoid M] (x : M), x ^ 0 = 1) → Prop" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n ⋯ = fun M [self : Monoid M] => self.6\nargument has type\n (M : Type u_2) → [self : Monoid M] → NPow M\nbut function has type\n (∀ (M : Type u_2) [self : Monoid M] (a : M), a * 1 = a) → Prop" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "Real.instAdd", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of Add.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.add", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.add", "xIn": "(Add.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.add)", "yIn": "(Add.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.add)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instAdd (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instAdd (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of Add.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.add", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.add", "xIn": "(Add.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.add)", "yIn": "(Add.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.add)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Basic.Real.Basic.#0.Real.add" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Data.Real.Basic.#0.Real.add" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "moved-file" }, { "name": "Real.instOne", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of One.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.one", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.one", "xIn": "(One.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.one)", "yIn": "(One.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.one)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instOne (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instOne (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of One.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.one", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.one", "xIn": "(One.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.one)", "yIn": "(One.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.one)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Basic.Real.Basic.#0.Real.one" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Data.Real.Basic.#0.Real.one" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "moved-file" }, { "name": "CauSeq.Completion.Cauchy", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#900982752._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "Rat.instField", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Field.Rat", "openai": "Mathlib.Algebra.Field.Rat" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "let __spread.#0._@.Mathlib.Algebra.Field.Rat.#310067971._hygCtx._hyg.#11 body › let __spread.#1._@.Mathlib.Algebra.Field.Rat.#310067971._hygCtx._hyg.#11 body › arg 16 of Field.mk.{0} › λ x._@.Mathlib.Algebra.Field.Rat.#310067971._hygCtx._hyg.#27 body › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Rat (Monoid.toSemigroup.{0} Rat (Semiring.toMonoid.{0} Rat (Ring.toSemiring.{0} Rat (CommRing.toRing.{0} Rat Rat.commRing)))))", "yIn": "(Monoid.toMul.{0} Rat (Semiring.toMonoid.{0} Rat (Ring.toSemiring.{0} Rat (CommRing.toRing.{0} Rat Rat.commRing))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "let __spread.#0._@.Mathlib.Algebra.Field.Rat.#310067971._hygCtx._hyg.#11 body › let __spread.#1._@.Mathlib.Algebra.Field.Rat.#310067971._hygCtx._hyg.#11 body › arg 16 of Field.mk.{0} › λ x._@.Mathlib.Algebra.Field.Rat.#310067971._hygCtx._hyg.#27 body › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Rat (Monoid.toSemigroup.{0} Rat (Semiring.toMonoid.{0} Rat (Ring.toSemiring.{0} Rat (CommRing.toRing.{0} Rat Rat.commRing)))))", "yIn": "(Monoid.toMul.{0} Rat (Semiring.toMonoid.{0} Rat (Ring.toSemiring.{0} Rat (CommRing.toRing.{0} Rat Rat.commRing))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CauSeq.Completion.instNatCastCauchy", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.instNatCastCauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.instNatCastCauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#794557932._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#5 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#8 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#11 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#5 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#8 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#11 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#5 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#8 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#11 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#5 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#8 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3479284576._hygCtx._hyg.#11 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.equiv", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2046334364._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2046334364._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2046334364._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2046334364._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2046334364._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2046334364._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 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"Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (CommMonoid.toMonoid.{u0} #3 (CommMonoidWithZero.toCommMonoid.{u0} #3 (CommGroupWithZero.toCommMonoidWithZero.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (CommMonoid.toMonoid.{u0} #3 (CommMonoidWithZero.toCommMonoid.{u0} #3 (CommGroupWithZero.toCommMonoidWithZero.{u0} #3 #2))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommGroupWithZero.zpow_succ'", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G₀ body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 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"type": { "at": "∀ G₀ body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (CommMonoid.toMonoid.{u0} #3 (CommMonoidWithZero.toCommMonoid.{u0} #3 (CommGroupWithZero.toCommMonoidWithZero.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (CommMonoid.toMonoid.{u0} #3 (CommMonoidWithZero.toCommMonoid.{u0} #3 (CommGroupWithZero.toCommMonoidWithZero.{u0} #3 #2))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommGroupWithZero.mul_inv_cancel", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G₀ body › ∀ self body › ∀ a body › ∀ a._@._internal._hyg.#0 body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (CommMonoid.toMonoid.{u0} #3 (CommMonoidWithZero.toCommMonoid.{u0} #3 (CommGroupWithZero.toCommMonoidWithZero.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (CommMonoid.toMonoid.{u0} #3 (CommMonoidWithZero.toCommMonoid.{u0} #3 (CommGroupWithZero.toCommMonoidWithZero.{u0} #3 #2))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CommGroupWithZero.mul_inv_cancel (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt 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OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Rat.addCommGroup", "kind": "def", "module": { "anthropic": "Mathlib.Data.Rat.Defs", "openai": "Mathlib.Data.Rat.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of AddCommGroup.mk.{0} › arg 2 of AddGroup.mk.{0} › arg 2 of SubNegMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} Rat (AddSemigroup.mk.{0} Rat Rat.instAdd Rat.add_assoc) (Zero.ofOfNat0.{0} Rat (Rat.instOfNat 0)) Rat.zero_add Rat.add_zero (NSMul.mk.{0} Rat (fun (x1._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Nat) => (fun (x2._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Rat) => (HMul.hMul.{0, 0…", "y": "(AddMonoid.mk.{0} Rat (Zero.ofOfNat0.{0} Rat (Rat.instOfNat 0)) Rat.instAdd Rat.add_assoc Rat.zero_add Rat.add_zero (NSMul.mk.{0} Rat (fun (x1._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Nat) => (fun (x2._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Rat) => (HMul.hMul.{0, 0, 0} Rat Rat Rat (instHMul…", "xIn": "(SubNegMonoid.mk.{0} Rat (AddMonoid.mk.{0} Rat (AddSemigroup.mk.{0} Rat Rat.instAdd Rat.add_assoc) (Zero.ofOfNat0.{0} Rat (Rat.instOfNat 0)) Rat.zero_add Rat.add_zero (NSMul.mk.{0} Rat (fun (x1._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Nat) => (fun (x2._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 :…", "yIn": "(SubNegMonoid.mk.{0} Rat (AddMonoid.mk.{0} Rat (Zero.ofOfNat0.{0} Rat (Rat.instOfNat 0)) Rat.instAdd Rat.add_assoc Rat.zero_add Rat.add_zero (NSMul.mk.{0} Rat (fun (x1._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Nat) => (fun (x2._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Rat) => (HMul.hMul.{0, 0,…" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Rat.addCommGroup (value of) ← Rat.addGroup (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Rat.addCommGroup (value of) ← Rat.addGroup (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of AddCommGroup.mk.{0} › arg 2 of AddGroup.mk.{0} › arg 2 of SubNegMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} Rat (AddSemigroup.mk.{0} Rat Rat.instAdd ⟨proof⟩) (Zero.ofOfNat0.{0} Rat (Rat.instOfNat 0)) ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Rat (fun (x1._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Nat) => (fun (x2._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Rat) => (HMul.hMul.{0, 0, 0} Rat Rat Rat…", "y": "(AddMonoid.mk.{0} Rat (Zero.ofOfNat0.{0} Rat (Rat.instOfNat 0)) Rat.instAdd ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Rat (fun (x1._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Nat) => (fun (x2._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Rat) => (HMul.hMul.{0, 0, 0} Rat Rat Rat (instHMul.{0} Rat Rat.ins…", "xIn": "(SubNegMonoid.mk.{0} Rat (AddMonoid.mk.{0} Rat (AddSemigroup.mk.{0} Rat Rat.instAdd ⟨proof⟩) (Zero.ofOfNat0.{0} Rat (Rat.instOfNat 0)) ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Rat (fun (x1._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Nat) => (fun (x2._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Rat) => (HMul.h…", "yIn": "(SubNegMonoid.mk.{0} Rat (AddMonoid.mk.{0} Rat (Zero.ofOfNat0.{0} Rat (Rat.instOfNat 0)) Rat.instAdd ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Rat (fun (x1._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Nat) => (fun (x2._@.Mathlib.Data.Rat.Defs.#405133445._hygCtx._hyg.#30 : Rat) => (HMul.hMul.{0, 0, 0} Rat Rat Rat …" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk ℚ Zero.ofOfNat0\nargument has type\n Zero ℚ\nbut function has type\n [toAddSemigroup : AddSemigroup ℚ] →\n [toZero : Zero ℚ] →\n (∀ (a : ℚ), 0 + a = a) →\n (∀ (a : ℚ), a + 0 = a) →\n [toNSMul : NSMul ℚ] →\n autoParam (∀ (x : ℚ), 0 • x = 0) AddMonoid.nsmul_zero._autoParam →\n autoParam (∀ (n : ℕ) (x : ℚ), (n …" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk ℚ { toAdd := Rat.instAdd, add_assoc := Rat.add_assoc }\nargument has type\n AddSemigroup ℚ\nbut function has type\n [toZero : Zero ℚ] →\n [toAdd : Add ℚ] →\n (∀ (a b c : ℚ), a + b + c = a + (b + c)) →\n (∀ (a : ℚ), 0 + a = a) →\n (∀ (a : ℚ), a + 0 = a) →\n [toNSMul : NSMul ℚ] →\n autoParam (∀ (x : ℚ), 0 • x …" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "CauSeq.Completion.mk", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.mk (value of) ← CauSeq.Completion.instNatCastCauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.mk (value of) ← CauSeq.Completion.instNatCastCauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1434432364._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.instNatCast", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.instNatCast (value of) ← CauSeq.Completion.instNatCastCauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instNatCast (value of) ← CauSeq.Completion.instNatCastCauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2682805263._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "Real.instDivInvMonoid", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 5 of DivInvMonoid.mk.{0} › arg 2 of ZPow.mk.{0} › arg 3 of zpowRec.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real Real.instMonoid))", "yIn": "(Monoid.toMul.{0} Real Real.instMonoid)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 5 of DivInvMonoid.mk.{0} › arg 2 of ZPow.mk.{0} › arg 3 of zpowRec.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real Real.instMonoid))", "yIn": "(Monoid.toMul.{0} Real Real.instMonoid)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Nat.instAddCancelCommMonoid", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Nat.Defs", "openai": "Mathlib.Algebra.Group.Nat.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of AddCancelCommMonoid.mk.{0} › arg 2 of AddCommMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} Nat (AddSemigroup.mk.{0} Nat (Add.mk.{0} Nat Nat.add) Nat.add_assoc) (Zero.mk.{0} Nat Nat.zero) Nat.zero_add Nat.add_zero (NSMul.mk.{0} Nat (fun (m : Nat) => (fun (n : Nat) => (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) #1 #0)))) Nat.zero_mul Nat.succ_mul)", "y": "(AddMonoid.mk.{0} Nat (Zero.mk.{0} Nat Nat.zero) (Add.mk.{0} Nat Nat.add) Nat.add_assoc Nat.zero_add Nat.add_zero (NSMul.mk.{0} Nat (fun (m : Nat) => (fun (n : Nat) => (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) #1 #0)))) Nat.zero_mul Nat.succ_mul)", "xIn": "(AddCommMonoid.mk.{0} Nat (AddMonoid.mk.{0} Nat (AddSemigroup.mk.{0} Nat (Add.mk.{0} Nat Nat.add) Nat.add_assoc) (Zero.mk.{0} Nat Nat.zero) Nat.zero_add Nat.add_zero (NSMul.mk.{0} Nat (fun (m : Nat) => (fun (n : Nat) => (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) #1 #0)))) Nat.zero_mul Nat.succ_mul) …", "yIn": "(AddCommMonoid.mk.{0} Nat (AddMonoid.mk.{0} Nat (Zero.mk.{0} Nat Nat.zero) (Add.mk.{0} Nat Nat.add) Nat.add_assoc Nat.zero_add Nat.add_zero (NSMul.mk.{0} Nat (fun (m : Nat) => (fun (n : Nat) => (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) #1 #0)))) Nat.zero_mul Nat.succ_mul) Nat.add_comm)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Nat.instAddCancelCommMonoid (value of) ← Nat.instAddCommMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Nat.instAddCancelCommMonoid (value of) ← Nat.instAddCommMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of AddCancelCommMonoid.mk.{0} › arg 2 of AddCommMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} Nat (AddSemigroup.mk.{0} Nat (Add.mk.{0} Nat Nat.add) ⟨proof⟩) (Zero.mk.{0} Nat Nat.zero) ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Nat (fun (m : Nat) => (fun (n : Nat) => (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) #1 #0)))) ⟨proof⟩ ⟨proof⟩)", "y": "(AddMonoid.mk.{0} Nat (Zero.mk.{0} Nat Nat.zero) (Add.mk.{0} Nat Nat.add) ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Nat (fun (m : Nat) => (fun (n : Nat) => (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) #1 #0)))) ⟨proof⟩ ⟨proof⟩)", "xIn": "(AddCommMonoid.mk.{0} Nat (AddMonoid.mk.{0} Nat (AddSemigroup.mk.{0} Nat (Add.mk.{0} Nat Nat.add) ⟨proof⟩) (Zero.mk.{0} Nat Nat.zero) ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Nat (fun (m : Nat) => (fun (n : Nat) => (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) #1 #0)))) ⟨proof⟩ ⟨proof⟩) ⟨proof⟩)", "yIn": "(AddCommMonoid.mk.{0} Nat (AddMonoid.mk.{0} Nat (Zero.mk.{0} Nat Nat.zero) (Add.mk.{0} Nat Nat.add) ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Nat (fun (m : Nat) => (fun (n : Nat) => (HMul.hMul.{0, 0, 0} Nat Nat Nat (instHMul.{0} Nat instMulNat) #1 #0)))) ⟨proof⟩ ⟨proof⟩) ⟨proof⟩)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk ℕ { zero := Nat.zero }\nargument has type\n Zero ℕ\nbut function has type\n [toAddSemigroup : AddSemigroup ℕ] →\n [toZero : Zero ℕ] →\n (∀ (a : ℕ), 0 + a = a) →\n (∀ (a : ℕ), a + 0 = a) →\n [toNSMul : NSMul ℕ] →\n autoParam (∀ (x : ℕ), 0 • x = 0) AddMonoid.nsmul_zero._autoParam →\n autoParam (∀ (n x : ℕ), (n…" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk ℕ { add := Nat.add, add_assoc := Nat.add_assoc }\nargument has type\n AddSemigroup ℕ\nbut function has type\n [toZero : Zero ℕ] →\n [toAdd : Add ℕ] →\n (∀ (a b c : ℕ), a + b + c = a + (b + c)) →\n (∀ (a : ℕ), 0 + a = a) →\n (∀ (a : ℕ), a + 0 = a) →\n [toNSMul : NSMul ℕ] →\n autoParam (∀ (x : ℕ), 0 • x = 0) A…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "Monoid.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": 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identified", "group": "monoid-hierarchy" }, { "name": "Monoid.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toSemigroup type › head", "why": "different leaves", "x": "Semigroup.{u1}", "y": "One.{u1}", "xIn": "(Semigroup.{u1} #1)", "yIn": "(One.{u1} #1)" }, "rules": { "x": [ [ "Monoid.mk", 7 ] ], "y": [ [ "Monoid.mk", 8 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Monoid.rec (rec of) ← Monoid (type of) ← Monoid.toNPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Monoid.rec (rec of) ← Monoid (type of) ← Monoid.toNPow (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toSemigroup type › head", "why": "different leaves", "x": "Semigroup.{u1}", "y": "One.{u1}", "xIn": "(Semigroup.{u1} #1)", "yIn": "(One.{u1} #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @Monoid.mk M toOne\nargument has type\n One M\nbut function has type\n [toSemigroup : Semigroup M] →\n [toOne : One M] →\n (∀ (a : M), 1 * a = a) →\n (∀ (a : M), a * 1 = a) →\n [toNPow : NPow M] →\n autoParam (∀ (x : M), x ^ 0 = 1) Monoid.npow_zero._autoParam →\n autoParam (∀ (n : ℕ) (x : M), x ^ (n + 1) = x ^ n * x) Mono…" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @Monoid.mk M toSemigroup\nargument has type\n Semigroup M\nbut function has type\n [toOne : One M] →\n [toMul : Mul M] →\n (∀ (a b c : M), a * b * c = a * (b * c)) →\n (∀ (a : M), 1 * a = a) →\n (∀ (a : M), a * 1 = a) →\n [toNPow : NPow M] →\n autoParam (∀ (x : M), x ^ 0 = 1) Monoid.npow_zero._autoParam →\n …" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "Monoid.toOne", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M body › λ self body", "why": "different projections", "x": "(#0).Monoid#1", "y": "(#0).Monoid#0", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Monoid.toOne (proj of) ← Monoid (type of) ← Monoid.toNPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Monoid.toOne (proj of) ← Monoid (type of) ← Monoid.toNPow (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ 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"Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ n body › ∀ x body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 #2))", "yIn": "(Monoid.toMul.{u0} #3 #2)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Monoid.npow_succ (proj of) ← Monoid (type of) ← Monoid.toNPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Monoid.npow_succ (proj of) ← Monoid (type of) ← Monoid.toNPow (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ n body › ∀ x body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 #2))", "yIn": "(Monoid.toMul.{u0} #3 #2)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Monoid.mul_one", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 #1))", "yIn": "(Monoid.toMul.{u0} #2 #1)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Monoid.mul_one (proj of) ← Monoid (type of) ← Monoid.toNPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Monoid.mul_one (proj of) ← Monoid (type of) ← Monoid.toNPow (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 #1))", "yIn": "(Monoid.toMul.{u0} #2 #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Monoid.one_mul", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 #1))", "yIn": "(Monoid.toMul.{u0} #2 #1)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Monoid.one_mul (proj of) ← Monoid (type of) ← Monoid.toNPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Monoid.one_mul (proj of) ← Monoid (type of) ← Monoid.toNPow (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 #1))", "yIn": "(Monoid.toMul.{u0} #2 #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Field.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ motive body › ∀ mk type › ∀ toCommRing body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 (Semiring.toMonoid.{u1} #7 (Ring.toSemiring.{u1} #7 (CommRing.toRing.{u1} #7 #5)))))", "yIn": "(Monoid.toMul.{u1} #7 (Semiring.toMonoid.{u1} #7 (Ring.toSemiring.{u1} #7 (CommRing.toRing.{u1} #7 #5))))" }, "rules": { "x": [ [ "Field.mk", 19 ] ], "y": [ [ "Field.mk", 19 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Field.rec (rec of) ← Field (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Field.rec (rec of) ← Field (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ motive body › ∀ mk type › ∀ toCommRing body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 (Semiring.toMonoid.{u1} #7 (Ring.toSemiring.{u1} #7 (CommRing.toRing.{u1} #7 #5)))))", "yIn": "(Monoid.toMul.{u1} #7 (Semiring.toMonoid.{u1} #7 (Ring.toSemiring.{u1} #7 (CommRing.toRing.{u1} #7 #5))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Field.qsmul_def", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ x body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2))))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2)))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Field.qsmul_def (proj of) ← Field (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Field.qsmul_def (proj of) ← Field (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ x body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2))))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 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"y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2))))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2)))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Field.mul_inv_cancel (proj of) ← Field (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Field.mul_inv_cancel (proj of) ← Field (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ a._@._internal._hyg.#0 body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2))))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2)))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Field.nnqsmul_def", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ self body › ∀ q body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2))))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2)))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Field.nnqsmul_def (proj of) ← Field (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Field.nnqsmul_def (proj of) ← Field (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ q body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2))))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2)))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Field.zpow_succ'", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2))))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2)))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Field.zpow_succ' (proj of) ← Field (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Field.zpow_succ' (proj of) ← Field (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2))))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2)))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionSemiring.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ toSemiring body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #6 (Monoid.toSemigroup.{u0} #6 (Semiring.toMonoid.{u0} #6 #5)))", "yIn": "(Monoid.toMul.{u0} #6 (Semiring.toMonoid.{u0} #6 #5))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionSemiring.mk (value of) ← Semifield.toDivisionSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivisionSemiring.mk (value of) ← DivisionRing.toDivisionSemiring (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ toSemiring body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #6 (Monoid.toSemigroup.{u0} #6 (Semiring.toMonoid.{u0} #6 #5)))", "yIn": "(Monoid.toMul.{u0} #6 (Semiring.toMonoid.{u0} #6 #5))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Semifield.div_eq_mul_inv", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semifield.div_eq_mul_inv (value of) ← Semifield.toDivisionSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semifield.div_eq_mul_inv (proj of) ← Semifield (type of) ← Semifield.toCommSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Semifield.zpow_succ'", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semifield.zpow_succ' (value of) ← Semifield.toDivisionSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semifield.zpow_succ' (proj of) ← Semifield (type of) ← Semifield.toCommSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": 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"anthropic": "Semifield.mul_inv_cancel (value of) ← Semifield.toDivisionSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semifield.mul_inv_cancel (proj of) ← Semifield (type of) ← Semifield.toCommSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ a._@._internal._hyg.#0 body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 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"y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 #2))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Semifield.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ toCommSemiring body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #6 (Monoid.toSemigroup.{u0} #6 (Semiring.toMonoid.{u0} #6 (CommSemiring.toSemiring.{u0} #6 #5))))", "yIn": "(Monoid.toMul.{u0} #6 (Semiring.toMonoid.{u0} #6 (CommSemiring.toSemiring.{u0} #6 #5)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semifield.mk (value of) ← Field.toSemifield (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semifield.mk (value of) ← Field.toSemifield (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ toCommSemiring body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #6 (Monoid.toSemigroup.{u0} #6 (Semiring.toMonoid.{u0} #6 (CommSemiring.toSemiring.{u0} #6 #5))))", "yIn": "(Monoid.toMul.{u0} #6 (Semiring.toMonoid.{u0} #6 (CommSemiring.toSemiring.{u0} #6 #5)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommSemiring.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ toSemiring body › ∀ mul_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 #2)))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 #2))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CommSemiring.mk (value of) ← Field.toSemifield (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CommSemiring.mk (value of) ← Field.toSemifield (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ toSemiring body › ∀ mul_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 #2)))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 #2))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Field.toSemifield._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ K body › ∀ inst._@.Mathlib.Algebra.Field.Defs.#4048198401._hygCtx._hyg.#3 body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2))))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 (Field.toCommRing.{u0} #3 #2)))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Field.toSemifield._proof_1 (value of) ← Field.toSemifield (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Field.toSemifield._proof_1 (value of) ← Field.toSemifield (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Ring.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ toSemiring body › ∀ toNeg body › ∀ toSub body › ∀ toZSMul body › ∀ sub_eq_add_neg type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #6 (AddMonoid.toAddSemigroup.{u0} #6 (AddCommMonoid.toAddMonoid.{u0} #6 (Semiring.toAddCommMonoid.{u0} #6 #5))))", "yIn": "(AddMonoid.toAdd.{u0} #6 (AddCommMonoid.toAddMonoid.{u0} #6 (Semiring.toAddCommMonoid.{u0} #6 #5)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Ring.mk (ctor of) ← Ring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Ring.mk (ctor of) ← Ring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ toSemiring body › ∀ toNeg body › ∀ toSub body › ∀ toZSMul body › ∀ sub_eq_add_neg type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › 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CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ motive body › ∀ mk type › ∀ toSemiring body › ∀ toNeg body › ∀ toSub body › ∀ toZSMul body › ∀ sub_eq_add_neg type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #7 (AddMonoid.toAddSemigroup.{u1} #7 (AddCommMonoid.toAddMonoid.{u1} #7 (Semiring.toAddCommMonoid.{u1} #7 #5))))", "yIn": "(AddMonoid.toAdd.{u1} #7 (AddCommMonoid.toAddMonoid.{u1} #7 (Semiring.toAddCommMonoid.{u1} #7 #5)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Ring.sub_eq_add_neg", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 #2)))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 #2))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Ring.sub_eq_add_neg (proj of) ← Ring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Ring.sub_eq_add_neg (proj of) ← Ring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 #2)))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 #2))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Ring.zsmul_succ'", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 #2)))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 #2))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Ring.zsmul_succ' (proj of) ← Ring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Ring.zsmul_succ' (proj of) ← Ring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 #2)))))", "yIn": "(AddMonoid.toAdd.{u0} #3 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(AddMonoid.toAddSemigroup.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (Semiring.toAddCommMonoid.{u0} #2 (Ring.toSemiring.{u0} #2 #1)))))", "yIn": "(AddMonoid.toAdd.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (Semiring.toAddCommMonoid.{u0} #2 (Ring.toSemiring.{u0} #2 #1))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "IsCauSeq", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#5 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#8 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#11 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#5 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#8 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#11 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "IsCauSeq (value of) ← CauSeq (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "IsCauSeq (value of) ← CauSeq (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#5 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#8 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#11 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#5 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#8 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1944376911._hygCtx._hyg.#11 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.LimZero", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.LimZero (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.LimZero (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#519966931._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.instSub", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#701254411._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#701254411._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#701254411._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#701254411._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#701254411._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#701254411._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← 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], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › ∀ b body › arg 3 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Rat (Monoid.toSemigroup.{0} Rat (CommMonoid.toMonoid.{0} Rat Rat.commMonoid)))", "yIn": "(Monoid.toMul.{0} Rat (CommMonoid.toMonoid.{0} Rat Rat.commMonoid))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Rat.commGroupWithZero._proof_1 (value of) ← Rat.commGroupWithZero (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Rat.commGroupWithZero._proof_1 (value of) ← Rat.commGroupWithZero (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Rat.commGroupWithZero._proof_2", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Rat", "openai": "Mathlib.Algebra.Ring.Rat" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ x._@.Mathlib.Algebra.Ring.Rat.#2336346949._hygCtx._hyg.#27 body › ∀ x._@.Mathlib.Algebra.Ring.Rat.#2336346949._hygCtx._hyg.#29 body › arg 3 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Rat (Monoid.toSemigroup.{0} Rat (CommMonoid.toMonoid.{0} Rat Rat.commMonoid)))", "yIn": "(Monoid.toMul.{0} Rat (CommMonoid.toMonoid.{0} Rat 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"Mathlib.Algebra.Group.Monoid" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M body › λ self body", "why": "different projections", "x": "(#0).AddMonoid#1", "y": "(#0).AddMonoid#0", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddMonoid.toZero (type of) ← Field.mk (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddMonoid.toZero (type of) ← Field.mk (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M body › λ self body", "why": "different projections", "x": "(#0).AddMonoid#1", "y": "(#0).AddMonoid#0", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n (fun M [self : AddMonoid M] => self.1) = fun M [self : AddMonoid M] => self.2\nargument has type\n (M : Type u) → [self : AddMonoid M] → Zero M\nbut function has type\n ((M : Type u) → [self : AddMonoid M] → AddSemigroup M) → Prop" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n (fun M [self : AddMonoid M] => self.2) = fun M [self : AddMonoid M] => self.1\nargument has type\n (M : Type u_2) → [self : AddMonoid M] → Zero M\nbut function has type\n ((M : Type u_2) → [self : AddMonoid M] → Add M) → Prop" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "DivisionRing.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ toRing body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #6 (Monoid.toSemigroup.{u0} #6 (Semiring.toMonoid.{u0} #6 (Ring.toSemiring.{u0} #6 #5))))", "yIn": "(Monoid.toMul.{u0} #6 (Semiring.toMonoid.{u0} #6 (Ring.toSemiring.{u0} #6 #5)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionRing.mk (ctor of) ← DivisionRing (type of) ← DivisionRing.toRing (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivisionRing.mk (ctor of) ← DivisionRing (type of) ← DivisionRing.toRing (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ toRing body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #6 (Monoid.toSemigroup.{u0} #6 (Semiring.toMonoid.{u0} #6 (Ring.toSemiring.{u0} #6 #5))))", "yIn": "(Monoid.toMul.{u0} #6 (Semiring.toMonoid.{u0} #6 (Ring.toSemiring.{u0} #6 #5)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionRing.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ motive body › ∀ mk type › ∀ toRing body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 (Semiring.toMonoid.{u1} #7 (Ring.toSemiring.{u1} #7 #5))))", "yIn": "(Monoid.toMul.{u1} #7 (Semiring.toMonoid.{u1} #7 (Ring.toSemiring.{u1} #7 #5)))" }, "rules": { "x": [ [ "DivisionRing.mk", 19 ] ], "y": [ [ "DivisionRing.mk", 19 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionRing.rec (rec of) ← DivisionRing (type of) ← DivisionRing.toRing (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivisionRing.rec (rec of) ← DivisionRing (type of) ← DivisionRing.toRing (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ motive body › ∀ mk type › ∀ toRing body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 (Semiring.toMonoid.{u1} #7 (Ring.toSemiring.{u1} #7 #5))))", "yIn": "(Monoid.toMul.{u1} #7 (Semiring.toMonoid.{u1} #7 (Ring.toSemiring.{u1} #7 #5)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, 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"DivisionRing.qsmul_def (proj of) ← DivisionRing (type of) ← DivisionRing.toRing (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivisionRing.qsmul_def (proj of) ← DivisionRing (type of) ← DivisionRing.toRing (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ x body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (DivisionRing.toRing.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (DivisionRing.toRing.{u0} #3 #2))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionRing.div_eq_mul_inv", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (DivisionRing.toRing.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (DivisionRing.toRing.{u0} 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(DivisionRing.toRing.{u0} #3 #2)))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (DivisionRing.toRing.{u0} #3 #2))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionRing.mul_inv_cancel (proj of) ← DivisionRing (type of) ← DivisionRing.toRing (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivisionRing.mul_inv_cancel (proj of) ← DivisionRing (type of) ← DivisionRing.toRing (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ a._@._internal._hyg.#0 body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": 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"AddGroup.toSubtractionMonoid._proof_2 (value of) ← AddGroup.toSubtractionMonoid (value of) ← abs (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddGroup.toSubtractionMonoid._proof_3", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ G body › ∀ inst._@.Mathlib.Algebra.Group.Defs.#1902858486._hygCtx._hyg.#3 body › ∀ x._@.Mathlib.Algebra.Group.Defs.#1902858486._hygCtx._hyg.#26 body › ∀ x._@.Mathlib.Algebra.Group.Defs.#1902858486._hygCtx._hyg.#28 body › ∀ a._@._internal._hyg.#0 type › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (AddGroup.toSubNegMonoid.{u0} #3 #2))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (AddGroup.toSubNegMonoid.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "AddGroup.toSubtractionMonoid._proof_3 (value of) ← AddGroup.toSubtractionMonoid (value of) ← abs (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddGroup.toSubtractionMonoid._proof_3 (value of) ← AddGroup.toSubtractionMonoid (value of) ← abs (value of) ← Real.instNatCast (type of) ← 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"AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (Semiring.toAddCommMonoid.{u0} #2 #1))))", "yIn": "(AddMonoid.toAdd.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (Semiring.toAddCommMonoid.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semiring.natCast_succ (value of) ← Ring.toAddGroupWithOne (type of) ← Real.equivCauchy._proof_1 (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semiring.natCast_succ (value of) ← Ring.toAddGroupWithOne (type of) ← Real.equivCauchy._proof_1 (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ self body › ∀ n body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (Semiring.toAddCommMonoid.{u0} #2 #1))))", "yIn": "(AddMonoid.toAdd.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (Semiring.toAddCommMonoid.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CauSeq.const", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.const (value of) ← CauSeq.instNatCast (value of) ← CauSeq.Completion.instNatCastCauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.const (value of) ← CauSeq.instNatCast (value of) ← CauSeq.Completion.instNatCastCauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309540._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "DivInvMonoid.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ toMonoid body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #6 (Monoid.toSemigroup.{u0} #6 #5))", "yIn": "(Monoid.toMul.{u0} #6 #5)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivInvMonoid.mk (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivInvMonoid.mk (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ toMonoid body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #6 (Monoid.toSemigroup.{u0} #6 #5))", "yIn": "(Monoid.toMul.{u0} #6 #5)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Real.instInv", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of Inv.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.inv'", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.inv'", "xIn": "(Inv.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.inv')", "yIn": "(Inv.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.inv')" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of Inv.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.inv'", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.inv'", "xIn": "(Inv.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.inv')", "yIn": "(Inv.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.inv')" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Basic.Real.Basic.#0.Real.inv'" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Data.Real.Basic.#0.Real.inv'" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "moved-file" }, { "name": "Real.instDivInvMonoid._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › ∀ b body › arg 2 of Eq.{1} › arg 4 of HDiv.hDiv.{0, 0, 0} › arg 2 of instHDiv.{0} › arg 2 of Div.mk.{0} › arg 2 of DivInvMonoid.div'.{0}", "why": "applications of different arity", "x": "(Monoid.mk.{0} Real (Semigroup.mk.{0} Real (Mul.mk.{0} Real (Mul.mul.{0} Real (Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real Real.instMonoid)))) (Semigroup.mul_assoc.{0} Real (Monoid.toSemigroup.{0} Real Real.instMonoid))) (One.mk.{0} Real (One.one.{0} Real (Monoid.toOne.{0} Real Real.instMonoid))) (Monoid.one_…", "y": "(Monoid.mk.{0} Real (One.mk.{0} Real (One.one.{0} Real (Monoid.toOne.{0} Real Real.instMonoid))) (Mul.mk.{0} Real (Mul.mul.{0} Real (Monoid.toMul.{0} Real Real.instMonoid))) (Monoid.mul_assoc.{0} Real Real.instMonoid) (Monoid.one_mul.{0} Real Real.instMonoid) (Monoid.mul_one.{0} Real Real.instMonoid) (NPow.mk.{0} Real …", "xIn": "(DivInvMonoid.div'.{0} Real (Monoid.mk.{0} Real (Semigroup.mk.{0} Real (Mul.mk.{0} Real (Mul.mul.{0} Real (Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real Real.instMonoid)))) (Semigroup.mul_assoc.{0} Real (Monoid.toSemigroup.{0} Real Real.instMonoid))) (One.mk.{0} Real (One.one.{0} Real (Monoid.toOne.{0} Real Rea…", "yIn": "(DivInvMonoid.div'.{0} Real (Monoid.mk.{0} Real (One.mk.{0} Real (One.one.{0} Real (Monoid.toOne.{0} Real Real.instMonoid))) (Mul.mk.{0} Real (Mul.mul.{0} Real (Monoid.toMul.{0} Real Real.instMonoid))) (Monoid.mul_assoc.{0} Real Real.instMonoid) (Monoid.one_mul.{0} Real Real.instMonoid) (Monoid.mul_one.{0} Real Real.in…" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Real.instDivInvMonoid._proof_1 (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instDivInvMonoid._proof_1 (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, Monoid.mul_assoc" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @Monoid.mk ℝ { mul := Mul.mul, mul_assoc := ⋯ }\nargument has type\n Semigroup ℝ\nbut function has type\n [toOne : One ℝ] →\n [toMul : Mul ℝ] →\n (∀ (a b c : ℝ), a * b * c = a * (b * c)) →\n (∀ (a : ℝ), 1 * a = a) →\n (∀ (a : ℝ), a * 1 = a) →\n [toNPow : NPow ℝ] →\n autoParam (∀ (x : ℝ), x ^ 0 = 1) Monoid.npow_zero._autoP…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "Real.instDivInvMonoid._proof_2", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › arg 2 of Eq.{1} › arg 4 of HPow.hPow.{0, 0, 0} › arg 3 of instHPow.{0, 0} › arg 2 of ZPow.toPow.{0} › arg 2 of ZPow.mk.{0} › arg 3 of zpowRec.{0} › arg 2 of Mul.mk.{0} › arg 2 of Mul.mul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real Real.instMonoid))", "yIn": "(Monoid.toMul.{0} Real Real.instMonoid)" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Real.instDivInvMonoid._proof_2 (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instDivInvMonoid._proof_2 (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Real.instDivInvMonoid._proof_3", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ n body › ∀ a body › arg 2 of Eq.{1} › arg 4 of HPow.hPow.{0, 0, 0} › arg 3 of instHPow.{0, 0} › arg 2 of ZPow.toPow.{0} › arg 2 of ZPow.mk.{0} › arg 3 of zpowRec.{0} › arg 2 of Mul.mk.{0} › arg 2 of Mul.mul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real Real.instMonoid))", "yIn": "(Monoid.toMul.{0} Real Real.instMonoid)" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Real.instDivInvMonoid._proof_3 (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instDivInvMonoid._proof_3 (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Real.instDivInvMonoid._proof_4", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ n body › ∀ a body › arg 2 of Eq.{1} › arg 4 of HPow.hPow.{0, 0, 0} › arg 3 of instHPow.{0, 0} › arg 2 of ZPow.toPow.{0} › arg 2 of ZPow.mk.{0} › arg 3 of zpowRec.{0} › arg 2 of Mul.mk.{0} › arg 2 of Mul.mul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real Real.instMonoid))", "yIn": "(Monoid.toMul.{0} Real Real.instMonoid)" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Real.instDivInvMonoid._proof_4 (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instDivInvMonoid._proof_4 (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddCommMonoid.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toAddMonoid body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #4 (AddMonoid.toAddSemigroup.{u1} #4 #2))", "yIn": "(AddMonoid.toAdd.{u1} #4 #2)" }, "rules": { "x": [ [ "AddCommMonoid.mk", 2 ] ], "y": [ [ "AddCommMonoid.mk", 2 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddCommMonoid.rec (rec of) ← AddCommMonoid (type of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddCommMonoid.rec (rec of) ← AddCommMonoid (type of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toAddMonoid body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #4 (AddMonoid.toAddSemigroup.{u1} #4 #2))", "yIn": "(AddMonoid.toAdd.{u1} #4 #2)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddCommMonoid.add_comm", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 #2)))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 #2))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddCommMonoid.add_comm (proj of) ← AddCommMonoid (type of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddCommMonoid.add_comm (proj of) ← AddCommMonoid (type of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 #2)))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 #2))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddZeroClass.toAddZero", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M body › λ self body", "why": "different node kinds", "x": "(#0).AddZeroClass#0", "y": "(AddZero.mk.{u0} #1 (AddZeroClass.toZero.{u0} #1 #0) (AddZeroClass.toAdd.{u0} #1 #0))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddZeroClass.toAddZero (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddZeroClass.toAddZero (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M body › λ self body", "why": "different node kinds", "x": "(#0).AddZeroClass#0", "y": "(AddZero.mk.{u0} #1 (AddZeroClass.toZero.{u0} #1 #0) (AddZeroClass.toAdd.{u0} #1 #0))", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "AddZeroClass.toZero, AddZeroClass.toAdd" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n (fun M [self : AddZeroClass M] => self.1) = fun M self => { toZero := self.toZero, toAdd := self.toAdd }\nargument has type\n (M : Type u_2) → AddZeroClass M → AddZero M\nbut function has type\n ((M : Type u_2) → [self : AddZeroClass M] → Zero M) → Prop" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "AddMonoid.toAddZeroClass", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M body › λ self body", "why": "applications of different arity", "x": "(AddZeroClass.mk.{u0} #1 (AddZero.mk.{u0} #1 (AddMonoid.toZero.{u0} #1 #0) (AddSemigroup.toAdd.{u0} #1 (AddMonoid.toAddSemigroup.{u0} #1 #0))) (AddMonoid.zero_add.{u0} #1 #0) (AddMonoid.add_zero.{u0} #1 #0))", "y": "(AddZeroClass.mk.{u0} #1 (AddMonoid.toZero.{u0} #1 #0) (AddMonoid.toAdd.{u0} #1 #0) (AddMonoid.zero_add.{u0} #1 #0) (AddMonoid.add_zero.{u0} #1 #0))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddMonoid.toAddZeroClass (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddMonoid.toAddZeroClass (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M body › λ self body", "why": "applications of different arity", "x": "(AddZeroClass.mk.{u0} #1 (AddZero.mk.{u0} #1 (AddMonoid.toZero.{u0} #1 #0) (AddSemigroup.toAdd.{u0} #1 (AddMonoid.toAddSemigroup.{u0} #1 #0))) ⟨proof⟩ ⟨proof⟩)", "y": "(AddZeroClass.mk.{u0} #1 (AddMonoid.toZero.{u0} #1 #0) (AddMonoid.toAdd.{u0} #1 #0) ⟨proof⟩ ⟨proof⟩)", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n instHAdd\nargument has type\n ∀ (a : M), 0 + a = a\nbut function has type\n [Add M] → HAdd M M M" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "AddCancelCommMonoid.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ toAddCommMonoid body › ∀ toIsLeftCancelAdd type › arg 2 of IsLeftCancelAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #1 (AddMonoid.toAddSemigroup.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0)))", "yIn": "(AddMonoid.toAdd.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddCancelCommMonoid.mk (value of) ← Nat.instAddCancelCommMonoid (value of) ← Nat.instAddCommMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddCancelCommMonoid.mk (value of) ← Nat.instAddCancelCommMonoid (value of) ← Nat.instAddCommMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ toAddCommMonoid body › ∀ toIsLeftCancelAdd type › arg 2 of IsLeftCancelAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #1 (AddMonoid.toAddSemigroup.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0)))", "yIn": "(AddMonoid.toAdd.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Semiring.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ motive body › ∀ mk type › ∀ toAddCommMonoid body › ∀ toMonoid body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #4 (Monoid.toSemigroup.{u1} #4 #1))", "yIn": "(Monoid.toMul.{u1} #4 #1)" }, "rules": { "x": [ [ "Semiring.mk", 9 ] ], "y": [ [ "Semiring.mk", 9 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semiring.rec (rec of) ← Semiring (type of) ← Semiring.toMonoid (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semiring.rec (rec of) ← Semiring (type of) ← Semiring.toMonoid (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ motive body › ∀ mk type › ∀ toAddCommMonoid body › ∀ toMonoid body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #4 (Monoid.toSemigroup.{u1} #4 #1))", "yIn": "(Monoid.toMul.{u1} #4 #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Semiring.zero_mul", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (Semiring.toMonoid.{u0} #2 #1)))", "yIn": "(Monoid.toMul.{u0} #2 (Semiring.toMonoid.{u0} #2 #1))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semiring.zero_mul (proj of) ← Semiring (type of) ← Semiring.toMonoid (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semiring.zero_mul (proj of) ← Semiring (type of) ← Semiring.toMonoid (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (Semiring.toMonoid.{u0} #2 #1)))", "yIn": "(Monoid.toMul.{u0} #2 (Semiring.toMonoid.{u0} #2 #1))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Semiring.right_distrib", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (Semiring.toMonoid.{u0} #4 #3)))", "yIn": "(Monoid.toMul.{u0} #4 (Semiring.toMonoid.{u0} #4 #3))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semiring.right_distrib (proj of) ← Semiring (type of) ← Semiring.toMonoid (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semiring.right_distrib (proj of) ← Semiring (type of) ← Semiring.toMonoid (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (Semiring.toMonoid.{u0} #4 #3)))", "yIn": "(Monoid.toMul.{u0} #4 (Semiring.toMonoid.{u0} #4 #3))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Semiring.mul_zero", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (Semiring.toMonoid.{u0} #2 #1)))", "yIn": "(Monoid.toMul.{u0} #2 (Semiring.toMonoid.{u0} #2 #1))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semiring.mul_zero (proj of) ← Semiring (type of) ← Semiring.toMonoid (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semiring.mul_zero (proj of) ← Semiring (type of) ← Semiring.toMonoid (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (Semiring.toMonoid.{u0} #2 #1)))", "yIn": "(Monoid.toMul.{u0} #2 (Semiring.toMonoid.{u0} #2 #1))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Semiring.left_distrib", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (Semiring.toMonoid.{u0} #4 #3)))", "yIn": "(Monoid.toMul.{u0} #4 (Semiring.toMonoid.{u0} #4 #3))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semiring.left_distrib (proj of) ← Semiring (type of) ← Semiring.toMonoid (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semiring.left_distrib (proj of) ← Semiring (type of) ← Semiring.toMonoid (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (Semiring.toMonoid.{u0} #4 #3)))", "yIn": "(Monoid.toMul.{u0} #4 (Semiring.toMonoid.{u0} #4 #3))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Real.commRing", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of CommRing.mk.{0} › arg 2 of Ring.mk.{0} › arg 2 of Semiring.mk.{0} › arg 2 of AddCommMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} Real (AddSemigroup.mk.{0} Real Real.instAdd (fun (a : Real) => (fun (b : Real) => (fun (c : Real) => (Real.commRing._proof_1 #2 #1 #0))))) Real.instZero (fun (a : Real) => (Real.commRing._proof_2 #0)) (fun (a : Real) => (Real.commRing._proof_3 #0)) (NSMul.mk.{0} Real (nsmulRec.{0} Real (Zero.mk.{0} Re…", "y": "(AddMonoid.mk.{0} Real Real.instZero Real.instAdd (fun (a : Real) => (fun (b : Real) => (fun (c : Real) => (Real.commRing._proof_1 #2 #1 #0)))) (fun (a : Real) => (Real.commRing._proof_2 #0)) (fun (a : Real) => (Real.commRing._proof_3 #0)) (NSMul.mk.{0} Real (nsmulRec.{0} Real (Zero.mk.{0} Real (OfNat.ofNat.{0} Real 0 …", "xIn": "(AddCommMonoid.mk.{0} Real (AddMonoid.mk.{0} Real (AddSemigroup.mk.{0} Real Real.instAdd (fun (a : Real) => (fun (b : Real) => (fun (c : Real) => (Real.commRing._proof_1 #2 #1 #0))))) Real.instZero (fun (a : Real) => (Real.commRing._proof_2 #0)) (fun (a : Real) => (Real.commRing._proof_3 #0)) (NSMul.mk.{0} Real (nsmulR…", "yIn": "(AddCommMonoid.mk.{0} Real (AddMonoid.mk.{0} Real Real.instZero Real.instAdd (fun (a : Real) => (fun (b : Real) => (fun (c : Real) => (Real.commRing._proof_1 #2 #1 #0)))) (fun (a : Real) => (Real.commRing._proof_2 #0)) (fun (a : Real) => (Real.commRing._proof_3 #0)) (NSMul.mk.{0} Real (nsmulRec.{0} Real (Zero.mk.{0} Re…" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of CommRing.mk.{0} › arg 2 of Ring.mk.{0} › arg 2 of Semiring.mk.{0} › arg 2 of AddCommMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} Real (AddSemigroup.mk.{0} Real Real.instAdd ⟨proof⟩) Real.instZero ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Real (nsmulRec.{0} Real (Zero.mk.{0} Real (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZero))) (Add.mk.{0} Real (fun (x1._@.Mathlib.Data.Real.Basic.#2614265405._hygCtx._hyg.#41 : Real) => (fun …", "y": "(AddMonoid.mk.{0} Real Real.instZero Real.instAdd ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Real (nsmulRec.{0} Real (Zero.mk.{0} Real (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZero))) (Add.mk.{0} Real (fun (x1._@.Mathlib.Basic.Real.Basic.#2614265405._hygCtx._hyg.#41 : Real) => (fun (x2._@.Mathlib.Basic.Real.…", "xIn": "(AddCommMonoid.mk.{0} Real (AddMonoid.mk.{0} Real (AddSemigroup.mk.{0} Real Real.instAdd ⟨proof⟩) Real.instZero ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Real (nsmulRec.{0} Real (Zero.mk.{0} Real (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZero))) (Add.mk.{0} Real (fun (x1._@.Mathlib.Data.Real.Basic.#2614265405._hygCt…", "yIn": "(AddCommMonoid.mk.{0} Real (AddMonoid.mk.{0} Real Real.instZero Real.instAdd ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} Real (nsmulRec.{0} Real (Zero.mk.{0} Real (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZero))) (Add.mk.{0} Real (fun (x1._@.Mathlib.Basic.Real.Basic.#2614265405._hygCtx._hyg.#41 : Real) => (fun…" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk ℝ Real.instZero\nargument has type\n Zero ℝ\nbut function has type\n [toAddSemigroup : AddSemigroup ℝ] →\n [toZero : Zero ℝ] →\n (∀ (a : ℝ), 0 + a = a) →\n (∀ (a : ℝ), a + 0 = a) →\n [toNSMul : NSMul ℝ] →\n autoParam (∀ (x : ℝ), 0 • x = 0) AddMonoid.nsmul_zero._autoParam →\n autoParam (∀ (n : ℕ) (x : ℝ), (n …" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk ℝ { toAdd := Real.instAdd, add_assoc := ⋯ }\nargument has type\n AddSemigroup ℝ\nbut function has type\n [toZero : Zero ℝ] →\n [toAdd : Add ℝ] →\n (∀ (a b c : ℝ), a + b + c = a + (b + c)) →\n (∀ (a : ℝ), 0 + a = a) →\n (∀ (a : ℝ), a + 0 = a) →\n [toNSMul : NSMul ℝ] →\n autoParam (∀ (x : ℝ), 0 • x = 0) AddMon…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "CauSeq.instLTAbs", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.instLTAbs (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.lt (value of) ← Real.instLT (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instLTAbs (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.lt (value of) ← Real.instLT (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.Completion.instZeroCauchy", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.instZeroCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1850581184._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1850581184._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.zero (value of) ← Real.instZero (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.instZeroCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#3335671075._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#3335671075._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.zero (value of) ← Real.instZero (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1564867275._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "Bool.not", "kind": "def", "module": { "anthropic": "Init.Prelude", "openai": "Init.Prelude" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ x._@.Init.Prelude.#2709464109._hygCtx._hyg.#5 body › head", "why": "different leaves", "x": "cond.match_1.{1}", "y": "Bool.rec.{1}", "xIn": "(cond.match_1.{1} (fun (x._@.Init.Prelude.#2709464109._hygCtx.#5.Init.Prelude.#2709464109._hygCtx._hyg.#16 : Bool) => Bool) #0 (fun (_ : Unit) => Bool.false) (fun (_ : Unit) => Bool.true))", "yIn": "(Bool.rec.{1} (fun (x._@.Init.Prelude.#2709464109._hygCtx._hyg.#6 : Bool) => Bool) Bool.true Bool.false #0)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Bool.not (value of) ← bne (value of) ← Nat.binaryRec (value of) ← Nat.bits (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.countWord (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Bool.not (value of) ← bne (value of) ← Nat.binaryRec (value of) ← Nat.bits (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.countWord (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ x._@.Init.Prelude.#2709464109._hygCtx._hyg.#5 body › head", "why": "different leaves", "x": "cond.match_1.{1}", "y": "Bool.rec.{1}", "xIn": "(cond.match_1.{1} (fun (x._@.Init.Prelude.#2709464109._hygCtx.#5.Init.Prelude.#2709464109._hygCtx._hyg.#16 : Bool) => Bool) #0 (fun (_ : Unit) => Bool.false) (fun (_ : Unit) => Bool.true))", "yIn": "(Bool.rec.{1} (fun (x._@.Init.Prelude.#2709464109._hygCtx._hyg.#6 : Bool) => Bool) Bool.true Bool.false #0)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "value" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "Semiring.toNonAssocSemiring", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ α body › λ self body › arg 2 of NonAssocSemiring.mk.{u0} › arg 3 of NonUnitalNonAssocSemiring.mk.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #1 (Monoid.toSemigroup.{u0} #1 (Semiring.toMonoid.{u0} #1 #0)))", "yIn": "(Monoid.toMul.{u0} #1 (Semiring.toMonoid.{u0} #1 #0))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semiring.toNonAssocSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semiring.toNonAssocSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ α body › λ self body › arg 2 of NonAssocSemiring.mk.{u0} › arg 3 of NonUnitalNonAssocSemiring.mk.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #1 (Monoid.toSemigroup.{u0} #1 (Semiring.toMonoid.{u0} #1 #0)))", "yIn": "(Monoid.toMul.{u0} #1 (Semiring.toMonoid.{u0} #1 #0))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionSemiring.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ motive body › ∀ mk type › ∀ toSemiring body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 (Semiring.toMonoid.{u1} #7 #5)))", "yIn": "(Monoid.toMul.{u1} #7 (Semiring.toMonoid.{u1} #7 #5))" }, "rules": { "x": [ [ "DivisionSemiring.mk", 15 ] ], "y": [ [ "DivisionSemiring.mk", 15 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionSemiring.rec (rec of) ← DivisionSemiring (type of) ← DivisionSemiring.toSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivisionSemiring.rec (rec of) ← DivisionSemiring (type of) ← DivisionSemiring.toGroupWithZero (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ motive body › ∀ mk type › ∀ toSemiring body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 (Semiring.toMonoid.{u1} #7 #5)))", "yIn": "(Monoid.toMul.{u1} #7 (Semiring.toMonoid.{u1} #7 #5))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionSemiring.div_eq_mul_inv", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionSemiring.div_eq_mul_inv (proj of) ← DivisionSemiring (type of) ← DivisionSemiring.toSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivisionSemiring.div_eq_mul_inv (value of) ← DivisionSemiring.toGroupWithZero (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionSemiring.mul_inv_cancel", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ a._@._internal._hyg.#0 body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionSemiring.mul_inv_cancel (proj of) ← DivisionSemiring (type of) ← DivisionSemiring.toSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivisionSemiring.mul_inv_cancel (value of) ← DivisionSemiring.toGroupWithZero (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ a body › ∀ a._@._internal._hyg.#0 body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionSemiring.nnqsmul_def", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ self body › ∀ q body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionSemiring.nnqsmul_def (proj of) ← DivisionSemiring (type of) ← DivisionSemiring.toSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivisionSemiring.nnqsmul_def (proj of) ← DivisionSemiring (type of) ← DivisionSemiring.toGroupWithZero (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ q body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionSemiring.zpow_succ'", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionSemiring.zpow_succ' (proj of) ← DivisionSemiring (type of) ← DivisionSemiring.toSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivisionSemiring.zpow_succ' (value of) ← DivisionSemiring.toGroupWithZero (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (DivisionSemiring.toSemiring.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Semifield.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Field.Defs", "openai": "Mathlib.Algebra.Field.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ K body › ∀ motive body › ∀ mk type › ∀ toCommSemiring body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 (Semiring.toMonoid.{u1} #7 (CommSemiring.toSemiring.{u1} #7 #5))))", "yIn": "(Monoid.toMul.{u1} #7 (Semiring.toMonoid.{u1} #7 (CommSemiring.toSemiring.{u1} #7 #5)))" }, "rules": { "x": [ [ "Semifield.mk", 15 ] ], "y": [ [ "Semifield.mk", 15 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Semifield.rec (rec of) ← Semifield (type of) ← Semifield.toDivisionSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Semifield.rec (rec of) ← Semifield (type of) ← Semifield.toCommSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ K body › ∀ motive body › ∀ mk type › ∀ toCommSemiring body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 (Semiring.toMonoid.{u1} #7 (CommSemiring.toSemiring.{u1} #7 #5))))", "yIn": "(Monoid.toMul.{u1} #7 (Semiring.toMonoid.{u1} #7 (CommSemiring.toSemiring.{u1} #7 #5)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddMonoid.toAddSemigroup", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M body › λ self body", "why": "different node kinds", "x": "(#0).AddMonoid#0", "y": "(AddSemigroup.mk.{u0} #1 (AddMonoid.toAdd.{u0} #1 #0) (AddMonoid.add_assoc.{u0} #1 #0))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddMonoid.toAddSemigroup (type of) ← Ring.mk (ctor of) ← Ring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddMonoid.toAddSemigroup (type of) ← Nonneg.nsmul (value of) ← NNReal.instSemiring._aux_6 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M body › λ self body", "why": "different node kinds", "x": "(#0).AddMonoid#0", "y": "(AddSemigroup.mk.{u0} #1 (AddMonoid.toAdd.{u0} #1 #0) ⟨proof⟩)", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "AddMonoid.toAdd, AddMonoid.add_assoc" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n (fun M [self : AddMonoid M] => self.1) = fun M self => { toAdd := self.toAdd, add_assoc := ⋯ }\nargument has type\n (M : Type u_2) → AddMonoid M → AddSemigroup M\nbut function has type\n ((M : Type u_2) → [self : AddMonoid M] → Zero M) → Prop" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "CauSeq.ofEq", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.ofEq (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.ofEq (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.instAdd", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.instAdd (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instAdd (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.instNeg", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.instNeg (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instNeg (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.instSub._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#701254411._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#701254411._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#701254411._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u1} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u1}", "y": "CommSemiring.toSemiring.{u1}", "xIn": "(DivisionSemiring.toSemiring.{u1} #3 (Semifield.toDivisionSemiring.{u1} #3 (Field.toSemifield.{u1} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u1} #3 (Semifield.toCommSemiring.{u1} #3 (Field.toSemifield.{u1} #3 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.instSub._proof_1 (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instSub._proof_1 (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "AddCommGroup.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toAddGroup body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #4 (AddMonoid.toAddSemigroup.{u1} #4 (SubNegMonoid.toAddMonoid.{u1} #4 (AddGroup.toSubNegMonoid.{u1} #4 #2))))", "yIn": "(AddMonoid.toAdd.{u1} #4 (SubNegMonoid.toAddMonoid.{u1} #4 (AddGroup.toSubNegMonoid.{u1} #4 #2)))" }, "rules": { "x": [ [ "AddCommGroup.mk", 2 ] ], "y": [ [ "AddCommGroup.mk", 2 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddCommGroup.rec (rec of) ← AddCommGroup (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddCommGroup.rec (rec of) ← AddCommGroup (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toAddGroup body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #4 (AddMonoid.toAddSemigroup.{u1} #4 (SubNegMonoid.toAddMonoid.{u1} #4 (AddGroup.toSubNegMonoid.{u1} #4 #2))))", "yIn": "(AddMonoid.toAdd.{u1} #4 (SubNegMonoid.toAddMonoid.{u1} #4 (AddGroup.toSubNegMonoid.{u1} #4 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommMonoid.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ toMonoid body › ∀ mul_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 #2))", "yIn": "(Monoid.toMul.{u0} #3 #2)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CommMonoid.mk (ctor of) ← CommMonoid (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CommMonoid.mk (ctor of) ← CommMonoid (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ toMonoid body › ∀ mul_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 #2))", "yIn": "(Monoid.toMul.{u0} #3 #2)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommMonoid.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toMonoid body › ∀ mul_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #4 (Monoid.toSemigroup.{u1} #4 #2))", "yIn": "(Monoid.toMul.{u1} #4 #2)" }, "rules": { "x": [ [ "CommMonoid.mk", 2 ] ], "y": [ [ "CommMonoid.mk", 2 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CommMonoid.rec (rec of) ← CommMonoid (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CommMonoid.rec (rec of) ← CommMonoid (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toMonoid body › ∀ mul_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #4 (Monoid.toSemigroup.{u1} #4 #2))", "yIn": "(Monoid.toMul.{u1} #4 #2)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Bool.and", "kind": "def", "module": { "anthropic": "Init.Prelude", "openai": "Init.Prelude" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ x body › λ y body › head", "why": "different leaves", "x": "Bool.and.match_1.{1}", "y": "Bool.rec.{1}", "xIn": "(Bool.and.match_1.{1} (fun (x._@.Init.Prelude.#2579035302._hygCtx._hyg.#8 : Bool) => Bool) #1 (fun (_ : Unit) => Bool.false) (fun (_ : Unit) => #1))", "yIn": "(Bool.rec.{1} (fun (x._@.Init.Prelude.#2579035302._hygCtx._hyg.#7 : Bool) => Bool) Bool.false #0 #1)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Bool.and (value of) ← Rat.blt (value of) ← Rat.instLE (value of) ← Rat.linearOrder (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Bool.and (value of) ← Rat.blt (value of) ← Rat.instLE (value of) ← Rat.linearOrder (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ x body › λ y body › head", "why": "different leaves", "x": "Bool.and.match_1.{1}", "y": "Bool.rec.{1}", "xIn": "(Bool.and.match_1.{1} (fun (x._@.Init.Prelude.#2579035302._hygCtx._hyg.#8 : Bool) => Bool) #1 (fun (_ : Unit) => Bool.false) (fun (_ : Unit) => #1))", "yIn": "(Bool.rec.{1} (fun (x._@.Init.Prelude.#2579035302._hygCtx._hyg.#7 : Bool) => Bool) Bool.false #0 #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "value" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "Bool.and.match_1" }, "both": false }, "defeqBothWays": false, "kernel": "identified in Anthropic's environment only", "group": "lean-core" }, { "name": "SubtractionMonoid.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toSubNegMonoid body › ∀ neg_neg body › ∀ neg_add_rev type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 3 of Neg.neg.{u1} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #5 (AddMonoid.toAddSemigroup.{u1} #5 (SubNegMonoid.toAddMonoid.{u1} #5 #3)))", "yIn": "(AddMonoid.toAdd.{u1} #5 (SubNegMonoid.toAddMonoid.{u1} #5 #3))" }, "rules": { "x": [ [ "SubtractionMonoid.mk", 4 ] ], "y": [ [ "SubtractionMonoid.mk", 4 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "SubtractionMonoid.rec (rec of) ← SubtractionMonoid (type of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "SubtractionMonoid.rec (rec of) ← SubtractionMonoid (type of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toSubNegMonoid body › ∀ neg_neg body › ∀ neg_add_rev type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 3 of Neg.neg.{u1} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #5 (AddMonoid.toAddSemigroup.{u1} #5 (SubNegMonoid.toAddMonoid.{u1} #5 #3)))", "yIn": "(AddMonoid.toAdd.{u1} #5 (SubNegMonoid.toAddMonoid.{u1} #5 #3))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "SubtractionMonoid.neg_add_rev", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 3 of Neg.neg.{u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "SubtractionMonoid.neg_add_rev (proj of) ← SubtractionMonoid (type of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "SubtractionMonoid.neg_add_rev (proj of) ← SubtractionMonoid (type of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 3 of Neg.neg.{u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "SubtractionMonoid.neg_eq_of_add", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › ∀ a._@._internal._hyg.#0 type › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "SubtractionMonoid.neg_eq_of_add (proj of) ← SubtractionMonoid (type of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "SubtractionMonoid.neg_eq_of_add (proj of) ← SubtractionMonoid (type of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › ∀ a._@._internal._hyg.#0 type › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "SubNegMonoid.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toAddMonoid body › ∀ toNeg body › ∀ toSub body › ∀ toZSMul body › ∀ sub_eq_add_neg type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #7 (AddMonoid.toAddSemigroup.{u1} #7 #5))", "yIn": "(AddMonoid.toAdd.{u1} #7 #5)" }, "rules": { "x": [ [ "SubNegMonoid.mk", 8 ] ], "y": [ [ "SubNegMonoid.mk", 8 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "SubNegMonoid.rec (rec of) ← SubNegMonoid (value of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "SubNegMonoid.rec (rec of) ← SubNegMonoid (value of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toAddMonoid body › ∀ toNeg body › ∀ toSub body › ∀ toZSMul body › ∀ sub_eq_add_neg type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #7 (AddMonoid.toAddSemigroup.{u1} #7 #5))", "yIn": "(AddMonoid.toAdd.{u1} #7 #5)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "SubNegMonoid.sub_eq_add_neg", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 #2)))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 #2))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "SubNegMonoid.sub_eq_add_neg (proj of) ← SubNegMonoid (value of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "SubNegMonoid.sub_eq_add_neg (proj of) ← SubNegMonoid (value of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 #2)))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 #2))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "SubNegMonoid.zsmul_succ'", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 #2)))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 #2))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "SubNegMonoid.zsmul_succ' (proj of) ← SubNegMonoid (value of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "SubNegMonoid.zsmul_succ' (proj of) ← SubNegMonoid (value of) ← SubtractionMonoid.toSubNegZeroMonoid (value of) ← abs (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 #2)))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 #2))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddGroupWithOne.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Data.Int.Cast.Defs", "openai": "Mathlib.Data.Int.Cast.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ motive body › ∀ mk type › ∀ toIntCast body › ∀ toAddMonoidWithOne body › ∀ toNeg body › ∀ toSub body › ∀ toZSMul body › ∀ sub_eq_add_neg type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #8 (AddMonoid.toAddSemigroup.{u1} #8 (AddMonoidWithOne.toAddMonoid.{u1} #8 #5)))", "yIn": "(AddMonoid.toAdd.{u1} #8 (AddMonoidWithOne.toAddMonoid.{u1} #8 #5))" }, "rules": { "x": [ [ "AddGroupWithOne.mk", 12 ] ], "y": [ [ "AddGroupWithOne.mk", 12 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddGroupWithOne.rec (rec of) ← AddGroupWithOne (type of) ← AddGroupWithOne.toAddGroup (type of) ← Real.equivCauchy._proof_1 (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddGroupWithOne.rec (rec of) ← AddGroupWithOne (type of) ← AddGroupWithOne.toAddGroup (type of) ← Real.equivCauchy._proof_1 (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ motive body › ∀ mk type › ∀ toIntCast body › ∀ toAddMonoidWithOne body › ∀ toNeg body › ∀ toSub body › ∀ toZSMul body › ∀ sub_eq_add_neg type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #8 (AddMonoid.toAddSemigroup.{u1} #8 (AddMonoidWithOne.toAddMonoid.{u1} #8 #5)))", "yIn": "(AddMonoid.toAdd.{u1} #8 (AddMonoidWithOne.toAddMonoid.{u1} #8 #5))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "IsCauSeq.const", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309539._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309539._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3831309539._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "IsCauSeq.const (value of) ← CauSeq.const (value of) ← CauSeq.instNatCast (value of) ← CauSeq.Completion.instNatCastCauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "IsCauSeq.const (value of) ← CauSeq.const (value of) ← CauSeq.instNatCast (value of) ← CauSeq.Completion.instNatCastCauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "DivInvMonoid.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toMonoid body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 #5))", "yIn": "(Monoid.toMul.{u1} #7 #5)" }, "rules": { "x": [ [ "DivInvMonoid.mk", 8 ] ], "y": [ [ "DivInvMonoid.mk", 8 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivInvMonoid.rec (rec of) ← DivInvMonoid (type of) ← DivInvMonoid.toDiv (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivInvMonoid.rec (rec of) ← DivInvMonoid (type of) ← DivInvMonoid.toDiv (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toMonoid body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 #5))", "yIn": "(Monoid.toMul.{u1} #7 #5)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivInvMonoid.div_eq_mul_inv", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 #2)))", "yIn": "(Monoid.toMul.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 #2))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivInvMonoid.div_eq_mul_inv (proj of) ← DivInvMonoid (type of) ← DivInvMonoid.toDiv (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivInvMonoid.div_eq_mul_inv (proj of) ← DivInvMonoid (type of) ← DivInvMonoid.toDiv (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 #2)))", "yIn": "(Monoid.toMul.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 #2))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivInvMonoid.zpow_succ'", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 #2)))", "yIn": "(Monoid.toMul.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 #2))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivInvMonoid.zpow_succ' (proj of) ← DivInvMonoid (type of) ← DivInvMonoid.toDiv (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "DivInvMonoid.zpow_succ' (proj of) ← DivInvMonoid (type of) ← DivInvMonoid.toDiv (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 #2)))", "yIn": "(Monoid.toMul.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 #2))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MulOneClass.toMulOne", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M body › λ self body", "why": "different node kinds", "x": "(#0).MulOneClass#0", "y": "(MulOne.mk.{u0} #1 (MulOneClass.toOne.{u0} #1 #0) (MulOneClass.toMul.{u0} #1 #0))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MulOneClass.toMulOne (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MulOneClass.toMulOne (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M body › λ self body", "why": "different node kinds", "x": "(#0).MulOneClass#0", "y": "(MulOne.mk.{u0} #1 (MulOneClass.toOne.{u0} #1 #0) (MulOneClass.toMul.{u0} #1 #0))", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "MulOneClass.toOne, MulOneClass.toMul" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n (fun M [self : MulOneClass M] => self.1) = fun M self => { toOne := self.toOne, toMul := self.toMul }\nargument has type\n (M : Type u_2) → MulOneClass M → MulOne M\nbut function has type\n ((M : Type u_2) → [self : MulOneClass M] → One M) → Prop" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "Monoid.toMulOneClass", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M body › λ self body", "why": "applications of different arity", "x": "(MulOneClass.mk.{u0} #1 (MulOne.mk.{u0} #1 (Monoid.toOne.{u0} #1 #0) (Semigroup.toMul.{u0} #1 (Monoid.toSemigroup.{u0} #1 #0))) (Monoid.one_mul.{u0} #1 #0) (Monoid.mul_one.{u0} #1 #0))", "y": "(MulOneClass.mk.{u0} #1 (Monoid.toOne.{u0} #1 #0) (Monoid.toMul.{u0} #1 #0) (Monoid.one_mul.{u0} #1 #0) (Monoid.mul_one.{u0} #1 #0))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Monoid.toMulOneClass (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Monoid.toMulOneClass (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M body › λ self body", "why": "applications of different arity", "x": "(MulOneClass.mk.{u0} #1 (MulOne.mk.{u0} #1 (Monoid.toOne.{u0} #1 #0) (Semigroup.toMul.{u0} #1 (Monoid.toSemigroup.{u0} #1 #0))) ⟨proof⟩ ⟨proof⟩)", "y": "(MulOneClass.mk.{u0} #1 (Monoid.toOne.{u0} #1 #0) (Monoid.toMul.{u0} #1 #0) ⟨proof⟩ ⟨proof⟩)", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n instHMul\nargument has type\n ∀ (a : M), 1 * a = a\nbut function has type\n [Mul M] → HMul M M M" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "StrictMono.orderIsoOfSurjective", "kind": "def", "module": { "anthropic": "Mathlib.Order.Hom.Set", "openai": "Mathlib.Order.Hom.Set" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Order.Hom.Set.#2866922817._hygCtx._hyg.#5 body › λ inst._@.Mathlib.Order.Hom.Set.#2866922817._hygCtx._hyg.#8 body › λ f body › λ h_mono body › λ h_surj body › arg 8 of OrderIso.trans.{u0, u1, u1} › arg 7 of OrderIso.trans.{u1, u1, u1} › head", "why": "different leaves", "x": "OrderIso.setCongr.{u1}", "y": "Set.orderIsoOfEq.{u1}", "xIn": "(OrderIso.setCongr.{u1} #5 #3 (Set.range.{u1, (u0+1)} #5 #6 #2) (Set.univ.{u1} #5) (Function.Surjective.range_eq.{u1, (u0+1)} #5 #6 #2 #0))", "yIn": "(Set.orderIsoOfEq.{u1} #5 #3 (Set.range.{u1, (u0+1)} #5 #6 #2) (Set.univ.{u1} #5) (Function.Surjective.range_eq.{u1, (u0+1)} #5 #6 #2 #0))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "StrictMono.orderIsoOfSurjective (value of) ← Real.expOrderIso (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "StrictMono.orderIsoOfSurjective (value of) ← Real.expOrderIso (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Order.Hom.Set.#2866922817._hygCtx._hyg.#5 body › λ inst._@.Mathlib.Order.Hom.Set.#2866922817._hygCtx._hyg.#8 body › λ f body › λ h_mono body › λ h_surj body › arg 8 of OrderIso.trans.{u0, u1, u1} › arg 7 of OrderIso.trans.{u1, u1, u1} › head", "why": "different leaves", "x": "OrderIso.setCongr.{u1}", "y": "Set.orderIsoOfEq.{u1}", "xIn": "(OrderIso.setCongr.{u1} #5 #3 (Set.range.{u1, (u0+1)} #5 #6 #2) (Set.univ.{u1} #5) ⟨proof⟩)", "yIn": "(Set.orderIsoOfEq.{u1} #5 #3 (Set.range.{u1, (u0+1)} #5 #6 #2) (Set.univ.{u1} #5) ⟨proof⟩)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Set.orderIsoOfEq" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "renamed" }, { "name": "Real.instMax", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of Max.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.sup", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.sup", "xIn": "(Max.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.sup)", "yIn": "(Max.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.sup)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of Max.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.sup", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.sup", "xIn": "(Max.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.sup)", "yIn": "(Max.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.sup)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Basic.Real.Basic.#0.Real.sup" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Data.Real.Basic.#0.Real.sup" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "moved-file" }, { "name": "AddZeroClass.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "kernel facts", "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ toAddZero type › head", "why": "different leaves", "x": "AddZero.{u0}", "y": "Zero.{u0}", "xIn": "(AddZero.{u0} #0)", "yIn": "(Zero.{u0} #0)" }, "meta": { "x": { "induct": "AddZeroClass", "cidx": 0, "numParams": 1, "numFields": 3, "unsafe": false }, "y": { "induct": "AddZeroClass", "cidx": 0, "numParams": 1, "numFields": 4, "unsafe": false } } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddZeroClass.mk (value of) ← AddMonoid.toAddZeroClass (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddZeroClass.mk (value of) ← AddMonoid.toAddZeroClass (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ toAddZero type › head", "why": "different leaves", "x": "AddZero.{u0}", "y": "Zero.{u0}", "xIn": "(AddZero.{u0} #0)", "yIn": "(Zero.{u0} #0)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "type", "detail": "(kernel) declaration type mismatch, '_seam_check_1285' has type\n ({M : Type u} → [toAddZero : AddZero M] → (∀ (a : M), 0 + a = a) → (∀ (a : M), a + 0 = a) → AddZeroClass M) =\n ({M : Type u} → [toAddZero : AddZero M] → (∀ (a : M), 0 + a = a) → (∀ (a : M), a + 0 = a) → AddZeroClass M)\nbut it is expected to have type\n ({M : Type u} →\n [toZero : Zero M] → [toAdd : Add M] → (∀ (a : M), 0 + a …" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) declaration type mismatch, '_seam_check_1306' has type\n ({M : Type u_2} →\n [toZero : Zero M] → [toAdd : Add M] → (∀ (a : M), 0 + a = a) → (∀ (a : M), a + 0 = a) → AddZeroClass M) =\n ({M : Type u_2} →\n [toZero : Zero M] → [toAdd : Add M] → (∀ (a : M), 0 + a = a) → (∀ (a : M), a + 0 = a) → AddZeroClass M)\nbut it is expected to have type\n ({M : Type u_2} → [toAddZero : AddZero…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "AddMonoid.zero_add", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 #1))", "yIn": "(AddMonoid.toAdd.{u0} #2 #1)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddMonoid.zero_add (value of) ← AddMonoid.toAddZeroClass (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddMonoid.zero_add (value of) ← AddMonoid.toAddZeroClass (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 #1))", "yIn": "(AddMonoid.toAdd.{u0} #2 #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddMonoid.add_zero", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 #1))", "yIn": "(AddMonoid.toAdd.{u0} #2 #1)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddMonoid.add_zero (value of) ← AddMonoid.toAddZeroClass (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddMonoid.add_zero (value of) ← AddMonoid.toAddZeroClass (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 #1))", "yIn": "(AddMonoid.toAdd.{u0} #2 #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddCancelCommMonoid.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toAddCommMonoid body › ∀ toIsLeftCancelAdd type › arg 2 of IsLeftCancelAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #2 (AddMonoid.toAddSemigroup.{u1} #2 (AddCommMonoid.toAddMonoid.{u1} #2 #0)))", "yIn": "(AddMonoid.toAdd.{u1} #2 (AddCommMonoid.toAddMonoid.{u1} #2 #0))" }, "rules": { "x": [ [ "AddCancelCommMonoid.mk", 2 ] ], "y": [ [ "AddCancelCommMonoid.mk", 2 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddCancelCommMonoid.rec (rec of) ← AddCancelCommMonoid (type of) ← AddCancelCommMonoid.toAddCommMonoid (value of) ← Nat.instAddCommMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddCancelCommMonoid.rec (rec of) ← AddCancelCommMonoid (type of) ← AddCancelCommMonoid.toAddCommMonoid (value of) ← Nat.instAddCommMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toAddCommMonoid body › ∀ toIsLeftCancelAdd type › arg 2 of IsLeftCancelAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #2 (AddMonoid.toAddSemigroup.{u1} #2 (AddCommMonoid.toAddMonoid.{u1} #2 #0)))", "yIn": "(AddMonoid.toAdd.{u1} #2 (AddCommMonoid.toAddMonoid.{u1} #2 #0))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddCancelCommMonoid.toIsLeftCancelAdd", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › arg 2 of IsLeftCancelAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #1 (AddMonoid.toAddSemigroup.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 (AddCancelCommMonoid.toAddCommMonoid.{u0} #1 #0))))", "yIn": "(AddMonoid.toAdd.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 (AddCancelCommMonoid.toAddCommMonoid.{u0} #1 #0)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddCancelCommMonoid.toIsLeftCancelAdd (proj of) ← AddCancelCommMonoid (type of) ← AddCancelCommMonoid.toAddCommMonoid (value of) ← Nat.instAddCommMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddCancelCommMonoid.toIsLeftCancelAdd (proj of) ← AddCancelCommMonoid (type of) ← AddCancelCommMonoid.toAddCommMonoid (value of) ← Nat.instAddCommMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › arg 2 of IsLeftCancelAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #1 (AddMonoid.toAddSemigroup.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 (AddCancelCommMonoid.toAddCommMonoid.{u0} #1 #0))))", "yIn": "(AddMonoid.toAdd.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 (AddCancelCommMonoid.toAddCommMonoid.{u0} #1 #0)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CauSeq.Completion.instMulCauchy", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.instMulCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.mul (value of) ← Real.instMul (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.instMulCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.mul (value of) ← Real.instMul (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3462426301._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CommSemiring.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ motive body › ∀ mk type › ∀ toSemiring body › ∀ mul_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #4 (Monoid.toSemigroup.{u1} #4 (Semiring.toMonoid.{u1} #4 #2)))", "yIn": "(Monoid.toMul.{u1} #4 (Semiring.toMonoid.{u1} #4 #2))" }, "rules": { "x": [ [ "CommSemiring.mk", 2 ] ], "y": [ [ "CommSemiring.mk", 2 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CommSemiring.rec (rec of) ← CommSemiring (type of) ← CommSemiring.toSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CommSemiring.rec (rec of) ← CommSemiring (type of) ← CommSemiring.toSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ motive body › ∀ mk type › ∀ toSemiring body › ∀ mul_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #4 (Monoid.toSemigroup.{u1} #4 (Semiring.toMonoid.{u1} #4 #2)))", "yIn": "(Monoid.toMul.{u1} #4 (Semiring.toMonoid.{u1} #4 #2))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommSemiring.mul_comm", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CommSemiring.mul_comm (proj of) ← CommSemiring (type of) ← CommSemiring.toSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CommSemiring.mul_comm (proj of) ← CommSemiring (type of) ← CommSemiring.toSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (Semiring.toMonoid.{u0} #3 (CommSemiring.toSemiring.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Real.instNeg", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of Neg.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.neg", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.neg", "xIn": "(Neg.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.neg)", "yIn": "(Neg.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.neg)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of Neg.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.neg", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.neg", "xIn": "(Neg.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.neg)", "yIn": "(Neg.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.neg)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Basic.Real.Basic.#0.Real.neg" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Data.Real.Basic.#0.Real.neg" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "moved-file" }, { "name": "CauSeq.Completion.instIntCastCauchy", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.instIntCastCauchy (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.instIntCastCauchy (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2526010602._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.Completion.instAddCauchy", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.instAddCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.add (value of) ← Real.instAdd (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.instAddCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.add (value of) ← Real.instAdd (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3207350876._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.Completion.instOneCauchy", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.instOneCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1279875089._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1279875089._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.one (value of) ← Real.instOne (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.instOneCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#6358291._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#6358291._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.one (value of) ← Real.instOne (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3458461013._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.Pos", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Pos (value of) ← CauSeq.instLTAbs (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.lt (value of) ← Real.instLT (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Pos (value of) ← CauSeq.instLTAbs (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.lt (value of) ← Real.instLT (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1887095945._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.instLTAbs._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1713505687._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.instLTAbs._proof_1 (value of) ← CauSeq.instLTAbs (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.lt (value of) ← Real.instLT (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instLTAbs._proof_1 (value of) ← CauSeq.instLTAbs (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.lt (value of) ← Real.instLT (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.Completion.ofRat", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.ofRat (value of) ← CauSeq.Completion.instZeroCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1850581184._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1850581184._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.zero (value of) ← Real.instZero (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.ofRat (value of) ← CauSeq.Completion.instZeroCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#3335671075._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#3335671075._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.zero (value of) ← Real.instZero (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2920143997._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "AddCommMonoidWithOne.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Data.Nat.Cast.Defs", "openai": "Mathlib.Data.Nat.Cast.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ toAddMonoidWithOne body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddMonoidWithOne.toAddMonoid.{u0} #3 #2)))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddMonoidWithOne.toAddMonoid.{u0} #3 #2))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddCommMonoidWithOne.mk (value of) ← NonAssocSemiring.toAddCommMonoidWithOne (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddCommMonoidWithOne.mk (value of) ← NonAssocSemiring.toAddCommMonoidWithOne (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ toAddMonoidWithOne body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddMonoidWithOne.toAddMonoid.{u0} #3 #2)))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddMonoidWithOne.toAddMonoid.{u0} #3 #2))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonAssocSemiring.natCast_succ", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ self body › ∀ n body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #2 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #2 #1)))))", "yIn": "(AddMonoid.toAdd.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #2 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #2 #1))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonAssocSemiring.natCast_succ (value of) ← NonAssocSemiring.toAddCommMonoidWithOne (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NonAssocSemiring.natCast_succ (value of) ← NonAssocSemiring.toAddCommMonoidWithOne (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ self body › ∀ n body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #2 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #2 #1)))))", "yIn": "(AddMonoid.toAdd.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #2 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #2 #1))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonAssocSemiring.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ toNonUnitalNonAssocSemiring body › ∀ toOne body › ∀ one_mul body › ∀ mul_one body › ∀ toNatCast body › ∀ natCast_zero body › ∀ natCast_succ type › arg 1 of autoParam.{0} › ∀ n body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #7 (AddMonoid.toAddSemigroup.{u0} #7 (AddCommMonoid.toAddMonoid.{u0} #7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #7 #6))))", "yIn": "(AddMonoid.toAdd.{u0} #7 (AddCommMonoid.toAddMonoid.{u0} #7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #7 #6)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonAssocSemiring.mk (value of) ← Semiring.toNonAssocSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NonAssocSemiring.mk (value of) ← Semiring.toNonAssocSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ toNonUnitalNonAssocSemiring body › ∀ toOne body › ∀ one_mul body › ∀ mul_one body › ∀ toNatCast body › ∀ natCast_zero body › ∀ natCast_succ type › arg 1 of autoParam.{0} › ∀ n body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #7 (AddMonoid.toAddSemigroup.{u0} #7 (AddCommMonoid.toAddMonoid.{u0} #7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #7 #6))))", "yIn": "(AddMonoid.toAdd.{u0} #7 (AddCommMonoid.toAddMonoid.{u0} #7 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #7 #6)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonUnitalNonAssocSemiring.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ toAddCommMonoid body › ∀ toMul body › ∀ left_distrib type › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 6 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #5 (AddMonoid.toAddSemigroup.{u0} #5 (AddCommMonoid.toAddMonoid.{u0} #5 #4)))", "yIn": "(AddMonoid.toAdd.{u0} #5 (AddCommMonoid.toAddMonoid.{u0} #5 #4))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonUnitalNonAssocSemiring.mk (value of) ← Semiring.toNonAssocSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NonUnitalNonAssocSemiring.mk (value of) ← Semiring.toNonAssocSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ toAddCommMonoid body › ∀ toMul body › ∀ left_distrib type › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 6 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #5 (AddMonoid.toAddSemigroup.{u0} #5 (AddCommMonoid.toAddMonoid.{u0} #5 #4)))", "yIn": "(AddMonoid.toAdd.{u0} #5 (AddCommMonoid.toAddMonoid.{u0} #5 #4))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonUnitalNonAssocSemiring.toDistrib", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ α body › λ self body › arg 3 of Distrib.mk.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #1 (AddMonoid.toAddSemigroup.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #1 #0))))", "yIn": "(AddMonoid.toAdd.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #1 #0)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonUnitalNonAssocSemiring.toDistrib (value of) ← instDistribOfSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NonUnitalNonAssocSemiring.toDistrib (value of) ← instDistribOfSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ α body › λ self body › arg 3 of Distrib.mk.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #1 (AddMonoid.toAddSemigroup.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #1 #0))))", "yIn": "(AddMonoid.toAdd.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #1 #0)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CauSeq.ofEq._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1921012482._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.ofEq._proof_1 (value of) ← CauSeq.ofEq (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.ofEq._proof_1 (value of) ← CauSeq.ofEq (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.instAdd._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1387507625._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.instAdd._proof_1 (value of) ← CauSeq.instAdd (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instAdd._proof_1 (value of) ← CauSeq.instAdd (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.instNeg._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1827621731._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.instNeg._proof_1 (value of) ← CauSeq.instNeg (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instNeg._proof_1 (value of) ← CauSeq.instNeg (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "AddMonoid.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toAddSemigroup type › head", "why": "different leaves", "x": "AddSemigroup.{u1}", "y": "Zero.{u1}", "xIn": "(AddSemigroup.{u1} #1)", "yIn": "(Zero.{u1} #1)" }, "rules": { "x": [ [ "AddMonoid.mk", 7 ] ], "y": [ [ "AddMonoid.mk", 8 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddMonoid.rec (rec of) ← AddMonoid (type of) ← AddCommMonoid.mk (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddMonoid.rec (rec of) ← AddMonoid (type of) ← AddCommMonoid.mk (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toAddSemigroup type › head", "why": "different leaves", "x": "AddSemigroup.{u1}", "y": "Zero.{u1}", "xIn": "(AddSemigroup.{u1} #1)", "yIn": "(Zero.{u1} #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @AddMonoid.mk M toZero\nargument has type\n Zero M\nbut function has type\n [toAddSemigroup : AddSemigroup M] →\n [toZero : Zero M] →\n (∀ (a : M), 0 + a = a) →\n (∀ (a : M), a + 0 = a) →\n [toNSMul : NSMul M] →\n autoParam (∀ (x : M), 0 • x = 0) AddMonoid.nsmul_zero._autoParam →\n autoParam (∀ (n : ℕ) (x : M), (n + 1) • …" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @AddMonoid.mk M toAddSemigroup\nargument has type\n AddSemigroup M\nbut function has type\n [toZero : Zero M] →\n [toAdd : Add M] →\n (∀ (a b c : M), a + b + c = a + (b + c)) →\n (∀ (a : M), 0 + a = a) →\n (∀ (a : M), a + 0 = a) →\n [toNSMul : NSMul M] →\n autoParam (∀ (x : M), 0 • x = 0) AddMonoid.nsmul_zero._autoParam →…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "AddMonoid.nsmul_succ", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ n body › ∀ x body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 #2))", "yIn": "(AddMonoid.toAdd.{u0} #3 #2)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddMonoid.nsmul_succ (proj of) ← AddMonoid (type of) ← AddCommMonoid.mk (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddMonoid.nsmul_succ (proj of) ← AddMonoid (type of) ← AddCommMonoid.mk (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ n body › ∀ x body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 #2))", "yIn": "(AddMonoid.toAdd.{u0} #3 #2)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddMonoid.toNSMul", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M body › λ self body", "why": "different projections", "x": "(#0).AddMonoid#4", "y": "(#0).AddMonoid#5", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddMonoid.toNSMul (proj of) ← AddMonoid (type of) ← AddCommMonoid.mk (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddMonoid.toNSMul (proj of) ← AddMonoid (type of) ← AddCommMonoid.mk (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M body › λ self body", "why": "different projections", "x": "(#0).AddMonoid#4", "y": "(#0).AddMonoid#5", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n ⋯ = fun M [self : AddMonoid M] => self.5\nargument has type\n (M : Type u) → [self : AddMonoid M] → NSMul M\nbut function has type\n (∀ (M : Type u) [self : AddMonoid M] (x : M), 0 • x = 0) → Prop" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n ⋯ = fun M [self : AddMonoid M] => self.6\nargument has type\n (M : Type u_2) → [self : AddMonoid M] → NSMul M\nbut function has type\n (∀ (M : Type u_2) [self : AddMonoid M] (a : M), a + 0 = a) → Prop" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "CommMonoidWithZero.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ motive body › ∀ mk type › ∀ toCommMonoid body › ∀ toZero body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #4 (Monoid.toSemigroup.{u1} #4 (CommMonoid.toMonoid.{u1} #4 #2)))", "yIn": "(Monoid.toMul.{u1} #4 (CommMonoid.toMonoid.{u1} #4 #2))" }, "rules": { "x": [ [ "CommMonoidWithZero.mk", 4 ] ], "y": [ [ "CommMonoidWithZero.mk", 4 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CommMonoidWithZero.rec (rec of) ← CommMonoidWithZero (type of) ← CommGroupWithZero.mk (ctor of) ← CommGroupWithZero (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CommMonoidWithZero.rec (rec of) ← CommMonoidWithZero (type of) ← CommGroupWithZero.mk (ctor of) ← CommGroupWithZero (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ motive body › ∀ mk type › ∀ toCommMonoid body › ∀ toZero body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #4 (Monoid.toSemigroup.{u1} #4 (CommMonoid.toMonoid.{u1} #4 #2)))", "yIn": "(Monoid.toMul.{u1} #4 (CommMonoid.toMonoid.{u1} #4 #2))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommMonoidWithZero.zero_mul", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (CommMonoid.toMonoid.{u0} #2 (CommMonoidWithZero.toCommMonoid.{u0} #2 #1))))", "yIn": "(Monoid.toMul.{u0} #2 (CommMonoid.toMonoid.{u0} #2 (CommMonoidWithZero.toCommMonoid.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CommMonoidWithZero.zero_mul (proj of) ← CommMonoidWithZero (type of) ← CommGroupWithZero.mk (ctor of) ← CommGroupWithZero (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CommMonoidWithZero.zero_mul (proj of) ← CommMonoidWithZero (type of) ← CommGroupWithZero.mk (ctor of) ← CommGroupWithZero (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (CommMonoid.toMonoid.{u0} #2 (CommMonoidWithZero.toCommMonoid.{u0} #2 #1))))", "yIn": "(Monoid.toMul.{u0} #2 (CommMonoid.toMonoid.{u0} #2 (CommMonoidWithZero.toCommMonoid.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommMonoidWithZero.mul_zero", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (CommMonoid.toMonoid.{u0} #2 (CommMonoidWithZero.toCommMonoid.{u0} #2 #1))))", "yIn": "(Monoid.toMul.{u0} #2 (CommMonoid.toMonoid.{u0} #2 (CommMonoidWithZero.toCommMonoid.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CommMonoidWithZero.mul_zero (proj of) ← CommMonoidWithZero (type of) ← CommGroupWithZero.mk (ctor of) ← CommGroupWithZero (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CommMonoidWithZero.mul_zero (proj of) ← CommMonoidWithZero (type of) ← CommGroupWithZero.mk (ctor of) ← CommGroupWithZero (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (CommMonoid.toMonoid.{u0} #2 (CommMonoidWithZero.toCommMonoid.{u0} #2 #1))))", "yIn": "(Monoid.toMul.{u0} #2 (CommMonoid.toMonoid.{u0} #2 (CommMonoidWithZero.toCommMonoid.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddMonoidWithOne.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Data.Nat.Cast.Defs", "openai": "Mathlib.Data.Nat.Cast.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ motive body › ∀ mk type › ∀ toNatCast body › ∀ toAddMonoid body › ∀ toOne body › ∀ natCast_zero body › ∀ natCast_succ type › ∀ n body › arg 3 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #6 (AddMonoid.toAddSemigroup.{u1} #6 #3))", "yIn": "(AddMonoid.toAdd.{u1} #6 #3)" }, "rules": { "x": [ [ "AddMonoidWithOne.mk", 5 ] ], "y": [ [ "AddMonoidWithOne.mk", 5 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddMonoidWithOne.rec (rec of) ← AddMonoidWithOne (type of) ← AddMonoidWithOne.toAddMonoid (value of) ← AddGroupWithOne.toAddGroup (type of) ← Real.equivCauchy._proof_1 (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddMonoidWithOne.rec (rec of) ← AddMonoidWithOne (type of) ← AddMonoidWithOne.toAddMonoid (value of) ← AddGroupWithOne.toAddGroup (type of) ← Real.equivCauchy._proof_1 (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ motive body › ∀ mk type › ∀ toNatCast body › ∀ toAddMonoid body › ∀ toOne body › ∀ natCast_zero body › ∀ natCast_succ type › ∀ n body › arg 3 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #6 (AddMonoid.toAddSemigroup.{u1} #6 #3))", "yIn": "(AddMonoid.toAdd.{u1} #6 #3)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddMonoidWithOne.natCast_succ", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Nat.Cast.Defs", "openai": "Mathlib.Data.Nat.Cast.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ self body › ∀ n body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 (AddMonoidWithOne.toAddMonoid.{u0} #2 #1)))", "yIn": "(AddMonoid.toAdd.{u0} #2 (AddMonoidWithOne.toAddMonoid.{u0} #2 #1))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddMonoidWithOne.natCast_succ (proj of) ← AddMonoidWithOne (type of) ← AddMonoidWithOne.toAddMonoid (value of) ← AddGroupWithOne.toAddGroup (type of) ← Real.equivCauchy._proof_1 (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddMonoidWithOne.natCast_succ (proj of) ← AddMonoidWithOne (type of) ← AddMonoidWithOne.toAddMonoid (value of) ← AddGroupWithOne.toAddGroup (type of) ← Real.equivCauchy._proof_1 (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ self body › ∀ n body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 (AddMonoidWithOne.toAddMonoid.{u0} #2 #1)))", "yIn": "(AddMonoid.toAdd.{u0} #2 (AddMonoidWithOne.toAddMonoid.{u0} #2 #1))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MulOneClass.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "kernel facts", "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ toMulOne type › head", "why": "different leaves", "x": "MulOne.{u0}", "y": "One.{u0}", "xIn": "(MulOne.{u0} #0)", "yIn": "(One.{u0} #0)" }, "meta": { "x": { "induct": "MulOneClass", "cidx": 0, "numParams": 1, "numFields": 3, "unsafe": false }, "y": { "induct": "MulOneClass", "cidx": 0, "numParams": 1, "numFields": 4, "unsafe": false } } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MulOneClass.mk (value of) ← Monoid.toMulOneClass (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MulOneClass.mk (value of) ← Monoid.toMulOneClass (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ toMulOne type › head", "why": "different leaves", "x": "MulOne.{u0}", "y": "One.{u0}", "xIn": "(MulOne.{u0} #0)", "yIn": "(One.{u0} #0)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "type", "detail": "(kernel) declaration type mismatch, '_seam_check_1541' has type\n ({M : Type u} → [toMulOne : MulOne M] → (∀ (a : M), 1 * a = a) → (∀ (a : M), a * 1 = a) → MulOneClass M) =\n ({M : Type u} → [toMulOne : MulOne M] → (∀ (a : M), 1 * a = a) → (∀ (a : M), a * 1 = a) → MulOneClass M)\nbut it is expected to have type\n ({M : Type u} → [toOne : One M] → [toMul : Mul M] → (∀ (a : M), 1 * a = a) → (∀ (a :…" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) declaration type mismatch, '_seam_check_1564' has type\n ({M : Type u_2} →\n [toOne : One M] → [toMul : Mul M] → (∀ (a : M), 1 * a = a) → (∀ (a : M), a * 1 = a) → MulOneClass M) =\n ({M : Type u_2} →\n [toOne : One M] → [toMul : Mul M] → (∀ (a : M), 1 * a = a) → (∀ (a : M), a * 1 = a) → MulOneClass M)\nbut it is expected to have type\n ({M : Type u_2} → [toMulOne : MulOne M] → (∀…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "Real.instMin", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of Min.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.inf", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.inf", "xIn": "(Min.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.inf)", "yIn": "(Min.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.inf)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of Min.mk.{0}", "why": "different leaves", "x": "_private.Mathlib.Data.Real.Basic.#0.Real.inf", "y": "_private.Mathlib.Basic.Real.Basic.#0.Real.inf", "xIn": "(Min.mk.{0} Real _private.Mathlib.Data.Real.Basic.#0.Real.inf)", "yIn": "(Min.mk.{0} Real _private.Mathlib.Basic.Real.Basic.#0.Real.inf)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Basic.Real.Basic.#0.Real.inf" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "_private.Mathlib.Data.Real.Basic.#0.Real.inf" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "moved-file" }, { "name": "NNReal.instSemiring", "kind": "def", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of Semiring.mk.{0} › arg 2 of AddCommMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3) NNReal.instZero NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) NNReal.instSemiring._proof_8 NNReal.instSemiring._proof_9)", "y": "(AddMonoid.mk.{0} NNReal NNReal.instZero (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3 NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) NNReal.instSemiring._proof_8 NNReal.instSemiring._proof_9)", "xIn": "(AddCommMonoid.mk.{0} NNReal (AddMonoid.mk.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3) NNReal.instZero NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) NNReal.instSemiring._proof_8 NNReal.in…", "yIn": "(AddCommMonoid.mk.{0} NNReal (AddMonoid.mk.{0} NNReal NNReal.instZero (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3 NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) NNReal.instSemiring._proof_8 NNReal.instSemiring._proof_9) NNReal.i…" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 2 of Semiring.mk.{0} › arg 2 of AddCommMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) ⟨proof⟩) NNReal.instZero ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) ⟨proof⟩ ⟨proof⟩)", "y": "(AddMonoid.mk.{0} NNReal NNReal.instZero (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) ⟨proof⟩ ⟨proof⟩)", "xIn": "(AddCommMonoid.mk.{0} NNReal (AddMonoid.mk.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) ⟨proof⟩) NNReal.instZero ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) ⟨proof⟩ ⟨proof⟩) ⟨proof⟩)", "yIn": "(AddCommMonoid.mk.{0} NNReal (AddMonoid.mk.{0} NNReal NNReal.instZero (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) ⟨proof⟩ ⟨proof⟩) ⟨proof⟩)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk NNReal NNReal.instZero\nargument has type\n Zero NNReal\nbut function has type\n [toAddSemigroup : AddSemigroup NNReal] →\n [toZero : Zero NNReal] →\n (∀ (a : NNReal), 0 + a = a) →\n (∀ (a : NNReal), a + 0 = a) →\n [toNSMul : NSMul NNReal] →\n autoParam (∀ (x : NNReal), 0 • x = 0) AddMonoid.nsmul_zero._autoParam →\n …" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk NNReal { add := NNReal.instSemiring._aux_1, add_assoc := NNReal.instSemiring._proof_3 }\nargument has type\n AddSemigroup NNReal\nbut function has type\n [toZero : Zero NNReal] →\n [toAdd : Add NNReal] →\n (∀ (a b c : NNReal), a + b + c = a + (b + c)) →\n (∀ (a : NNReal), 0 + a = a) →\n (∀ (a : NNReal), a + 0 = a) →\n […" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "AddZeroClass.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toAddZero type › head", "why": "different leaves", "x": "AddZero.{u1}", "y": "Zero.{u1}", "xIn": "(AddZero.{u1} #1)", "yIn": "(Zero.{u1} #1)" }, "rules": { "x": [ [ "AddZeroClass.mk", 3 ] ], "y": [ [ "AddZeroClass.mk", 4 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddZeroClass.rec (rec of) ← AddZeroClass (type of) ← AddZeroClass.toAddZero (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddZeroClass.rec (rec of) ← AddZeroClass (type of) ← AddZeroClass.toAddZero (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toAddZero type › head", "why": "different leaves", "x": "AddZero.{u1}", "y": "Zero.{u1}", "xIn": "(AddZero.{u1} #1)", "yIn": "(Zero.{u1} #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n AddZeroClass.mk\nargument has type\n Zero M\nbut function has type\n [toAddZero : AddZero M] → (∀ (a : M), 0 + a = a) → (∀ (a : M), a + 0 = a) → AddZeroClass M" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @AddZeroClass.mk M toAddZero\nargument has type\n AddZero M\nbut function has type\n [toZero : Zero M] → [toAdd : Add M] → (∀ (a : M), 0 + a = a) → (∀ (a : M), a + 0 = a) → AddZeroClass M" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "AddZeroClass.zero_add", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddZero.toAdd.{u0}", "y": "AddZeroClass.toAdd.{u0}", "xIn": "(AddZero.toAdd.{u0} #2 (AddZeroClass.toAddZero.{u0} #2 #1))", "yIn": "(AddZeroClass.toAdd.{u0} #2 #1)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddZeroClass.zero_add (proj of) ← AddZeroClass (type of) ← AddZeroClass.toAddZero (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddZeroClass.zero_add (proj of) ← AddZeroClass (type of) ← AddZeroClass.toAddZero (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddZero.toAdd.{u0}", "y": "AddZeroClass.toAdd.{u0}", "xIn": "(AddZero.toAdd.{u0} #2 (AddZeroClass.toAddZero.{u0} #2 #1))", "yIn": "(AddZeroClass.toAdd.{u0} #2 #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddZeroClass.toAdd, AddZeroClass.toZero" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddZeroClass.add_zero", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddZero.toAdd.{u0}", "y": "AddZeroClass.toAdd.{u0}", "xIn": "(AddZero.toAdd.{u0} #2 (AddZeroClass.toAddZero.{u0} #2 #1))", "yIn": "(AddZeroClass.toAdd.{u0} #2 #1)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddZeroClass.add_zero (proj of) ← AddZeroClass (type of) ← AddZeroClass.toAddZero (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddZeroClass.add_zero (proj of) ← AddZeroClass (type of) ← AddZeroClass.toAddZero (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddZero.toAdd.{u0}", "y": "AddZeroClass.toAdd.{u0}", "xIn": "(AddZero.toAdd.{u0} #2 (AddZeroClass.toAddZero.{u0} #2 #1))", "yIn": "(AddZeroClass.toAdd.{u0} #2 #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddZeroClass.toAdd, AddZeroClass.toZero" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CauSeq.instMul", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.instMul (value of) ← CauSeq.Completion.instMulCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.mul (value of) ← Real.instMul (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instMul (value of) ← CauSeq.Completion.instMulCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.mul (value of) ← Real.instMul (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.mul_equiv_mul", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#484956367._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#484956367._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#484956367._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.mul_equiv_mul (value of) ← CauSeq.Completion.instMulCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.mul (value of) ← Real.instMul (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.mul_equiv_mul (value of) ← CauSeq.Completion.instMulCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.mul (value of) ← Real.instMul (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.instIntCast", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.instIntCast (value of) ← CauSeq.Completion.instIntCastCauchy (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instIntCast (value of) ← CauSeq.Completion.instIntCastCauchy (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#693615396._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.add_equiv_add", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1556837457._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1556837457._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1556837457._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.add_equiv_add (value of) ← CauSeq.Completion.instAddCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.add (value of) ← Real.instAdd (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.add_equiv_add (value of) ← CauSeq.Completion.instAddCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.add (value of) ← Real.instAdd (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "AddCommMonoid.toAddCommSemigroup", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M body › λ self body › arg 2 of AddCommSemigroup.mk.{u0}", "why": "applications of different arity", "x": "(AddMonoid.toAddSemigroup.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0))", "y": "(AddSemigroup.mk.{u0} #1 (AddMonoid.toAdd.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0)) (AddMonoid.add_assoc.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0)))", "xIn": "(AddCommSemigroup.mk.{u0} #1 (AddMonoid.toAddSemigroup.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0)) (AddCommMonoid.add_comm.{u0} #1 #0))", "yIn": "(AddCommSemigroup.mk.{u0} #1 (AddSemigroup.mk.{u0} #1 (AddMonoid.toAdd.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0)) (AddMonoid.add_assoc.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0))) (AddCommMonoid.add_comm.{u0} #1 #0))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddCommMonoid.toAddCommSemigroup (type of) ← IsOrderedCancelAddMonoid.mk (ctor of) ← IsOrderedCancelAddMonoid (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddCommMonoid.toAddCommSemigroup (type of) ← IsOrderedCancelAddMonoid.mk (ctor of) ← IsOrderedCancelAddMonoid (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M body › λ self body › arg 2 of AddCommSemigroup.mk.{u0}", "why": "applications of different arity", "x": "(AddMonoid.toAddSemigroup.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0))", "y": "(AddSemigroup.mk.{u0} #1 (AddMonoid.toAdd.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0)) ⟨proof⟩)", "xIn": "(AddCommSemigroup.mk.{u0} #1 (AddMonoid.toAddSemigroup.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0)) ⟨proof⟩)", "yIn": "(AddCommSemigroup.mk.{u0} #1 (AddSemigroup.mk.{u0} #1 (AddMonoid.toAdd.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 #0)) ⟨proof⟩) ⟨proof⟩)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "AddMonoid.toAdd, AddMonoid.add_assoc" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddCommMonoidWithOne.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Data.Nat.Cast.Defs", "openai": "Mathlib.Data.Nat.Cast.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ motive body › ∀ mk type › ∀ toAddMonoidWithOne body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #4 (AddMonoid.toAddSemigroup.{u1} #4 (AddMonoidWithOne.toAddMonoid.{u1} #4 #2)))", "yIn": "(AddMonoid.toAdd.{u1} #4 (AddMonoidWithOne.toAddMonoid.{u1} #4 #2))" }, "rules": { "x": [ [ "AddCommMonoidWithOne.mk", 2 ] ], "y": [ [ "AddCommMonoidWithOne.mk", 2 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddCommMonoidWithOne.rec (rec of) ← AddCommMonoidWithOne (type of) ← AddCommMonoidWithOne.toAddMonoidWithOne (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddCommMonoidWithOne.rec (rec of) ← AddCommMonoidWithOne (type of) ← AddCommMonoidWithOne.toAddMonoidWithOne (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ motive body › ∀ mk type › ∀ toAddMonoidWithOne body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #4 (AddMonoid.toAddSemigroup.{u1} #4 (AddMonoidWithOne.toAddMonoid.{u1} #4 #2)))", "yIn": "(AddMonoid.toAdd.{u1} #4 (AddMonoidWithOne.toAddMonoid.{u1} #4 #2))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "AddCommMonoidWithOne.add_comm", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Nat.Cast.Defs", "openai": "Mathlib.Data.Nat.Cast.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ R body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddMonoidWithOne.toAddMonoid.{u0} #3 (AddCommMonoidWithOne.toAddMonoidWithOne.{u0} #3 #2))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddMonoidWithOne.toAddMonoid.{u0} #3 (AddCommMonoidWithOne.toAddMonoidWithOne.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "AddCommMonoidWithOne.add_comm (proj of) ← AddCommMonoidWithOne (type of) ← AddCommMonoidWithOne.toAddMonoidWithOne (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "AddCommMonoidWithOne.add_comm (proj of) ← AddCommMonoidWithOne (type of) ← AddCommMonoidWithOne.toAddMonoidWithOne (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ R body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddMonoidWithOne.toAddMonoid.{u0} #3 (AddCommMonoidWithOne.toAddMonoidWithOne.{u0} #3 #2))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddMonoidWithOne.toAddMonoid.{u0} #3 (AddCommMonoidWithOne.toAddMonoidWithOne.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonAssocSemiring.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ motive body › ∀ mk type › ∀ toNonUnitalNonAssocSemiring body › ∀ toOne body › ∀ one_mul body › ∀ mul_one body › ∀ toNatCast body › ∀ natCast_zero body › ∀ natCast_succ type › ∀ n body › arg 3 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #8 (AddMonoid.toAddSemigroup.{u1} #8 (AddCommMonoid.toAddMonoid.{u1} #8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} #8 #6))))", "yIn": "(AddMonoid.toAdd.{u1} #8 (AddCommMonoid.toAddMonoid.{u1} #8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} #8 #6)))" }, "rules": { "x": [ [ "NonAssocSemiring.mk", 7 ] ], "y": [ [ "NonAssocSemiring.mk", 7 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonAssocSemiring.rec (rec of) ← NonAssocSemiring (type of) ← NonAssocSemiring.toAddCommMonoidWithOne (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NonAssocSemiring.rec (rec of) ← NonAssocSemiring (type of) ← NonAssocSemiring.toAddCommMonoidWithOne (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ motive body › ∀ mk type › ∀ toNonUnitalNonAssocSemiring body › ∀ toOne body › ∀ one_mul body › ∀ mul_one body › ∀ toNatCast body › ∀ natCast_zero body › ∀ natCast_succ type › ∀ n body › arg 3 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #8 (AddMonoid.toAddSemigroup.{u1} #8 (AddCommMonoid.toAddMonoid.{u1} #8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} #8 #6))))", "yIn": "(AddMonoid.toAdd.{u1} #8 (AddCommMonoid.toAddMonoid.{u1} #8 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} #8 #6)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonUnitalNonAssocSemiring.left_distrib", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 6 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #4 (AddMonoid.toAddSemigroup.{u0} #4 (AddCommMonoid.toAddMonoid.{u0} #4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #4 #3))))", "yIn": "(AddMonoid.toAdd.{u0} #4 (AddCommMonoid.toAddMonoid.{u0} #4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #4 #3)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonUnitalNonAssocSemiring.left_distrib (value of) ← NonUnitalNonAssocSemiring.toDistrib (value of) ← instDistribOfSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NonUnitalNonAssocSemiring.left_distrib (value of) ← NonUnitalNonAssocSemiring.toDistrib (value of) ← instDistribOfSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 6 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #4 (AddMonoid.toAddSemigroup.{u0} #4 (AddCommMonoid.toAddMonoid.{u0} #4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #4 #3))))", "yIn": "(AddMonoid.toAdd.{u0} #4 (AddCommMonoid.toAddMonoid.{u0} #4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #4 #3)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonUnitalNonAssocSemiring.right_distrib", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 5 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #4 (AddMonoid.toAddSemigroup.{u0} #4 (AddCommMonoid.toAddMonoid.{u0} #4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #4 #3))))", "yIn": "(AddMonoid.toAdd.{u0} #4 (AddCommMonoid.toAddMonoid.{u0} #4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #4 #3)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonUnitalNonAssocSemiring.right_distrib (value of) ← NonUnitalNonAssocSemiring.toDistrib (value of) ← instDistribOfSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NonUnitalNonAssocSemiring.right_distrib (value of) ← NonUnitalNonAssocSemiring.toDistrib (value of) ← instDistribOfSemiring (type of) ← IsStrictOrderedRing.mk (ctor of) ← IsStrictOrderedRing (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 5 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #4 (AddMonoid.toAddSemigroup.{u0} #4 (AddCommMonoid.toAddMonoid.{u0} #4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #4 #3))))", "yIn": "(AddMonoid.toAdd.{u0} #4 (AddCommMonoid.toAddMonoid.{u0} #4 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #4 #3)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "SubtractionCommMonoid.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ toSubtractionMonoid body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "SubtractionCommMonoid.mk (value of) ← AddCommGroup.toDivisionAddCommMonoid (value of) ← CauSeq.instNeg (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "SubtractionCommMonoid.mk (value of) ← AddCommGroup.toDivisionAddCommMonoid (value of) ← CauSeq.instNeg (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ toSubtractionMonoid body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonUnitalNonAssocSemiring.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ motive body › ∀ mk type › ∀ toAddCommMonoid body › ∀ toMul body › ∀ left_distrib type › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u1+1)} › arg 6 of HMul.hMul.{u1, u1, u1} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #6 (AddMonoid.toAddSemigroup.{u1} #6 (AddCommMonoid.toAddMonoid.{u1} #6 #4)))", "yIn": "(AddMonoid.toAdd.{u1} #6 (AddCommMonoid.toAddMonoid.{u1} #6 #4))" }, "rules": { "x": [ [ "NonUnitalNonAssocSemiring.mk", 6 ] ], "y": [ [ "NonUnitalNonAssocSemiring.mk", 6 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonUnitalNonAssocSemiring.rec (rec of) ← NonUnitalNonAssocSemiring (type of) ← NonUnitalNonAssocSemiring.toMulZeroClass (value of) ← instMulZeroClassOfSemiring (value of) ← Rat.commGroupWithZero (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NonUnitalNonAssocSemiring.rec (rec of) ← NonUnitalNonAssocSemiring (type of) ← NonUnitalNonAssocSemiring.toMulZeroClass (value of) ← instMulZeroClassOfSemiring (value of) ← Rat.commGroupWithZero (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ motive body › ∀ mk type › ∀ toAddCommMonoid body › ∀ toMul body › ∀ left_distrib type › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u1+1)} › arg 6 of HMul.hMul.{u1, u1, u1} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #6 (AddMonoid.toAddSemigroup.{u1} #6 (AddCommMonoid.toAddMonoid.{u1} #6 #4)))", "yIn": "(AddMonoid.toAdd.{u1} #6 (AddCommMonoid.toAddMonoid.{u1} #6 #4))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MulOneClass.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toMulOne type › head", "why": "different leaves", "x": "MulOne.{u1}", "y": "One.{u1}", "xIn": "(MulOne.{u1} #1)", "yIn": "(One.{u1} #1)" }, "rules": { "x": [ [ "MulOneClass.mk", 3 ] ], "y": [ [ "MulOneClass.mk", 4 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MulOneClass.rec (rec of) ← MulOneClass (type of) ← MulOneClass.toMulOne (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MulOneClass.rec (rec of) ← MulOneClass (type of) ← MulOneClass.toMulOne (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ motive body › ∀ mk type › ∀ toMulOne type › head", "why": "different leaves", "x": "MulOne.{u1}", "y": "One.{u1}", "xIn": "(MulOne.{u1} #1)", "yIn": "(One.{u1} #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n MulOneClass.mk\nargument has type\n One M\nbut function has type\n [toMulOne : MulOne M] → (∀ (a : M), 1 * a = a) → (∀ (a : M), a * 1 = a) → MulOneClass M" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @MulOneClass.mk M toMulOne\nargument has type\n MulOne M\nbut function has type\n [toOne : One M] → [toMul : Mul M] → (∀ (a : M), 1 * a = a) → (∀ (a : M), a * 1 = a) → MulOneClass M" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "MulOneClass.mul_one", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #2 (MulOneClass.toMulOne.{u0} #2 #1))", "yIn": "(MulOneClass.toMul.{u0} #2 #1)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MulOneClass.mul_one (proj of) ← MulOneClass (type of) ← MulOneClass.toMulOne (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MulOneClass.mul_one (proj of) ← MulOneClass (type of) ← MulOneClass.toMulOne (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #2 (MulOneClass.toMulOne.{u0} #2 #1))", "yIn": "(MulOneClass.toMul.{u0} #2 #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "MulOneClass.toMul, MulOneClass.toOne" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MulOneClass.one_mul", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.Monoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #2 (MulOneClass.toMulOne.{u0} #2 #1))", "yIn": "(MulOneClass.toMul.{u0} #2 #1)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MulOneClass.one_mul (proj of) ← MulOneClass (type of) ← MulOneClass.toMulOne (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MulOneClass.one_mul (proj of) ← MulOneClass (type of) ← MulOneClass.toMulOne (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #2 (MulOneClass.toMulOne.{u0} #2 #1))", "yIn": "(MulOneClass.toMul.{u0} #2 #1)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "MulOneClass.toMul, MulOneClass.toOne" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NNReal.instSemiring._aux_1", "kind": "def", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ x type", "why": "applications of different arity", "x": "(Subtype.{1} Real (fun (x : Real) => (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (AddZero.toZero.{0} Real (AddZeroClass.toAddZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (Semiring.to…", "y": "(Nonneg.{0} Real (AddZero.toZero.{0} Real (AddZeroClass.toAddZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (Semiring.toAddCommMonoid.{0} Real Real.semiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NNReal.instSemiring._aux_1 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._aux_1 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ x type", "why": "applications of different arity", "x": "(Subtype.{1} Real (fun (x : Real) => (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (AddZero.toZero.{0} Real (AddZeroClass.toAddZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (Semiring.to…", "y": "(Nonneg.{0} Real (AddZero.toZero.{0} Real (AddZeroClass.toAddZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (Semiring.toAddCommMonoid.{0} Real Real.semiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)))", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Nonneg" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "nonneg" }, { "name": "NNReal.instSemiring._proof_4", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › arg 2 of Eq.{1} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "Add.mk.{0}", "xIn": "(AddSemigroup.toAdd.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3))", "yIn": "(Add.mk.{0} NNReal NNReal.instSemiring._aux_1)" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_4 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_4 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "NNReal.instSemiring._proof_5", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › arg 2 of Eq.{1} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "Add.mk.{0}", "xIn": "(AddSemigroup.toAdd.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3))", "yIn": "(Add.mk.{0} NNReal NNReal.instSemiring._aux_1)" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_5 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_5 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "NNReal.instSemiring._aux_6", "kind": "def", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ n body › λ x type", "why": "applications of different arity", "x": "(Subtype.{1} Real (fun (x : Real) => (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (AddZero.toZero.{0} Real (AddZeroClass.toAddZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (Semiring.to…", "y": "(Nonneg.{0} Real (AddZero.toZero.{0} Real (AddZeroClass.toAddZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (Semiring.toAddCommMonoid.{0} Real Real.semiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NNReal.instSemiring._aux_6 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._aux_6 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ n body › λ x type", "why": "applications of different arity", "x": "(Subtype.{1} Real (fun (x : Real) => (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (AddZero.toZero.{0} Real (AddZeroClass.toAddZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (Semiring.to…", "y": "(Nonneg.{0} Real (AddZero.toZero.{0} Real (AddZeroClass.toAddZero.{0} Real (AddMonoid.toAddZeroClass.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (Semiring.toAddCommMonoid.{0} Real Real.semiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)))", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Nonneg" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "nonneg" }, { "name": "NNReal.instSemiring._proof_9", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "arg 1 of autoParam.{0} › ∀ n body › ∀ x body › arg 3 of Eq.{1} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "Add.mk.{0}", "xIn": "(AddSemigroup.toAdd.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3))", "yIn": "(Add.mk.{0} NNReal NNReal.instSemiring._aux_1)" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_9 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_9 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "NNReal.instSemiring._proof_10", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › ∀ b body › arg 2 of Eq.{1} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "AddMonoid.toAdd.{0}", "xIn": "(AddSemigroup.toAdd.{0} NNReal (AddMonoid.toAddSemigroup.{0} NNReal (AddMonoid.mk.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3) NNReal.instZero NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6)…", "yIn": "(AddMonoid.toAdd.{0} NNReal (AddMonoid.mk.{0} NNReal NNReal.instZero (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3 NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) NNReal.instSemiring._proof_8 NNReal.instSemiring._proof_9))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_10 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_10 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @AddMonoid.mk NNReal { add := NNReal.instSemiring._aux_1, add_assoc := NNReal.instSemiring._proof_3 }\nargument has type\n AddSemigroup NNReal\nbut function has type\n [toZero : Zero NNReal] →\n [toAdd : Add NNReal] →\n (∀ (a b c : NNReal), a + b + c = a + (b + c)) →\n (∀ (a : NNReal), 0 + a = a) →\n (∀ (a : NNReal), a + 0 = a) →\n […" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "NNReal.instSemiring._aux_11", "kind": "def", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ x type", "why": "applications of different arity", "x": "(Subtype.{1} Real (fun (x : Real) => (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (MulZeroClass.toZero.{0} Real (instMulZeroClassOfSemiring.{0} Real Real.semiring)))) #0)))", "y": "(Nonneg.{0} Real (MulZeroClass.toZero.{0} Real (instMulZeroClassOfSemiring.{0} Real Real.semiring)) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NNReal.instSemiring._aux_11 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._aux_11 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ x type", "why": "applications of different arity", "x": "(Subtype.{1} Real (fun (x : Real) => (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (MulZeroClass.toZero.{0} Real (instMulZeroClassOfSemiring.{0} Real Real.semiring)))) #0)))", "y": "(Nonneg.{0} Real (MulZeroClass.toZero.{0} Real (instMulZeroClassOfSemiring.{0} Real Real.semiring)) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)))", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Nonneg" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "nonneg" }, { "name": "NNReal.instSemiring._proof_14", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › arg 2 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Mul.mk.{0}", "xIn": "(Semigroup.toMul.{0} NNReal (Semigroup.mk.{0} NNReal (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13))", "yIn": "(Mul.mk.{0} NNReal NNReal.instSemiring._aux_11)" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_14 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_14 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "NNReal.instSemiring._proof_15", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › arg 2 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Mul.mk.{0}", "xIn": "(Semigroup.toMul.{0} NNReal (Semigroup.mk.{0} NNReal (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13))", "yIn": "(Mul.mk.{0} NNReal NNReal.instSemiring._aux_11)" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_15 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_15 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "NNReal.instSemiring._aux_16", "kind": "def", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ n body › λ x type", "why": "applications of different arity", "x": "(Subtype.{1} Real (fun (x : Real) => (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (MulZeroClass.toZero.{0} Real (instMulZeroClassOfSemiring.{0} Real Real.semiring)))) #0)))", "y": "(Nonneg.{0} Real (MulZeroClass.toZero.{0} Real (instMulZeroClassOfSemiring.{0} Real Real.semiring)) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NNReal.instSemiring._aux_16 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._aux_16 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ n body › λ x type", "why": "applications of different arity", "x": "(Subtype.{1} Real (fun (x : Real) => (LE.le.{0} Real (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real (MulZeroClass.toZero.{0} Real (instMulZeroClassOfSemiring.{0} Real Real.semiring)))) #0)))", "y": "(Nonneg.{0} Real (MulZeroClass.toZero.{0} Real (instMulZeroClassOfSemiring.{0} Real Real.semiring)) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real Real.partialOrder)))", "xIn": null, "yIn": null } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Nonneg" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "nonneg" }, { "name": "NNReal.instSemiring._proof_19", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "arg 1 of autoParam.{0} › ∀ n body › ∀ x body › arg 3 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Mul.mk.{0}", "xIn": "(Semigroup.toMul.{0} NNReal (Semigroup.mk.{0} NNReal (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13))", "yIn": "(Mul.mk.{0} NNReal NNReal.instSemiring._aux_11)" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_19 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_19 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "NNReal.instSemiring._proof_20", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › arg 2 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} NNReal (Monoid.toSemigroup.{0} NNReal (Monoid.mk.{0} NNReal (Semigroup.mk.{0} NNReal (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13) NNReal.instOne NNReal.instSemiring._proof_14 NNReal.instSemiring._proof_15 (NPow.mk.{0} NNReal NNReal.instSemiring._aux_16) NNReal.inst…", "yIn": "(Monoid.toMul.{0} NNReal (Monoid.mk.{0} NNReal NNReal.instOne (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13 NNReal.instSemiring._proof_14 NNReal.instSemiring._proof_15 (NPow.mk.{0} NNReal NNReal.instSemiring._aux_16) NNReal.instSemiring._proof_18 NNReal.instSemiring._proof_19))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_20 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_20 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @Monoid.mk NNReal { mul := NNReal.instSemiring._aux_11, mul_assoc := NNReal.instSemiring._proof_13 }\nargument has type\n Semigroup NNReal\nbut function has type\n [toOne : One NNReal] →\n [toMul : Mul NNReal] →\n (∀ (a b c : NNReal), a * b * c = a * (b * c)) →\n (∀ (a : NNReal), 1 * a = a) →\n (∀ (a : NNReal), a * 1 = a) →\n [toNPow…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "NNReal.instSemiring._proof_21", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › arg 2 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} NNReal (Monoid.toSemigroup.{0} NNReal (Monoid.mk.{0} NNReal (Semigroup.mk.{0} NNReal (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13) NNReal.instOne NNReal.instSemiring._proof_14 NNReal.instSemiring._proof_15 (NPow.mk.{0} NNReal NNReal.instSemiring._aux_16) NNReal.inst…", "yIn": "(Monoid.toMul.{0} NNReal (Monoid.mk.{0} NNReal NNReal.instOne (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13 NNReal.instSemiring._proof_14 NNReal.instSemiring._proof_15 (NPow.mk.{0} NNReal NNReal.instSemiring._aux_16) NNReal.instSemiring._proof_18 NNReal.instSemiring._proof_19))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_21 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_21 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @Monoid.mk NNReal { mul := NNReal.instSemiring._aux_11, mul_assoc := NNReal.instSemiring._proof_13 }\nargument has type\n Semigroup NNReal\nbut function has type\n [toOne : One NNReal] →\n [toMul : Mul NNReal] →\n (∀ (a b c : NNReal), a * b * c = a * (b * c)) →\n (∀ (a : NNReal), 1 * a = a) →\n (∀ (a : NNReal), a * 1 = a) →\n [toNPow…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "NNReal.instSemiring._proof_22", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} NNReal (Monoid.toSemigroup.{0} NNReal (Monoid.mk.{0} NNReal (Semigroup.mk.{0} NNReal (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13) NNReal.instOne NNReal.instSemiring._proof_14 NNReal.instSemiring._proof_15 (NPow.mk.{0} NNReal NNReal.instSemiring._aux_16) NNReal.inst…", "yIn": "(Monoid.toMul.{0} NNReal (Monoid.mk.{0} NNReal NNReal.instOne (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13 NNReal.instSemiring._proof_14 NNReal.instSemiring._proof_15 (NPow.mk.{0} NNReal NNReal.instSemiring._aux_16) NNReal.instSemiring._proof_18 NNReal.instSemiring._proof_19))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_22 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_22 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @Monoid.mk NNReal { mul := NNReal.instSemiring._aux_11, mul_assoc := NNReal.instSemiring._proof_13 }\nargument has type\n Semigroup NNReal\nbut function has type\n [toOne : One NNReal] →\n [toMul : Mul NNReal] →\n (∀ (a b c : NNReal), a * b * c = a * (b * c)) →\n (∀ (a : NNReal), 1 * a = a) →\n (∀ (a : NNReal), a * 1 = a) →\n [toNPow…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "NNReal.instSemiring._proof_23", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} NNReal (Monoid.toSemigroup.{0} NNReal (Monoid.mk.{0} NNReal (Semigroup.mk.{0} NNReal (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13) NNReal.instOne NNReal.instSemiring._proof_14 NNReal.instSemiring._proof_15 (NPow.mk.{0} NNReal NNReal.instSemiring._aux_16) NNReal.inst…", "yIn": "(Monoid.toMul.{0} NNReal (Monoid.mk.{0} NNReal NNReal.instOne (Mul.mk.{0} NNReal NNReal.instSemiring._aux_11) NNReal.instSemiring._proof_13 NNReal.instSemiring._proof_14 NNReal.instSemiring._proof_15 (NPow.mk.{0} NNReal NNReal.instSemiring._aux_16) NNReal.instSemiring._proof_18 NNReal.instSemiring._proof_19))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_23 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_23 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @Monoid.mk NNReal { mul := NNReal.instSemiring._aux_11, mul_assoc := NNReal.instSemiring._proof_13 }\nargument has type\n Semigroup NNReal\nbut function has type\n [toOne : One NNReal] →\n [toMul : Mul NNReal] →\n (∀ (a b c : NNReal), a * b * c = a * (b * c)) →\n (∀ (a : NNReal), 1 * a = a) →\n (∀ (a : NNReal), a * 1 = a) →\n [toNPow…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "NNReal.instSemiring._proof_26", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "arg 1 of autoParam.{0} › arg 3 of Eq.{1} › arg 3 of OfNat.ofNat.{0} › arg 2 of Zero.toOfNat0.{0} › arg 2 of AddMonoid.toZero.{0} › arg 2 of AddCommMonoid.toAddMonoid.{0} › arg 2 of AddCommMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3) NNReal.instZero NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) NNReal.instSemiring._proof_8 NNReal.instSemiring._proof_9)", "y": "(AddMonoid.mk.{0} NNReal NNReal.instZero (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3 NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) NNReal.instSemiring._proof_8 NNReal.instSemiring._proof_9)", "xIn": "(AddCommMonoid.mk.{0} NNReal (AddMonoid.mk.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3) NNReal.instZero NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) NNReal.instSemiring._proof_8 NNReal.in…", "yIn": "(AddCommMonoid.mk.{0} NNReal (AddMonoid.mk.{0} NNReal NNReal.instZero (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3 NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) NNReal.instSemiring._proof_8 NNReal.instSemiring._proof_9) NNReal.i…" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_26 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_26 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @AddMonoid.mk NNReal NNReal.instZero\nargument has type\n Zero NNReal\nbut function has type\n [toAddSemigroup : AddSemigroup NNReal] →\n [toZero : Zero NNReal] →\n (∀ (a : NNReal), 0 + a = a) →\n (∀ (a : NNReal), a + 0 = a) →\n [toNSMul : NSMul NNReal] →\n autoParam (∀ (x : NNReal), 0 • x = 0) AddMonoid.nsmul_zero._autoParam →\n …" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @AddMonoid.mk NNReal { add := NNReal.instSemiring._aux_1, add_assoc := NNReal.instSemiring._proof_3 }\nargument has type\n AddSemigroup NNReal\nbut function has type\n [toZero : Zero NNReal] →\n [toAdd : Add NNReal] →\n (∀ (a b c : NNReal), a + b + c = a + (b + c)) →\n (∀ (a : NNReal), 0 + a = a) →\n (∀ (a : NNReal), a + 0 = a) →\n […" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "NNReal.instSemiring._proof_27", "kind": "thm", "module": { "anthropic": "Mathlib.Data.NNReal.Defs", "openai": "Mathlib.Basic.NNReal.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "arg 1 of autoParam.{0} › ∀ n body › arg 3 of Eq.{1} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "AddMonoid.toAdd.{0}", "xIn": "(AddSemigroup.toAdd.{0} NNReal (AddMonoid.toAddSemigroup.{0} NNReal (AddCommMonoid.toAddMonoid.{0} NNReal (AddCommMonoid.mk.{0} NNReal (AddMonoid.mk.{0} NNReal (AddSemigroup.mk.{0} NNReal (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3) NNReal.instZero NNReal.instSemiring._proof_4 NNReal.ins…", "yIn": "(AddMonoid.toAdd.{0} NNReal (AddCommMonoid.toAddMonoid.{0} NNReal (AddCommMonoid.mk.{0} NNReal (AddMonoid.mk.{0} NNReal NNReal.instZero (Add.mk.{0} NNReal NNReal.instSemiring._aux_1) NNReal.instSemiring._proof_3 NNReal.instSemiring._proof_4 NNReal.instSemiring._proof_5 (NSMul.mk.{0} NNReal NNReal.instSemiring._aux_6) N…" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "NNReal.instSemiring._proof_27 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NNReal.instSemiring._proof_27 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @AddMonoid.mk NNReal { add := NNReal.instSemiring._aux_1, add_assoc := NNReal.instSemiring._proof_3 }\nargument has type\n AddSemigroup NNReal\nbut function has type\n [toZero : Zero NNReal] →\n [toAdd : Add NNReal] →\n (∀ (a b c : NNReal), a + b + c = a + (b + c)) →\n (∀ (a : NNReal), 0 + a = a) →\n (∀ (a : NNReal), a + 0 = a) →\n […" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "MulZeroOneClass.toMulZeroClass", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M₀ body › λ self body › arg 2 of MulZeroClass.mk.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #1 (MulOneClass.toMulOne.{u0} #1 (MulZeroOneClass.toMulOneClass.{u0} #1 #0)))", "yIn": "(MulOneClass.toMul.{u0} #1 (MulZeroOneClass.toMulOneClass.{u0} #1 #0))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MulZeroOneClass.toMulZeroClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MulZeroOneClass.toMulZeroClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M₀ body › λ self body › arg 2 of MulZeroClass.mk.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #1 (MulOneClass.toMulOne.{u0} #1 (MulZeroOneClass.toMulOneClass.{u0} #1 #0)))", "yIn": "(MulOneClass.toMul.{u0} #1 (MulZeroOneClass.toMulOneClass.{u0} #1 #0))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "MulOneClass.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MonoidWithZero.toMulZeroOneClass", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ M₀ body › λ self body › arg 2 of MulZeroOneClass.mk.{u0}", "why": "applications of different arity", "x": "(MulOneClass.mk.{u0} #1 (MulOne.mk.{u0} #1 (Monoid.toOne.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Semigroup.toMul.{u0} #1 (Monoid.toSemigroup.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)))) (Monoid.one_mul.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Monoid.mul_one.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)))", "y": "(MulOneClass.mk.{u0} #1 (Monoid.toOne.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Monoid.toMul.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Monoid.one_mul.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Monoid.mul_one.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)))", "xIn": "(MulZeroOneClass.mk.{u0} #1 (MulOneClass.mk.{u0} #1 (MulOne.mk.{u0} #1 (Monoid.toOne.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Semigroup.toMul.{u0} #1 (Monoid.toSemigroup.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)))) (Monoid.one_mul.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Monoid.mul_one.{u0} #1 (MonoidWit…", "yIn": "(MulZeroOneClass.mk.{u0} #1 (MulOneClass.mk.{u0} #1 (Monoid.toOne.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Monoid.toMul.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Monoid.one_mul.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Monoid.mul_one.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0))) (MonoidWithZero.toZero.…" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MonoidWithZero.toMulZeroOneClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MonoidWithZero.toMulZeroOneClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ M₀ body › λ self body › arg 2 of MulZeroOneClass.mk.{u0}", "why": "applications of different arity", "x": "(MulOneClass.mk.{u0} #1 (MulOne.mk.{u0} #1 (Monoid.toOne.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Semigroup.toMul.{u0} #1 (Monoid.toSemigroup.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)))) ⟨proof⟩ ⟨proof⟩)", "y": "(MulOneClass.mk.{u0} #1 (Monoid.toOne.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Monoid.toMul.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) ⟨proof⟩ ⟨proof⟩)", "xIn": "(MulZeroOneClass.mk.{u0} #1 (MulOneClass.mk.{u0} #1 (MulOne.mk.{u0} #1 (Monoid.toOne.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Semigroup.toMul.{u0} #1 (Monoid.toSemigroup.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)))) ⟨proof⟩ ⟨proof⟩) (MonoidWithZero.toZero.{u0} #1 #0) ⟨proof⟩ ⟨proof⟩)", "yIn": "(MulZeroOneClass.mk.{u0} #1 (MulOneClass.mk.{u0} #1 (Monoid.toOne.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) (Monoid.toMul.{u0} #1 (MonoidWithZero.toMonoid.{u0} #1 #0)) ⟨proof⟩ ⟨proof⟩) (MonoidWithZero.toZero.{u0} #1 #0) ⟨proof⟩ ⟨proof⟩)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @MulOneClass.mk M₀ { toOne := self.toOne, toMul := self.toSemigroup.toMul }\nargument has type\n MulOne M₀\nbut function has type\n [toOne : One M₀] → [toMul : Mul M₀] → (∀ (a : M₀), 1 * a = a) → (∀ (a : M₀), a * 1 = a) → MulOneClass M₀" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "CauSeq.instMul._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3379617806._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.instMul._proof_1 (value of) ← CauSeq.instMul (value of) ← CauSeq.Completion.instMulCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.mul (value of) ← Real.instMul (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instMul._proof_1 (value of) ← CauSeq.instMul (value of) ← CauSeq.Completion.instMulCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.mul (value of) ← Real.instMul (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "SubtractionCommMonoid.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toSubtractionMonoid body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #4 (AddMonoid.toAddSemigroup.{u1} #4 (SubNegMonoid.toAddMonoid.{u1} #4 (SubtractionMonoid.toSubNegMonoid.{u1} #4 #2))))", "yIn": "(AddMonoid.toAdd.{u1} #4 (SubNegMonoid.toAddMonoid.{u1} #4 (SubtractionMonoid.toSubNegMonoid.{u1} #4 #2)))" }, "rules": { "x": [ [ "SubtractionCommMonoid.mk", 2 ] ], "y": [ [ "SubtractionCommMonoid.mk", 2 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "SubtractionCommMonoid.rec (rec of) ← SubtractionCommMonoid (type of) ← SubtractionCommMonoid.toSubtractionMonoid (value of) ← CauSeq.instNeg (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "SubtractionCommMonoid.rec (rec of) ← SubtractionCommMonoid (type of) ← SubtractionCommMonoid.toSubtractionMonoid (value of) ← CauSeq.instNeg (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toSubtractionMonoid body › ∀ add_comm type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #4 (AddMonoid.toAddSemigroup.{u1} #4 (SubNegMonoid.toAddMonoid.{u1} #4 (SubtractionMonoid.toSubNegMonoid.{u1} #4 #2))))", "yIn": "(AddMonoid.toAdd.{u1} #4 (SubNegMonoid.toAddMonoid.{u1} #4 (SubtractionMonoid.toSubNegMonoid.{u1} #4 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "SubtractionCommMonoid.add_comm", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 (SubtractionCommMonoid.toSubtractionMonoid.{u0} #3 #2)))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 (SubtractionCommMonoid.toSubtractionMonoid.{u0} #3 #2))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "SubtractionCommMonoid.add_comm (proj of) ← SubtractionCommMonoid (type of) ← SubtractionCommMonoid.toSubtractionMonoid (value of) ← CauSeq.instNeg (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "SubtractionCommMonoid.add_comm (proj of) ← SubtractionCommMonoid (type of) ← SubtractionCommMonoid.toSubtractionMonoid (value of) ← CauSeq.instNeg (value of) ← CauSeq.instSub (value of) ← CauSeq.equiv (value of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 (SubtractionCommMonoid.toSubtractionMonoid.{u0} #3 #2)))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (SubNegMonoid.toAddMonoid.{u0} #3 (SubtractionMonoid.toSubNegMonoid.{u0} #3 (SubtractionCommMonoid.toSubtractionMonoid.{u0} #3 #2))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CauSeq.Completion.instInvCauchy", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "Nonneg.add._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.Nonneg.Basic", "openai": "Mathlib.Algebra.Order.Nonneg.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2314059840._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2314059840._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2314059840._hygCtx._hyg.#9 body › ∀ x type", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #3 (fun (x : #3) => (LE.le.{u0} #4 (Preorder.toLE.{u0} #4 #2) (OfNat.ofNat.{u0} #4 0 (Zero.toOfNat0.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 #3)))) #0)))", "y": "(Nonneg.{u0} #3 (AddZero.toZero.{u0} #3 (AddZeroClass.toAddZero.{u0} #3 #2)) (Preorder.toLE.{u0} #3 #1))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Nonneg.add._proof_1 (value of) ← NNReal.instSemiring._aux_1 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Nonneg.add._proof_1 (value of) ← NNReal.instSemiring._aux_1 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Nonneg" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "nonneg" }, { "name": "Nonneg.nsmul", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.Nonneg.Basic", "openai": "Mathlib.Algebra.Order.Nonneg.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#9 body › arg 2 of SMul.{0, u0}", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #3 (fun (x : #3) => (LE.le.{u0} #4 (Preorder.toLE.{u0} #4 #2) (OfNat.ofNat.{u0} #4 0 (Zero.toOfNat0.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))))) #0)))", "y": "(Nonneg.{u0} #3 (AddZero.toZero.{u0} #3 (AddZeroClass.toAddZero.{u0} #3 (AddMonoid.toAddZeroClass.{u0} #3 #2))) (Preorder.toLE.{u0} #3 #1))", "xIn": "(SMul.{0, u0} Nat (Subtype.{(u0+1)} #3 (fun (x : #3) => (LE.le.{u0} #4 (Preorder.toLE.{u0} #4 #2) (OfNat.ofNat.{u0} #4 0 (Zero.toOfNat0.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))))) #0))))", "yIn": "(SMul.{0, u0} Nat (Nonneg.{u0} #3 (AddZero.toZero.{u0} #3 (AddZeroClass.toAddZero.{u0} #3 (AddMonoid.toAddZeroClass.{u0} #3 #2))) (Preorder.toLE.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#9 body › arg 2 of SMul.mk.{0, u0}", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #3 (fun (x : #3) => (LE.le.{u0} #4 (Preorder.toLE.{u0} #4 #2) (OfNat.ofNat.{u0} #4 0 (Zero.toOfNat0.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))))) #0)))", "y": "(Nonneg.{u0} #3 (AddZero.toZero.{u0} #3 (AddZeroClass.toAddZero.{u0} #3 (AddMonoid.toAddZeroClass.{u0} #3 #2))) (Preorder.toLE.{u0} #3 #1))", "xIn": "(SMul.mk.{0, u0} Nat (Subtype.{(u0+1)} #3 (fun (x : #3) => (LE.le.{u0} #4 (Preorder.toLE.{u0} #4 #2) (OfNat.ofNat.{u0} #4 0 (Zero.toOfNat0.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))))) #0))) (fun (n : Nat) => (fun (x : (Subtype.{(u0+1)} #4 (fun (x : #4) => (LE…", "yIn": "(SMul.mk.{0, u0} Nat (Nonneg.{u0} #3 (AddZero.toZero.{u0} #3 (AddZeroClass.toAddZero.{u0} #3 (AddMonoid.toAddZeroClass.{u0} #3 #2))) (Preorder.toLE.{u0} #3 #1)) (fun (n : Nat) => (fun (x : (Nonneg.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))) (Preorder.toLE.{u0}…" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Nonneg.nsmul (value of) ← NNReal.instSemiring._aux_6 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Nonneg.nsmul (value of) ← NNReal.instSemiring._aux_6 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#9 body › arg 2 of SMul.{0, u0}", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #3 (fun (x : #3) => (LE.le.{u0} #4 (Preorder.toLE.{u0} #4 #2) (OfNat.ofNat.{u0} #4 0 (Zero.toOfNat0.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))))) #0)))", "y": "(Nonneg.{u0} #3 (AddZero.toZero.{u0} #3 (AddZeroClass.toAddZero.{u0} #3 (AddMonoid.toAddZeroClass.{u0} #3 #2))) (Preorder.toLE.{u0} #3 #1))", "xIn": "(SMul.{0, u0} Nat (Subtype.{(u0+1)} #3 (fun (x : #3) => (LE.le.{u0} #4 (Preorder.toLE.{u0} #4 #2) (OfNat.ofNat.{u0} #4 0 (Zero.toOfNat0.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))))) #0))))", "yIn": "(SMul.{0, u0} Nat (Nonneg.{u0} #3 (AddZero.toZero.{u0} #3 (AddZeroClass.toAddZero.{u0} #3 (AddMonoid.toAddZeroClass.{u0} #3 #2))) (Preorder.toLE.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#9 body › arg 2 of SMul.mk.{0, u0}", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #3 (fun (x : #3) => (LE.le.{u0} #4 (Preorder.toLE.{u0} #4 #2) (OfNat.ofNat.{u0} #4 0 (Zero.toOfNat0.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))))) #0)))", "y": "(Nonneg.{u0} #3 (AddZero.toZero.{u0} #3 (AddZeroClass.toAddZero.{u0} #3 (AddMonoid.toAddZeroClass.{u0} #3 #2))) (Preorder.toLE.{u0} #3 #1))", "xIn": "(SMul.mk.{0, u0} Nat (Subtype.{(u0+1)} #3 (fun (x : #3) => (LE.le.{u0} #4 (Preorder.toLE.{u0} #4 #2) (OfNat.ofNat.{u0} #4 0 (Zero.toOfNat0.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))))) #0))) (fun (n : Nat) => (fun (x : (Subtype.{(u0+1)} #4 (fun (x : #4) => (LE…", "yIn": "(SMul.mk.{0, u0} Nat (Nonneg.{u0} #3 (AddZero.toZero.{u0} #3 (AddZeroClass.toAddZero.{u0} #3 (AddMonoid.toAddZeroClass.{u0} #3 #2))) (Preorder.toLE.{u0} #3 #1)) (fun (n : Nat) => (fun (x : (Nonneg.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))) (Preorder.toLE.{u0}…" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Nonneg" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "nonneg" }, { "name": "Nonneg.mul._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.Nonneg.Basic", "openai": "Mathlib.Algebra.Order.Nonneg.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2075127268._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2075127268._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2075127268._hygCtx._hyg.#9 body › ∀ x type", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #3 (fun (x : #3) => (LE.le.{u0} #4 (Preorder.toLE.{u0} #4 #2) (OfNat.ofNat.{u0} #4 0 (Zero.toOfNat0.{u0} #4 (MulZeroClass.toZero.{u0} #4 #3))) #0)))", "y": "(Nonneg.{u0} #3 (MulZeroClass.toZero.{u0} #3 #2) (Preorder.toLE.{u0} #3 #1))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Nonneg.mul._proof_1 (value of) ← NNReal.instSemiring._aux_11 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Nonneg.mul._proof_1 (value of) ← NNReal.instSemiring._aux_11 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Nonneg" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "nonneg" }, { "name": "Nonneg.pow", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.Nonneg.Basic", "openai": "Mathlib.Algebra.Order.Nonneg.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#9 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#12 body › arg 1 of Pow.{u0, 0}", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #4 (fun (x : #4) => (LE.le.{u0} #5 (Preorder.toLE.{u0} #5 #3) (OfNat.ofNat.{u0} #5 0 (Zero.toOfNat0.{u0} #5 (MulZeroClass.toZero.{u0} #5 (MulZeroOneClass.toMulZeroClass.{u0} #5 (MonoidWithZero.toMulZeroOneClass.{u0} #5 #4))))) #0)))", "y": "(Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3))) (Preorder.toLE.{u0} #4 #2))", "xIn": "(Pow.{u0, 0} (Subtype.{(u0+1)} #4 (fun (x : #4) => (LE.le.{u0} #5 (Preorder.toLE.{u0} #5 #3) (OfNat.ofNat.{u0} #5 0 (Zero.toOfNat0.{u0} #5 (MulZeroClass.toZero.{u0} #5 (MulZeroOneClass.toMulZeroClass.{u0} #5 (MonoidWithZero.toMulZeroOneClass.{u0} #5 #4))))) #0))) Nat)", "yIn": "(Pow.{u0, 0} (Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3))) (Preorder.toLE.{u0} #4 #2)) Nat)" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#9 body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#12 body › arg 1 of Pow.mk.{u0, 0}", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #4 (fun (x : #4) => (LE.le.{u0} #5 (Preorder.toLE.{u0} #5 #3) (OfNat.ofNat.{u0} #5 0 (Zero.toOfNat0.{u0} #5 (MulZeroClass.toZero.{u0} #5 (MulZeroOneClass.toMulZeroClass.{u0} #5 (MonoidWithZero.toMulZeroOneClass.{u0} #5 #4))))) #0)))", "y": "(Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3))) (Preorder.toLE.{u0} #4 #2))", "xIn": "(Pow.mk.{u0, 0} (Subtype.{(u0+1)} #4 (fun (x : #4) => (LE.le.{u0} #5 (Preorder.toLE.{u0} #5 #3) (OfNat.ofNat.{u0} #5 0 (Zero.toOfNat0.{u0} #5 (MulZeroClass.toZero.{u0} #5 (MulZeroOneClass.toMulZeroClass.{u0} #5 (MonoidWithZero.toMulZeroOneClass.{u0} #5 #4))))) #0))) Nat (fun (x : (Subtype.{(u0+1)} #4 (fun (x : #4) => (…", "yIn": "(Pow.mk.{u0, 0} (Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3))) (Preorder.toLE.{u0} #4 #2)) Nat (fun (x : (Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3…" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Nonneg.pow (value of) ← NNReal.instSemiring._aux_16 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Nonneg.pow (value of) ← NNReal.instSemiring._aux_16 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#9 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#12 body › arg 1 of Pow.{u0, 0}", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #4 (fun (x : #4) => (LE.le.{u0} #5 (Preorder.toLE.{u0} #5 #3) (OfNat.ofNat.{u0} #5 0 (Zero.toOfNat0.{u0} #5 (MulZeroClass.toZero.{u0} #5 (MulZeroOneClass.toMulZeroClass.{u0} #5 (MonoidWithZero.toMulZeroOneClass.{u0} #5 #4))))) #0)))", "y": "(Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3))) (Preorder.toLE.{u0} #4 #2))", "xIn": "(Pow.{u0, 0} (Subtype.{(u0+1)} #4 (fun (x : #4) => (LE.le.{u0} #5 (Preorder.toLE.{u0} #5 #3) (OfNat.ofNat.{u0} #5 0 (Zero.toOfNat0.{u0} #5 (MulZeroClass.toZero.{u0} #5 (MulZeroOneClass.toMulZeroClass.{u0} #5 (MonoidWithZero.toMulZeroOneClass.{u0} #5 #4))))) #0))) Nat)", "yIn": "(Pow.{u0, 0} (Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3))) (Preorder.toLE.{u0} #4 #2)) Nat)" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#9 body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#12 body › arg 1 of Pow.mk.{u0, 0}", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #4 (fun (x : #4) => (LE.le.{u0} #5 (Preorder.toLE.{u0} #5 #3) (OfNat.ofNat.{u0} #5 0 (Zero.toOfNat0.{u0} #5 (MulZeroClass.toZero.{u0} #5 (MulZeroOneClass.toMulZeroClass.{u0} #5 (MonoidWithZero.toMulZeroOneClass.{u0} #5 #4))))) #0)))", "y": "(Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3))) (Preorder.toLE.{u0} #4 #2))", "xIn": "(Pow.mk.{u0, 0} (Subtype.{(u0+1)} #4 (fun (x : #4) => (LE.le.{u0} #5 (Preorder.toLE.{u0} #5 #3) (OfNat.ofNat.{u0} #5 0 (Zero.toOfNat0.{u0} #5 (MulZeroClass.toZero.{u0} #5 (MulZeroOneClass.toMulZeroClass.{u0} #5 (MonoidWithZero.toMulZeroOneClass.{u0} #5 #4))))) #0))) Nat (fun (x : (Subtype.{(u0+1)} #4 (fun (x : #4) => (…", "yIn": "(Pow.mk.{u0, 0} (Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3))) (Preorder.toLE.{u0} #4 #2)) Nat (fun (x : (Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3…" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Nonneg" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "nonneg" }, { "name": "MulZeroOneClass.zero_mul", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #2 (MulOneClass.toMulOne.{u0} #2 (MulZeroOneClass.toMulOneClass.{u0} #2 #1)))", "yIn": "(MulOneClass.toMul.{u0} #2 (MulZeroOneClass.toMulOneClass.{u0} #2 #1))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MulZeroOneClass.zero_mul (value of) ← MulZeroOneClass.toMulZeroClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MulZeroOneClass.zero_mul (value of) ← MulZeroOneClass.toMulZeroClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #2 (MulOneClass.toMulOne.{u0} #2 (MulZeroOneClass.toMulOneClass.{u0} #2 #1)))", "yIn": "(MulOneClass.toMul.{u0} #2 (MulZeroOneClass.toMulOneClass.{u0} #2 #1))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "MulOneClass.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MulZeroOneClass.mul_zero", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #2 (MulOneClass.toMulOne.{u0} #2 (MulZeroOneClass.toMulOneClass.{u0} #2 #1)))", "yIn": "(MulOneClass.toMul.{u0} #2 (MulZeroOneClass.toMulOneClass.{u0} #2 #1))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MulZeroOneClass.mul_zero (value of) ← MulZeroOneClass.toMulZeroClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MulZeroOneClass.mul_zero (value of) ← MulZeroOneClass.toMulZeroClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #2 (MulOneClass.toMulOne.{u0} #2 (MulZeroOneClass.toMulOneClass.{u0} #2 #1)))", "yIn": "(MulOneClass.toMul.{u0} #2 (MulZeroOneClass.toMulOneClass.{u0} #2 #1))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "MulOneClass.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MulZeroOneClass.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ toMulOneClass body › ∀ toZero body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #3 (MulOneClass.toMulOne.{u0} #3 #2))", "yIn": "(MulOneClass.toMul.{u0} #3 #2)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MulZeroOneClass.mk (value of) ← MonoidWithZero.toMulZeroOneClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MulZeroOneClass.mk (value of) ← MonoidWithZero.toMulZeroOneClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ toMulOneClass body › ∀ toZero body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "MulOne.toMul.{u0}", "y": "MulOneClass.toMul.{u0}", "xIn": "(MulOne.toMul.{u0} #3 (MulOneClass.toMulOne.{u0} #3 #2))", "yIn": "(MulOneClass.toMul.{u0} #3 #2)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "MulOneClass.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MonoidWithZero.zero_mul", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (MonoidWithZero.toMonoid.{u0} #2 #1)))", "yIn": "(Monoid.toMul.{u0} #2 (MonoidWithZero.toMonoid.{u0} #2 #1))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MonoidWithZero.zero_mul (value of) ← MonoidWithZero.toMulZeroOneClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MonoidWithZero.zero_mul (value of) ← MonoidWithZero.toMulZeroOneClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (MonoidWithZero.toMonoid.{u0} #2 #1)))", "yIn": "(Monoid.toMul.{u0} #2 (MonoidWithZero.toMonoid.{u0} #2 #1))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MonoidWithZero.mul_zero", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (MonoidWithZero.toMonoid.{u0} #2 #1)))", "yIn": "(Monoid.toMul.{u0} #2 (MonoidWithZero.toMonoid.{u0} #2 #1))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MonoidWithZero.mul_zero (value of) ← MonoidWithZero.toMulZeroOneClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MonoidWithZero.mul_zero (value of) ← MonoidWithZero.toMulZeroOneClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ self body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (MonoidWithZero.toMonoid.{u0} #2 #1)))", "yIn": "(Monoid.toMul.{u0} #2 (MonoidWithZero.toMonoid.{u0} #2 #1))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MonoidWithZero.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ toMonoid body › ∀ toZero body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 #2))", "yIn": "(Monoid.toMul.{u0} #3 #2)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MonoidWithZero.mk (value of) ← Semiring.toMonoidWithZero (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MonoidWithZero.mk (value of) ← Semiring.toMonoidWithZero (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ toMonoid body › ∀ toZero body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 #2))", "yIn": "(Monoid.toMul.{u0} #3 #2)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Multiset.instAddCancelCommMonoid", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.Group.Multiset", "openai": "Mathlib.Algebra.Order.Group.Multiset" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ α body › arg 2 of AddCancelCommMonoid.mk.{u0} › arg 2 of AddCommMonoid.mk.{u0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{u0} (Multiset.{u0} #0) (AddSemigroup.mk.{u0} (Multiset.{u0} #0) (Multiset.instAdd.{u0} #0) (Multiset.add_assoc.{u0} #0)) (Multiset.instZero.{u0} #0) (Multiset.zero_add.{u0} #0) (Multiset.add_zero.{u0} #0) (NSMul.mk.{u0} (Multiset.{u0} #0) (nsmulRec.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Mul…", "y": "(AddMonoid.mk.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Multiset.instAdd.{u0} #0) (Multiset.add_assoc.{u0} #0) (Multiset.zero_add.{u0} #0) (Multiset.add_zero.{u0} #0) (NSMul.mk.{u0} (Multiset.{u0} #0) (nsmulRec.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Multiset.instAdd.{u0} #0))) (Multiset.instAdd…", "xIn": "(AddCommMonoid.mk.{u0} (Multiset.{u0} #0) (AddMonoid.mk.{u0} (Multiset.{u0} #0) (AddSemigroup.mk.{u0} (Multiset.{u0} #0) (Multiset.instAdd.{u0} #0) (Multiset.add_assoc.{u0} #0)) (Multiset.instZero.{u0} #0) (Multiset.zero_add.{u0} #0) (Multiset.add_zero.{u0} #0) (NSMul.mk.{u0} (Multiset.{u0} #0) (nsmulRec.{u0} (Multiset…", "yIn": "(AddCommMonoid.mk.{u0} (Multiset.{u0} #0) (AddMonoid.mk.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Multiset.instAdd.{u0} #0) (Multiset.add_assoc.{u0} #0) (Multiset.zero_add.{u0} #0) (Multiset.add_zero.{u0} #0) (NSMul.mk.{u0} (Multiset.{u0} #0) (nsmulRec.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Mul…" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Multiset.instAddCancelCommMonoid (value of) ← Multiset.join (value of) ← Multiset.bind (value of) ← Multiset.pi (value of) ← Finset.pi (value of) ← Fintype.piFinset (value of) ← Pi.instFintype (value of) ← OAI.Algorithms.SubexponentialSAT.SAT.satisfyingAssignments (value of) ← OAI.Algorithms.SubexponentialSAT.SAT.count (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Multiset.instAddCancelCommMonoid (value of) ← Multiset.join (value of) ← Multiset.bind (value of) ← Multiset.pi (value of) ← Finset.pi (value of) ← Fintype.piFinset (value of) ← Pi.instFintype (value of) ← OAI.Algorithms.SubexponentialSAT.SAT.satisfyingAssignments (value of) ← OAI.Algorithms.SubexponentialSAT.SAT.count (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ α body › arg 2 of AddCancelCommMonoid.mk.{u0} › arg 2 of AddCommMonoid.mk.{u0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{u0} (Multiset.{u0} #0) (AddSemigroup.mk.{u0} (Multiset.{u0} #0) (Multiset.instAdd.{u0} #0) ⟨proof⟩) (Multiset.instZero.{u0} #0) ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{u0} (Multiset.{u0} #0) (nsmulRec.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Multiset.instAdd.{u0} #0))) ⟨proof⟩ ⟨proof⟩)", "y": "(AddMonoid.mk.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Multiset.instAdd.{u0} #0) ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{u0} (Multiset.{u0} #0) (nsmulRec.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Multiset.instAdd.{u0} #0))) ⟨proof⟩ ⟨proof⟩)", "xIn": "(AddCommMonoid.mk.{u0} (Multiset.{u0} #0) (AddMonoid.mk.{u0} (Multiset.{u0} #0) (AddSemigroup.mk.{u0} (Multiset.{u0} #0) (Multiset.instAdd.{u0} #0) ⟨proof⟩) (Multiset.instZero.{u0} #0) ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{u0} (Multiset.{u0} #0) (nsmulRec.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Multiset.instAdd.{u0} …", "yIn": "(AddCommMonoid.mk.{u0} (Multiset.{u0} #0) (AddMonoid.mk.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Multiset.instAdd.{u0} #0) ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.mk.{u0} (Multiset.{u0} #0) (nsmulRec.{u0} (Multiset.{u0} #0) (Multiset.instZero.{u0} #0) (Multiset.instAdd.{u0} #0))) ⟨proof⟩ ⟨proof⟩) ⟨proof⟩)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk (Multiset α) Multiset.instZero\nargument has type\n Zero (Multiset α)\nbut function has type\n [toAddSemigroup : AddSemigroup (Multiset α)] →\n [toZero : Zero (Multiset α)] →\n (∀ (a : Multiset α), 0 + a = a) →\n (∀ (a : Multiset α), a + 0 = a) →\n [toNSMul : NSMul (Multiset α)] →\n autoParam (∀ (x : Multiset α), 0 • x …" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk (Multiset α) { toAdd := Multiset.instAdd, add_assoc := ⋯ }\nargument has type\n AddSemigroup (Multiset α)\nbut function has type\n [toZero : Zero (Multiset α)] →\n [toAdd : Add (Multiset α)] →\n (∀ (a b c : Multiset α), a + b + c = a + (b + c)) →\n (∀ (a : Multiset α), 0 + a = a) →\n (∀ (a : Multiset α), a + 0 = a) →\n …" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "CauSeq.lim", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#3764775877._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "Real.instField", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 16 of Field.mk.{0} › λ x._@.Mathlib.Data.Real.Basic.#310067971._hygCtx._hyg.#25 body › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real (Semiring.toMonoid.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))))", "yIn": "(Monoid.toMul.{0} Real (Semiring.toMonoid.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.instField (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instField (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 16 of Field.mk.{0} › λ x._@.Mathlib.Data.Real.Basic.#310067971._hygCtx._hyg.#25 body › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real (Semiring.toMonoid.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))))", "yIn": "(Monoid.toMul.{0} Real (Semiring.toMonoid.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonAssocSemiring.toMulZeroOneClass", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ α body › λ self body › arg 2 of MulZeroOneClass.mk.{u0}", "why": "applications of different arity", "x": "(MulOneClass.mk.{u0} #1 (MulOne.mk.{u0} #1 (NonAssocSemiring.toOne.{u0} #1 #0) (NonUnitalNonAssocSemiring.toMul.{u0} #1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #1 #0))) (NonAssocSemiring.one_mul.{u0} #1 #0) (NonAssocSemiring.mul_one.{u0} #1 #0))", "y": "(MulOneClass.mk.{u0} #1 (NonAssocSemiring.toOne.{u0} #1 #0) (NonUnitalNonAssocSemiring.toMul.{u0} #1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #1 #0)) (NonAssocSemiring.one_mul.{u0} #1 #0) (NonAssocSemiring.mul_one.{u0} #1 #0))", "xIn": "(MulZeroOneClass.mk.{u0} #1 (MulOneClass.mk.{u0} #1 (MulOne.mk.{u0} #1 (NonAssocSemiring.toOne.{u0} #1 #0) (NonUnitalNonAssocSemiring.toMul.{u0} #1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #1 #0))) (NonAssocSemiring.one_mul.{u0} #1 #0) (NonAssocSemiring.mul_one.{u0} #1 #0)) (AddMonoid.toZero.{u0} #1 (AddCommM…", "yIn": "(MulZeroOneClass.mk.{u0} #1 (MulOneClass.mk.{u0} #1 (NonAssocSemiring.toOne.{u0} #1 #0) (NonUnitalNonAssocSemiring.toMul.{u0} #1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #1 #0)) (NonAssocSemiring.one_mul.{u0} #1 #0) (NonAssocSemiring.mul_one.{u0} #1 #0)) (AddMonoid.toZero.{u0} #1 (AddCommMonoid.toAddMonoid.{u…" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonAssocSemiring.toMulZeroOneClass (value of) ← instMulZeroOneClassOfSemiring (value of) ← Complex.instNorm (value of) ← Complex.log (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "NonAssocSemiring.toMulZeroOneClass (value of) ← instMulZeroOneClassOfSemiring (value of) ← Complex.instNorm (value of) ← Complex.log (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "λ α body › λ self body › arg 2 of MulZeroOneClass.mk.{u0}", "why": "applications of different arity", "x": "(MulOneClass.mk.{u0} #1 (MulOne.mk.{u0} #1 (NonAssocSemiring.toOne.{u0} #1 #0) (NonUnitalNonAssocSemiring.toMul.{u0} #1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #1 #0))) ⟨proof⟩ ⟨proof⟩)", "y": "(MulOneClass.mk.{u0} #1 (NonAssocSemiring.toOne.{u0} #1 #0) (NonUnitalNonAssocSemiring.toMul.{u0} #1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #1 #0)) ⟨proof⟩ ⟨proof⟩)", "xIn": "(MulZeroOneClass.mk.{u0} #1 (MulOneClass.mk.{u0} #1 (MulOne.mk.{u0} #1 (NonAssocSemiring.toOne.{u0} #1 #0) (NonUnitalNonAssocSemiring.toMul.{u0} #1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #1 #0))) ⟨proof⟩ ⟨proof⟩) (AddMonoid.toZero.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 (NonUnitalNonAssocSemiring.toAddCo…", "yIn": "(MulZeroOneClass.mk.{u0} #1 (MulOneClass.mk.{u0} #1 (NonAssocSemiring.toOne.{u0} #1 #0) (NonUnitalNonAssocSemiring.toMul.{u0} #1 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u0} #1 #0)) ⟨proof⟩ ⟨proof⟩) (AddMonoid.toZero.{u0} #1 (AddCommMonoid.toAddMonoid.{u0} #1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u0} #1 (No…" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n MulOneClass.mk\nargument has type\n One α\nbut function has type\n [toMulOne : MulOne α] → (∀ (a : α), 1 * a = a) → (∀ (a : α), a * 1 = a) → MulOneClass α" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @MulOneClass.mk α { toOne := self.toOne, toMul := self.toMul }\nargument has type\n MulOne α\nbut function has type\n [toOne : One α] → [toMul : Mul α] → (∀ (a : α), 1 * a = a) → (∀ (a : α), a * 1 = a) → MulOneClass α" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "Real.sinOrderIso", "kind": "def", "module": { "anthropic": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic", "openai": "Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 8 of OrderIso.trans.{0, 0, 0} › head", "why": "different leaves", "x": "OrderIso.setCongr.{0}", "y": "Set.orderIsoOfEq.{0}", "xIn": "(OrderIso.setCongr.{0} Real Real.instPreorder (Set.image.{0, 0} Real Real Real.sin (Set.Icc.{0} Real Real.instPreorder (Neg.neg.{0} Real Real.instNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toDiv.{0} Real Real.instDivInvMonoid)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNatAtLeastTwo.{0} Real …", "yIn": "(Set.orderIsoOfEq.{0} Real Real.instPreorder (Set.image.{0, 0} Real Real Real.sin (Set.Icc.{0} Real Real.instPreorder (Neg.neg.{0} Real Real.instNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toDiv.{0} Real Real.instDivInvMonoid)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNatAtLeastTwo.{0} Real 2…" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Real.sinOrderIso (value of) ← Real.arcsin (value of) ← Complex.arg (value of) ← Complex.log (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.sinOrderIso (value of) ← Real.arcsin (value of) ← Complex.arg (value of) ← Complex.log (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 8 of OrderIso.trans.{0, 0, 0} › head", "why": "different leaves", "x": "OrderIso.setCongr.{0}", "y": "Set.orderIsoOfEq.{0}", "xIn": "(OrderIso.setCongr.{0} Real Real.instPreorder (Set.image.{0, 0} Real Real Real.sin (Set.Icc.{0} Real Real.instPreorder (Neg.neg.{0} Real Real.instNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toDiv.{0} Real Real.instDivInvMonoid)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNatAtLeastTwo.{0} Real …", "yIn": "(Set.orderIsoOfEq.{0} Real Real.instPreorder (Set.image.{0, 0} Real Real Real.sin (Set.Icc.{0} Real Real.instPreorder (Neg.neg.{0} Real Real.instNeg (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toDiv.{0} Real Real.instDivInvMonoid)) Real.pi (OfNat.ofNat.{0} Real 2 (instOfNatAtLeastTwo.{0} Real 2…" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Set.orderIsoOfEq" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "renamed" }, { "name": "CauSeq.instZero", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.instZero (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instZero (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2736031858._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.inv", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" }, "value": { "at": "λ α body › λ β body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#3294888691._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.Completion.instInvCauchy._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1860227065._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u1} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u1}", "y": "CommSemiring.toSemiring.{u1}", "xIn": "(DivisionSemiring.toSemiring.{u1} #2 (Semifield.toDivisionSemiring.{u1} #2 (Field.toSemifield.{u1} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u1} #2 (Semifield.toCommSemiring.{u1} #2 (Field.toSemifield.{u1} #2 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.Completion.instInvCauchy._proof_1 (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.instInvCauchy._proof_1 (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "Nonneg.semilatticeSup._aux_1", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.Nonneg.Lattice", "openai": "Mathlib.Algebra.Order.Nonneg.Lattice" }, "differs": [ "value" ], "class": "proof-internal", "diffs": { "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.Nonneg.Lattice.#2570191386._hygCtx._hyg.#3 body › λ a body › λ x body › λ y body › arg 4 of Subtype.mk.{(u0+1)} › arg 4 of Subtype.semilatticeSup._proof_1.{u0} › arg 2 of Set.Ici.semilatticeSup._proof_1.{u0}", "why": "different leaves", "x": "#3", "y": "#2", "xIn": "(Set.Ici.semilatticeSup._proof_1.{u0} #4 #3 #2)", "yIn": "(Set.Ici.semilatticeSup._proof_1.{u0} #4 #2 #3)" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Nonneg.semilatticeSup._aux_1 (value of) ← NNReal.instSemilatticeSup._aux_1 (value of) ← NNReal.instSemilatticeSup (value of) ← NNReal.instLinearOrder (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Nonneg.semilatticeSup._aux_1 (value of) ← NNReal.instSemilatticeSup._aux_1 (value of) ← NNReal.instSemilatticeSup (value of) ← NNReal.instLinearOrder (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @Set.Ici.semilatticeSup._proof_1 α a\nargument has type\n α\nbut function has type\n ∀ [inst : SemilatticeSup α] {a : α} (x x_1 : α), x ∈ Set.Ici a → x_1 ∈ Set.Ici a → a ≤ x ⊔ x_1" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @Set.Ici.semilatticeSup._proof_1 α inst✝\nargument has type\n SemilatticeSup α\nbut function has type\n ∀ {a : α} [inst : SemilatticeSup α] (x x_1 : α), x ∈ Set.Ici a → x_1 ∈ Set.Ici a → a ≤ x ⊔ x_1" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "nonneg" }, { "name": "Nonneg.nsmul._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.Nonneg.Basic", "openai": "Mathlib.Algebra.Order.Nonneg.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2688423265._hygCtx._hyg.#9 body › ∀ n body › ∀ x type", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #4 (fun (x : #4) => (LE.le.{u0} #5 (Preorder.toLE.{u0} #5 #3) (OfNat.ofNat.{u0} #5 0 (Zero.toOfNat0.{u0} #5 (AddZero.toZero.{u0} #5 (AddZeroClass.toAddZero.{u0} #5 (AddMonoid.toAddZeroClass.{u0} #5 #4))))) #0)))", "y": "(Nonneg.{u0} #4 (AddZero.toZero.{u0} #4 (AddZeroClass.toAddZero.{u0} #4 (AddMonoid.toAddZeroClass.{u0} #4 #3))) (Preorder.toLE.{u0} #4 #2))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Nonneg.nsmul._proof_1 (value of) ← Nonneg.nsmul (value of) ← NNReal.instSemiring._aux_6 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Nonneg.nsmul._proof_1 (value of) ← Nonneg.nsmul (value of) ← NNReal.instSemiring._aux_6 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Nonneg" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "nonneg" }, { "name": "Nonneg.pow._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.Nonneg.Basic", "openai": "Mathlib.Algebra.Order.Nonneg.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#9 body › ∀ inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#427477602._hygCtx._hyg.#12 body › ∀ x type", "why": "applications of different arity", "x": "(Subtype.{(u0+1)} #4 (fun (x : #4) => (LE.le.{u0} #5 (Preorder.toLE.{u0} #5 #3) (OfNat.ofNat.{u0} #5 0 (Zero.toOfNat0.{u0} #5 (MulZeroClass.toZero.{u0} #5 (MulZeroOneClass.toMulZeroClass.{u0} #5 (MonoidWithZero.toMulZeroOneClass.{u0} #5 #4))))) #0)))", "y": "(Nonneg.{u0} #4 (MulZeroClass.toZero.{u0} #4 (MulZeroOneClass.toMulZeroClass.{u0} #4 (MonoidWithZero.toMulZeroOneClass.{u0} #4 #3))) (Preorder.toLE.{u0} #4 #2))", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Nonneg.pow._proof_1 (value of) ← Nonneg.pow (value of) ← NNReal.instSemiring._aux_16 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Nonneg.pow._proof_1 (value of) ← Nonneg.pow (value of) ← NNReal.instSemiring._aux_16 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Nonneg" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "nonneg" }, { "name": "MonoidWithZero.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ motive body › ∀ mk type › ∀ toMonoid body › ∀ toZero body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #4 (Monoid.toSemigroup.{u1} #4 #2))", "yIn": "(Monoid.toMul.{u1} #4 #2)" }, "rules": { "x": [ [ "MonoidWithZero.mk", 4 ] ], "y": [ [ "MonoidWithZero.mk", 4 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MonoidWithZero.rec (rec of) ← MonoidWithZero (type of) ← MonoidWithZero.toMonoid (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MonoidWithZero.rec (rec of) ← MonoidWithZero (type of) ← MonoidWithZero.toMonoid (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ motive body › ∀ mk type › ∀ toMonoid body › ∀ toZero body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #4 (Monoid.toSemigroup.{u1} #4 #2))", "yIn": "(Monoid.toMul.{u1} #4 #2)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "MulZeroOneClass.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ M₀ body › ∀ motive body › ∀ mk type › ∀ toMulOneClass body › ∀ toZero body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "MulOne.toMul.{u1}", "y": "MulOneClass.toMul.{u1}", "xIn": "(MulOne.toMul.{u1} #4 (MulOneClass.toMulOne.{u1} #4 #2))", "yIn": "(MulOneClass.toMul.{u1} #4 #2)" }, "rules": { "x": [ [ "MulZeroOneClass.mk", 4 ] ], "y": [ [ "MulZeroOneClass.mk", 4 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "MulZeroOneClass.rec (rec of) ← MulZeroOneClass (type of) ← MulZeroOneClass.toMulZeroClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "MulZeroOneClass.rec (rec of) ← MulZeroOneClass (type of) ← MulZeroOneClass.toMulZeroClass (type of) ← NNReal.powOrderIso._proof_1 (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ M₀ body › ∀ motive body › ∀ mk type › ∀ toMulOneClass body › ∀ toZero body › ∀ zero_mul type › ∀ a body › arg 2 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "MulOne.toMul.{u1}", "y": "MulOneClass.toMul.{u1}", "xIn": "(MulOne.toMul.{u1} #4 (MulOneClass.toMulOne.{u1} #4 #2))", "yIn": "(MulOneClass.toMul.{u1} #4 #2)" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "MulOneClass.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CauSeq.instMaxAbs", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.instMaxAbs (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instMaxAbs (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.sup_equiv_sup", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#440353694._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#440353694._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#440353694._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.sup_equiv_sup (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.sup_equiv_sup (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.Completion.instNegCauchy", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.instNegCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.Completion.instNegCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2940001164._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.IsComplete", "kind": "induct", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#23 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#26 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#29 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.IsComplete (type of) ← CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.IsComplete (type of) ← CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#23 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#26 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#29 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.complete", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2554959330._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2554959330._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#2554959330._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.complete (value of) ← CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.complete (value of) ← CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "Real.instField._proof_5", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › ∀ a._@._internal._hyg.#0 body › arg 2 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real (Semiring.toMonoid.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))))", "yIn": "(Monoid.toMul.{0} Real (Semiring.toMonoid.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Real.instField._proof_5 (value of) ← Real.instField (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instField._proof_5 (value of) ← Real.instField (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Real.instField._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ x._@.Mathlib.Data.Real.Basic.#310067971._hygCtx._hyg.#25 body › ∀ x._@.Mathlib.Data.Real.Basic.#310067971._hygCtx._hyg.#27 body › arg 2 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real (Semiring.toMonoid.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))))", "yIn": "(Monoid.toMul.{0} Real (Semiring.toMonoid.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Real.instField._proof_1 (value of) ← Real.instField (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instField._proof_1 (value of) ← Real.instField (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Real.instField._proof_2", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic", "openai": "Mathlib.Basic.Real.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ x._@.Mathlib.Data.Real.Basic.#310067971._hygCtx._hyg.#37 body › ∀ x._@.Mathlib.Data.Real.Basic.#310067971._hygCtx._hyg.#39 body › arg 2 of Eq.{1} › arg 4 of HMul.hMul.{0, 0, 0} › arg 2 of instHMul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Real (Monoid.toSemigroup.{0} Real (Semiring.toMonoid.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing)))))", "yIn": "(Monoid.toMul.{0} Real (Semiring.toMonoid.{0} Real (Ring.toSemiring.{0} Real (CommRing.toRing.{0} Real Real.commRing))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Real.instField._proof_2 (value of) ← Real.instField (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Real.instField._proof_2 (value of) ← Real.instField (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Complex.commRing", "kind": "def", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "let __src._@.Mathlib.Data.Complex.Basic.#2614265405._hygCtx._hyg.#10 body › arg 2 of CommRing.mk.{0} › arg 2 of Ring.mk.{0} › arg 3 of Semiring.mk.{0}", "why": "applications of different arity", "x": "(Monoid.mk.{0} Complex (Semigroup.mk.{0} Complex Complex.instMul Complex.commRing._proof_2) (AddMonoidWithOne.toOne.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)) Complex.commRing._proof_3 Complex.commRing._proof_4 (NPow.mk.{0} Complex (npowRec.{0} Complex (One.mk.{0} Complex (OfNat.ofNat.{0} Complex …", "y": "(Monoid.mk.{0} Complex (AddMonoidWithOne.toOne.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)) Complex.instMul Complex.commRing._proof_2 Complex.commRing._proof_3 Complex.commRing._proof_4 (NPow.mk.{0} Complex (npowRec.{0} Complex (One.mk.{0} Complex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex…", "xIn": "(Semiring.mk.{0} Complex (AddCommMonoid.mk.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)) Complex.commRing._proof_1) (Monoid.mk.{0} Complex (Semigroup.mk.{0} Complex Complex.instMul Complex.commRing._proof_2) (AddMonoidWithOne.toOne.{0} Complex (AddGroupWithOn…", "yIn": "(Semiring.mk.{0} Complex (AddCommMonoid.mk.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)) Complex.commRing._proof_1) (Monoid.mk.{0} Complex (AddMonoidWithOne.toOne.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)) Complex.instMul Complex.commRin…" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "let __src._@.Mathlib.Data.Complex.Basic.#2614265405._hygCtx._hyg.#10 body › arg 2 of CommRing.mk.{0} › arg 2 of Ring.mk.{0} › arg 3 of Semiring.mk.{0}", "why": "applications of different arity", "x": "(Monoid.mk.{0} Complex (Semigroup.mk.{0} Complex Complex.instMul ⟨proof⟩) (AddMonoidWithOne.toOne.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)) ⟨proof⟩ ⟨proof⟩ (NPow.mk.{0} Complex (npowRec.{0} Complex (One.mk.{0} Complex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOne))) (Mul.mk…", "y": "(Monoid.mk.{0} Complex (AddMonoidWithOne.toOne.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)) Complex.instMul ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NPow.mk.{0} Complex (npowRec.{0} Complex (One.mk.{0} Complex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOne))) (Mul.mk.{0} Complex (fun (x1._@.Ma…", "xIn": "(Semiring.mk.{0} Complex (AddCommMonoid.mk.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)) ⟨proof⟩) (Monoid.mk.{0} Complex (Semigroup.mk.{0} Complex Complex.instMul ⟨proof⟩) (AddMonoidWithOne.toOne.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)…", "yIn": "(Semiring.mk.{0} Complex (AddCommMonoid.mk.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)) ⟨proof⟩) (Monoid.mk.{0} Complex (AddMonoidWithOne.toOne.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex #0)) Complex.instMul ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NPow.mk.…" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @Monoid.mk ℂ __src✝.toOne\nargument has type\n One ℂ\nbut function has type\n [toSemigroup : Semigroup ℂ] →\n [toOne : One ℂ] →\n (∀ (a : ℂ), 1 * a = a) →\n (∀ (a : ℂ), a * 1 = a) →\n [toNPow : NPow ℂ] →\n autoParam (∀ (x : ℂ), x ^ 0 = 1) Monoid.npow_zero._autoParam →\n autoParam (∀ (n : ℕ) (x : ℂ), x ^ (n + 1) = x ^ n * …" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @Monoid.mk ℂ { toMul := Complex.instMul, mul_assoc := Complex.commRing._proof_2 }\nargument has type\n Semigroup ℂ\nbut function has type\n [toOne : One ℂ] →\n [toMul : Mul ℂ] →\n (∀ (a b c : ℂ), a * b * c = a * (b * c)) →\n (∀ (a : ℂ), 1 * a = a) →\n (∀ (a : ℂ), a * 1 = a) →\n [toNPow : NPow ℂ] →\n autoParam (∀ (x : ℂ), …" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "Complex.instDivInvMonoid", "kind": "def", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 5 of DivInvMonoid.mk.{0} › arg 2 of ZPow.mk.{0} › arg 3 of zpowRec.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Complex (Monoid.toSemigroup.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring)))", "yIn": "(Monoid.toMul.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "value": { "at": "arg 5 of DivInvMonoid.mk.{0} › arg 2 of ZPow.mk.{0} › arg 3 of zpowRec.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Complex (Monoid.toSemigroup.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring)))", "yIn": "(Monoid.toMul.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CauSeq.inv_aux", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#350765176._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#350765176._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#350765176._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.inv_aux (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.inv_aux (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.instMinAbs", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.instMinAbs (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instMinAbs (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#4 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#7 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.inf_equiv_inf", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2759569379._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2759569379._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#2759569379._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.inf_equiv_inf (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.inf_equiv_inf (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "Set.Ici.semilatticeSup._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Order.LatticeIntervals", "openai": "Mathlib.Order.LatticeIntervals" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Order.LatticeIntervals.#2570191389._hygCtx._hyg.#3 type", "why": "different node kinds", "x": "(SemilatticeSup.{u0} #0)", "y": "#0", "xIn": null, "yIn": null } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Set.Ici.semilatticeSup._proof_1 (value of) ← Nonneg.semilatticeSup._aux_1 (value of) ← NNReal.instSemilatticeSup._aux_1 (value of) ← NNReal.instSemilatticeSup (value of) ← NNReal.instLinearOrder (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "Set.Ici.semilatticeSup._proof_1 (value of) ← Nonneg.semilatticeSup._aux_1 (value of) ← NNReal.instSemilatticeSup._aux_1 (value of) ← NNReal.instSemilatticeSup (value of) ← NNReal.instLinearOrder (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "type", "detail": "(kernel) declaration type mismatch, '_seam_check_2204' has type\n (∀ {α : Type u_1} [inst : SemilatticeSup α] {a : α} (x x_1 : α), x ∈ Set.Ici a → x_1 ∈ Set.Ici a → a ≤ x ⊔ x_1) =\n ∀ {α : Type u_1} [inst : SemilatticeSup α] {a : α} (x x_1 : α), x ∈ Set.Ici a → x_1 ∈ Set.Ici a → a ≤ x ⊔ x_1\nbut it is expected to have type\n (∀ {α : Type u_1} {a : α} [inst : SemilatticeSup α] (x x_1 : α), x ∈ Set…" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) declaration type mismatch, '_seam_check_2220' has type\n (∀ {α : Type u_1} {a : α} [inst : SemilatticeSup α] (x x_1 : α), x ∈ Set.Ici a → x_1 ∈ Set.Ici a → a ≤ x ⊔ x_1) =\n ∀ {α : Type u_1} {a : α} [inst : SemilatticeSup α] (x x_1 : α), x ∈ Set.Ici a → x_1 ∈ Set.Ici a → a ≤ x ⊔ x_1\nbut it is expected to have type\n (∀ {α : Type u_1} [inst : SemilatticeSup α] {a : α} (x x_1 : α), x ∈ Set…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "binder-order" }, { "name": "CauSeq.instMaxAbs._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#4166183114._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.instMaxAbs._proof_1 (value of) ← CauSeq.instMaxAbs (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.instMaxAbs._proof_1 (value of) ← CauSeq.instMaxAbs (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.neg_equiv_neg", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ β body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1260660991._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1260660991._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#1260660991._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #3 (Semifield.toDivisionSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #3 (Semifield.toCommSemiring.{u0} #3 (Field.toSemifield.{u0} #3 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.neg_equiv_neg (value of) ← CauSeq.Completion.instNegCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "openai": "CauSeq.neg_equiv_neg (value of) ← CauSeq.Completion.instNegCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.IsComplete.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#23 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#26 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#29 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.IsComplete.mk (ctor of) ← CauSeq.IsComplete (type of) ← CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "CauSeq.IsComplete.mk (ctor of) ← CauSeq.IsComplete (type of) ← CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#23 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#26 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#29 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.IsComplete.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#23 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#26 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#29 type › arg 2 of IsStrictOrderedRing.{u1} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u1}", "y": "CommSemiring.toSemiring.{u1}", "xIn": "(DivisionSemiring.toSemiring.{u1} #2 (Semifield.toDivisionSemiring.{u1} #2 (Field.toSemifield.{u1} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u1} #2 (Semifield.toCommSemiring.{u1} #2 (Field.toSemifield.{u1} #2 #1)))" }, "rules": { "x": [ [ "CauSeq.IsComplete.mk", 1 ] ], "y": [ [ "CauSeq.IsComplete.mk", 1 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.IsComplete.rec (rec of) ← CauSeq.IsComplete (type of) ← CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "CauSeq.IsComplete.rec (rec of) ← CauSeq.IsComplete (type of) ← CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#23 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#26 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#29 type › arg 2 of IsStrictOrderedRing.{u1} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u1}", "y": "CommSemiring.toSemiring.{u1}", "xIn": "(DivisionSemiring.toSemiring.{u1} #2 (Semifield.toDivisionSemiring.{u1} #2 (Field.toSemifield.{u1} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u1} #2 (Semifield.toCommSemiring.{u1} #2 (Field.toSemifield.{u1} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.IsComplete.isComplete", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#23 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#26 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#29 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.IsComplete.isComplete (proj of) ← CauSeq.IsComplete (type of) ← CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "CauSeq.IsComplete.isComplete (proj of) ← CauSeq.IsComplete (type of) ← CauSeq.lim (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#23 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#26 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1468632836._hygCtx._hyg.#29 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "CauSeq.Completion.instNNRatCast", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Completion", "openai": "Mathlib.Algebra.Order.CauSeq.Completion" }, "differs": [ "type", "value" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CauSeq.Completion.instNNRatCast (value of) ← Real.instNNRatCast (value of) ← Real.instField (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "CauSeq.Completion.instNNRatCast (value of) ← Real.instNNRatCast (value of) ← Real.instField (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#6 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1126745635._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": 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OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1542641068._hygCtx._hyg.#3 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1542641068._hygCtx._hyg.#6 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1542641068._hygCtx._hyg.#9 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" }, "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1542641068._hygCtx._hyg.#3 body › λ inst._@.Mathlib.Algebra.Order.CauSeq.Completion.#1542641068._hygCtx._hyg.#6 body › λ 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Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "Complex.commRing._proof_9 (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Complex.commRing._proof_10", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{1} › arg 5 of HMul.hMul.{0, 0, 0} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "AddMonoid.toAdd.{0}", "xIn": "(AddSemigroup.toAdd.{0} Complex (AddMonoid.toAddSemigroup.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))", "yIn": "(AddMonoid.toAdd.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Complex.commRing._proof_10 (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "Complex.commRing._proof_10 (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Complex.commRing._proof_13", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ n body › arg 3 of Eq.{1} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "AddMonoid.toAdd.{0}", "xIn": "(AddSemigroup.toAdd.{0} Complex (AddMonoid.toAddSemigroup.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))", "yIn": "(AddMonoid.toAdd.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Complex.commRing._proof_13 (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "Complex.commRing._proof_13 (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Complex.instDivInvMonoid._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › ∀ b body › arg 2 of Eq.{1} › arg 4 of HDiv.hDiv.{0, 0, 0} › arg 2 of instHDiv.{0} › arg 2 of Div.mk.{0} › arg 2 of DivInvMonoid.div'.{0}", "why": "applications of different arity", "x": "(Monoid.mk.{0} Complex (Semigroup.mk.{0} Complex (Mul.mk.{0} Complex (Mul.mul.{0} Complex (Semigroup.toMul.{0} Complex (Monoid.toSemigroup.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring))))) (Semigroup.mul_assoc.{0} Complex (Monoid.toSemigroup.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemi…", "y": "(Monoid.mk.{0} Complex (One.mk.{0} Complex (One.one.{0} Complex (Monoid.toOne.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring)))) (Mul.mk.{0} Complex (Mul.mul.{0} Complex (Monoid.toMul.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring)))) (Monoid.mul_assoc.{0} Complex (Semiring.toMonoid.{0…", "xIn": "(DivInvMonoid.div'.{0} Complex (Monoid.mk.{0} Complex (Semigroup.mk.{0} Complex (Mul.mk.{0} Complex (Mul.mul.{0} Complex (Semigroup.toMul.{0} Complex (Monoid.toSemigroup.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring))))) (Semigroup.mul_assoc.{0} Complex (Monoid.toSemigroup.{0} Complex (Semiring.toMono…", "yIn": "(DivInvMonoid.div'.{0} Complex (Monoid.mk.{0} Complex (One.mk.{0} Complex (One.one.{0} Complex (Monoid.toOne.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring)))) (Mul.mk.{0} Complex (Mul.mul.{0} Complex (Monoid.toMul.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring)))) (Monoid.mul_assoc.{0…" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Complex.instDivInvMonoid._proof_1 (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "Complex.instDivInvMonoid._proof_1 (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, Monoid.mul_assoc" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "type", "detail": "(kernel) application type mismatch\n @Monoid.mk ℂ { mul := Mul.mul, mul_assoc := ⋯ }\nargument has type\n Semigroup ℂ\nbut function has type\n [toOne : One ℂ] →\n [toMul : Mul ℂ] →\n (∀ (a b c : ℂ), a * b * c = a * (b * c)) →\n (∀ (a : ℂ), 1 * a = a) →\n (∀ (a : ℂ), a * 1 = a) →\n [toNPow : NPow ℂ] →\n autoParam (∀ (x : ℂ), x ^ 0 = 1) Monoid.npow_zero._autoP…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "Complex.instDivInvMonoid._proof_2", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › arg 2 of Eq.{1} › arg 4 of HPow.hPow.{0, 0, 0} › arg 3 of instHPow.{0, 0} › arg 2 of ZPow.toPow.{0} › arg 2 of ZPow.mk.{0} › arg 3 of zpowRec.{0} › arg 2 of Mul.mk.{0} › arg 2 of Mul.mul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Complex (Monoid.toSemigroup.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring)))", "yIn": "(Monoid.toMul.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Complex.instDivInvMonoid._proof_2 (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "Complex.instDivInvMonoid._proof_2 (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Complex.instDivInvMonoid._proof_3", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ n body › ∀ a body › arg 2 of Eq.{1} › arg 4 of HPow.hPow.{0, 0, 0} › arg 3 of instHPow.{0, 0} › arg 2 of ZPow.toPow.{0} › arg 2 of ZPow.mk.{0} › arg 3 of zpowRec.{0} › arg 2 of Mul.mk.{0} › arg 2 of Mul.mul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Complex (Monoid.toSemigroup.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring)))", "yIn": "(Monoid.toMul.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Complex.instDivInvMonoid._proof_3 (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "Complex.instDivInvMonoid._proof_3 (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Complex.instDivInvMonoid._proof_4", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ n body › ∀ a body › arg 2 of Eq.{1} › arg 4 of HPow.hPow.{0, 0, 0} › arg 3 of instHPow.{0, 0} › arg 2 of ZPow.toPow.{0} › arg 2 of ZPow.mk.{0} › arg 3 of zpowRec.{0} › arg 2 of Mul.mk.{0} › arg 2 of Mul.mul.{0} › head", "why": "different leaves", "x": "Semigroup.toMul.{0}", "y": "Monoid.toMul.{0}", "xIn": "(Semigroup.toMul.{0} Complex (Monoid.toSemigroup.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring)))", "yIn": "(Monoid.toMul.{0} Complex (Semiring.toMonoid.{0} Complex Complex.instSemiring))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Complex.instDivInvMonoid._proof_4 (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "Complex.instDivInvMonoid._proof_4 (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionMonoid.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ toDivInvMonoid body › ∀ inv_inv body › ∀ mul_inv_rev type › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 3 of Inv.inv.{u0} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (DivInvMonoid.toMonoid.{u0} #4 #3)))", "yIn": "(Monoid.toMul.{u0} #4 (DivInvMonoid.toMonoid.{u0} #4 #3))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionMonoid.mk (value of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "DivisionMonoid.mk (value of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ toDivInvMonoid body › ∀ inv_inv body › ∀ mul_inv_rev type › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 3 of Inv.inv.{u0} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (DivInvMonoid.toMonoid.{u0} #4 #3)))", "yIn": "(Monoid.toMul.{u0} #4 (DivInvMonoid.toMonoid.{u0} #4 #3))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "GroupWithZero.toDivisionMonoid._proof_2", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Basic", "openai": "Mathlib.Algebra.GroupWithZero.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ G₀ body › ∀ inst._@.Mathlib.Algebra.GroupWithZero.Basic.#1902858486._hygCtx._hyg.#4 body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 3 of Inv.inv.{u0} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (GroupWithZero.toDivInvMonoid.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (GroupWithZero.toDivInvMonoid.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "GroupWithZero.toDivisionMonoid._proof_2 (value of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "GroupWithZero.toDivisionMonoid._proof_2 (value of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "GroupWithZero.toDivisionMonoid._proof_3", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Basic", "openai": "Mathlib.Algebra.GroupWithZero.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ G₀ body › ∀ inst._@.Mathlib.Algebra.GroupWithZero.Basic.#1902858486._hygCtx._hyg.#4 body › ∀ x._@.Mathlib.Algebra.GroupWithZero.Basic.#1902858486._hygCtx._hyg.#28 body › ∀ x._@.Mathlib.Algebra.GroupWithZero.Basic.#1902858486._hygCtx._hyg.#30 body › ∀ a._@._internal._hyg.#0 type › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (GroupWithZero.toDivInvMonoid.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (GroupWithZero.toDivInvMonoid.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "GroupWithZero.toDivisionMonoid._proof_3 (value of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "GroupWithZero.toDivisionMonoid._proof_3 (value of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "GroupWithZero.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G₀ body › ∀ toMonoidWithZero body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #6 (Monoid.toSemigroup.{u0} #6 (MonoidWithZero.toMonoid.{u0} #6 #5)))", "yIn": "(Monoid.toMul.{u0} #6 (MonoidWithZero.toMonoid.{u0} #6 #5))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "GroupWithZero.mk (value of) ← DivisionSemiring.toGroupWithZero (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "GroupWithZero.mk (value of) ← DivisionSemiring.toGroupWithZero (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "erasedDiffs": { "type": { "at": "∀ G₀ body › ∀ toMonoidWithZero body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › arg 1 of autoParam.{0} › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #6 (Monoid.toSemigroup.{u0} #6 (MonoidWithZero.toMonoid.{u0} #6 #5)))", "yIn": "(Monoid.toMul.{u0} #6 (MonoidWithZero.toMonoid.{u0} #6 #5))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CauSeq.instMinAbs._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Order.CauSeq.Basic", "openai": "Mathlib.Algebra.Order.CauSeq.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#4 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#7 body › ∀ inst._@.Mathlib.Algebra.Order.CauSeq.Basic.#675413479._hygCtx._hyg.#10 type › arg 2 of IsStrictOrderedRing.{u0} › head", "why": "different leaves", "x": "DivisionSemiring.toSemiring.{u0}", "y": "CommSemiring.toSemiring.{u0}", "xIn": "(DivisionSemiring.toSemiring.{u0} #2 (Semifield.toDivisionSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))", "yIn": "(CommSemiring.toSemiring.{u0} #2 (Semifield.toCommSemiring.{u0} #2 (Field.toSemifield.{u0} #2 #1)))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CauSeq.instMinAbs._proof_1 (value of) ← CauSeq.instMinAbs (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of)", "openai": "CauSeq.instMinAbs._proof_1 (value of) ← CauSeq.instMinAbs (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat" }, "cross": { "openaiTermReadInAnthropic": { "status": "defeq", "part": "type" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": true }, "defeqBothWays": true, "kernel": "identified both ways", "group": "kernel-identified" }, { "name": "Complex.addCommGroup", "kind": "def", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "arg 2 of AddCommGroup.mk.{0} › arg 2 of AddGroup.mk.{0} › arg 2 of SubNegMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} Complex (AddSemigroup.mk.{0} Complex Complex.instAdd Complex.addCommGroup._proof_1) Complex.instZero Complex.addCommGroup._proof_2 Complex.addCommGroup._proof_3 (NSMul.ofSMul.{0} Complex (Complex.SMul.instSMulRealComplex.{0} Nat (NSMul.toSMul.{0} Real (AddMonoid.toNSMul.{0} Real Real.instAddMonoid))))…", "y": "(AddMonoid.mk.{0} Complex Complex.instZero Complex.instAdd Complex.addCommGroup._proof_1 Complex.addCommGroup._proof_2 Complex.addCommGroup._proof_3 (NSMul.ofSMul.{0} Complex (Complex.SMul.instSMulRealComplex.{0} Nat (NSMul.toSMul.{0} Real (AddMonoid.toNSMul.{0} Real Real.instAddMonoid)))) Complex.addCommGroup._proof_4…", "xIn": "(SubNegMonoid.mk.{0} Complex (AddMonoid.mk.{0} Complex (AddSemigroup.mk.{0} Complex Complex.instAdd Complex.addCommGroup._proof_1) Complex.instZero Complex.addCommGroup._proof_2 Complex.addCommGroup._proof_3 (NSMul.ofSMul.{0} Complex (Complex.SMul.instSMulRealComplex.{0} Nat (NSMul.toSMul.{0} Real (AddMonoid.toNSMul.{0…", "yIn": "(SubNegMonoid.mk.{0} Complex (AddMonoid.mk.{0} Complex Complex.instZero Complex.instAdd Complex.addCommGroup._proof_1 Complex.addCommGroup._proof_2 Complex.addCommGroup._proof_3 (NSMul.ofSMul.{0} Complex (Complex.SMul.instSMulRealComplex.{0} Nat (NSMul.toSMul.{0} Real (AddMonoid.toNSMul.{0} Real Real.instAddMonoid)))) …" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "Complex.addCommGroup (value of) ← Complex.addGroupWithOne (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "Complex.addCommGroup (value of) ← Complex.addGroupWithOne (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "erasedDiffs": { "value": { "at": "arg 2 of AddCommGroup.mk.{0} › arg 2 of AddGroup.mk.{0} › arg 2 of SubNegMonoid.mk.{0}", "why": "applications of different arity", "x": "(AddMonoid.mk.{0} Complex (AddSemigroup.mk.{0} Complex Complex.instAdd ⟨proof⟩) Complex.instZero ⟨proof⟩ ⟨proof⟩ (NSMul.ofSMul.{0} Complex (Complex.SMul.instSMulRealComplex.{0} Nat (NSMul.toSMul.{0} Real (AddMonoid.toNSMul.{0} Real Real.instAddMonoid)))) ⟨proof⟩ ⟨proof⟩)", "y": "(AddMonoid.mk.{0} Complex Complex.instZero Complex.instAdd ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.ofSMul.{0} Complex (Complex.SMul.instSMulRealComplex.{0} Nat (NSMul.toSMul.{0} Real (AddMonoid.toNSMul.{0} Real Real.instAddMonoid)))) ⟨proof⟩ ⟨proof⟩)", "xIn": "(SubNegMonoid.mk.{0} Complex (AddMonoid.mk.{0} Complex (AddSemigroup.mk.{0} Complex Complex.instAdd ⟨proof⟩) Complex.instZero ⟨proof⟩ ⟨proof⟩ (NSMul.ofSMul.{0} Complex (Complex.SMul.instSMulRealComplex.{0} Nat (NSMul.toSMul.{0} Real (AddMonoid.toNSMul.{0} Real Real.instAddMonoid)))) ⟨proof⟩ ⟨proof⟩) Complex.instNeg Com…", "yIn": "(SubNegMonoid.mk.{0} Complex (AddMonoid.mk.{0} Complex Complex.instZero Complex.instAdd ⟨proof⟩ ⟨proof⟩ ⟨proof⟩ (NSMul.ofSMul.{0} Complex (Complex.SMul.instSMulRealComplex.{0} Nat (NSMul.toSMul.{0} Real (AddMonoid.toNSMul.{0} Real Real.instAddMonoid)))) ⟨proof⟩ ⟨proof⟩) Complex.instNeg Complex.instSub (ZSMul.ofSMul.{0}…" } }, "cross": { "openaiTermReadInAnthropic": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk ℂ Complex.instZero\nargument has type\n Zero ℂ\nbut function has type\n [toAddSemigroup : AddSemigroup ℂ] →\n [toZero : Zero ℂ] →\n (∀ (a : ℂ), 0 + a = a) →\n (∀ (a : ℂ), a + 0 = a) →\n [toNSMul : NSMul ℂ] →\n autoParam (∀ (x : ℂ), 0 • x = 0) AddMonoid.nsmul_zero._autoParam →\n autoParam (∀ (n : ℕ) (x : ℂ), …" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n @AddMonoid.mk ℂ { toAdd := Complex.instAdd, add_assoc := Complex.addCommGroup._proof_1 }\nargument has type\n AddSemigroup ℂ\nbut function has type\n [toZero : Zero ℂ] →\n [toAdd : Add ℂ] →\n (∀ (a b c : ℂ), a + b + c = a + (b + c)) →\n (∀ (a : ℂ), 0 + a = a) →\n (∀ (a : ℂ), a + 0 = a) →\n [toNSMul : NSMul ℂ] →\n autoPara…" }, "both": false }, "defeqBothWays": false, "kernel": "not identified", "group": "monoid-hierarchy" }, { "name": "Complex.addGroupWithOne._proof_2", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ x._@.Mathlib.Data.Complex.Basic.#401502261._hygCtx._hyg.#24 body › arg 3 of Eq.{1} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "AddMonoid.toAdd.{0}", "xIn": "(AddSemigroup.toAdd.{0} Complex (AddMonoid.toAddSemigroup.{0} Complex (SubNegMonoid.toAddMonoid.{0} Complex (AddGroup.toSubNegMonoid.{0} Complex (AddCommGroup.toAddGroup.{0} Complex Complex.addCommGroup)))))", "yIn": "(AddMonoid.toAdd.{0} Complex (SubNegMonoid.toAddMonoid.{0} Complex (AddGroup.toSubNegMonoid.{0} Complex (AddCommGroup.toAddGroup.{0} Complex Complex.addCommGroup))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Complex.addGroupWithOne._proof_2 (value of) ← Complex.addGroupWithOne (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "Complex.addGroupWithOne._proof_2 (value of) ← Complex.addGroupWithOne (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Complex.addGroupWithOne._proof_5", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › ∀ b body › arg 3 of Eq.{1} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "AddMonoid.toAdd.{0}", "xIn": "(AddSemigroup.toAdd.{0} Complex (AddMonoid.toAddSemigroup.{0} Complex (SubNegMonoid.toAddMonoid.{0} Complex (AddGroup.toSubNegMonoid.{0} Complex (AddCommGroup.toAddGroup.{0} Complex Complex.addCommGroup)))))", "yIn": "(AddMonoid.toAdd.{0} Complex (SubNegMonoid.toAddMonoid.{0} Complex (AddGroup.toSubNegMonoid.{0} Complex (AddCommGroup.toAddGroup.{0} Complex Complex.addCommGroup))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Complex.addGroupWithOne._proof_5 (value of) ← Complex.addGroupWithOne (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "Complex.addGroupWithOne._proof_5 (value of) ← Complex.addGroupWithOne (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Complex.addGroupWithOne._proof_7", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ n body › ∀ a body › arg 3 of Eq.{1} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "AddMonoid.toAdd.{0}", "xIn": "(AddSemigroup.toAdd.{0} Complex (AddMonoid.toAddSemigroup.{0} Complex (SubNegMonoid.toAddMonoid.{0} Complex (AddGroup.toSubNegMonoid.{0} Complex (AddCommGroup.toAddGroup.{0} Complex Complex.addCommGroup)))))", "yIn": "(AddMonoid.toAdd.{0} Complex (SubNegMonoid.toAddMonoid.{0} Complex (AddGroup.toSubNegMonoid.{0} Complex (AddCommGroup.toAddGroup.{0} Complex Complex.addCommGroup))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Complex.addGroupWithOne._proof_7 (value of) ← Complex.addGroupWithOne (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "Complex.addGroupWithOne._proof_7 (value of) ← Complex.addGroupWithOne (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "Complex.addGroupWithOne._proof_9", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Complex.Basic", "openai": "Mathlib.Basic.Complex.Basic" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ a body › arg 2 of Eq.{1} › arg 4 of HAdd.hAdd.{0, 0, 0} › arg 2 of instHAdd.{0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{0}", "y": "AddMonoid.toAdd.{0}", "xIn": "(AddSemigroup.toAdd.{0} Complex (AddMonoid.toAddSemigroup.{0} Complex (SubNegMonoid.toAddMonoid.{0} Complex (AddGroup.toSubNegMonoid.{0} Complex (AddCommGroup.toAddGroup.{0} Complex Complex.addCommGroup)))))", "yIn": "(AddMonoid.toAdd.{0} Complex (SubNegMonoid.toAddMonoid.{0} Complex (AddGroup.toSubNegMonoid.{0} Complex (AddCommGroup.toAddGroup.{0} Complex Complex.addCommGroup))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "Complex.addGroupWithOne._proof_9 (value of) ← Complex.addGroupWithOne (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "Complex.addGroupWithOne._proof_9 (value of) ← Complex.addGroupWithOne (value of) ← Complex.commRing (value of) ← Complex.instRing (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of) ← Real.instPow (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionMonoid.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toDivInvMonoid body › ∀ inv_inv body › ∀ mul_inv_rev type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 3 of Inv.inv.{u1} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #5 (Monoid.toSemigroup.{u1} #5 (DivInvMonoid.toMonoid.{u1} #5 #3)))", "yIn": "(Monoid.toMul.{u1} #5 (DivInvMonoid.toMonoid.{u1} #5 #3))" }, "rules": { "x": [ [ "DivisionMonoid.mk", 4 ] ], "y": [ [ "DivisionMonoid.mk", 4 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionMonoid.rec (rec of) ← DivisionMonoid (type of) ← DivisionMonoid.toDivInvOneMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "DivisionMonoid.rec (rec of) ← DivisionMonoid (type of) ← DivisionMonoid.toDivInvOneMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ motive body › ∀ mk type › ∀ toDivInvMonoid body › ∀ inv_inv body › ∀ mul_inv_rev type › ∀ a body › ∀ b body › arg 2 of Eq.{(u1+1)} › arg 3 of Inv.inv.{u1} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #5 (Monoid.toSemigroup.{u1} #5 (DivInvMonoid.toMonoid.{u1} #5 #3)))", "yIn": "(Monoid.toMul.{u1} #5 (DivInvMonoid.toMonoid.{u1} #5 #3))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionMonoid.mul_inv_rev", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 3 of Inv.inv.{u0} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (DivisionMonoid.toDivInvMonoid.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (DivisionMonoid.toDivInvMonoid.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionMonoid.mul_inv_rev (proj of) ← DivisionMonoid (type of) ← DivisionMonoid.toDivInvOneMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "DivisionMonoid.mul_inv_rev (proj of) ← DivisionMonoid (type of) ← DivisionMonoid.toDivInvOneMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 3 of Inv.inv.{u0} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (DivisionMonoid.toDivInvMonoid.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (DivisionMonoid.toDivInvMonoid.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "DivisionMonoid.inv_eq_of_mul", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Group.Defs", "openai": "Mathlib.Algebra.Group.DivInvMonoid" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › ∀ a._@._internal._hyg.#0 type › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (DivisionMonoid.toDivInvMonoid.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (DivisionMonoid.toDivInvMonoid.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "DivisionMonoid.inv_eq_of_mul (proj of) ← DivisionMonoid (type of) ← DivisionMonoid.toDivInvOneMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "DivisionMonoid.inv_eq_of_mul (proj of) ← DivisionMonoid (type of) ← DivisionMonoid.toDivInvOneMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "erasedDiffs": { "type": { "at": "∀ G body › ∀ self body › ∀ a body › ∀ b body › ∀ a._@._internal._hyg.#0 type › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (DivisionMonoid.toDivInvMonoid.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (DivInvMonoid.toMonoid.{u0} #3 (DivisionMonoid.toDivInvMonoid.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "GroupWithZero.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ G₀ body › ∀ motive body › ∀ mk type › ∀ toMonoidWithZero body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 (MonoidWithZero.toMonoid.{u1} #7 #5)))", "yIn": "(Monoid.toMul.{u1} #7 (MonoidWithZero.toMonoid.{u1} #7 #5))" }, "rules": { "x": [ [ "GroupWithZero.mk", 11 ] ], "y": [ [ "GroupWithZero.mk", 11 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "GroupWithZero.rec (rec of) ← GroupWithZero (type of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "GroupWithZero.rec (rec of) ← GroupWithZero (type of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "erasedDiffs": { "type": { "at": "∀ G₀ body › ∀ motive body › ∀ mk type › ∀ toMonoidWithZero body › ∀ toInv body › ∀ toDiv body › ∀ toZPow body › ∀ div_eq_mul_inv type › ∀ a body › ∀ b body › arg 3 of Eq.{(u1+1)} › arg 4 of HMul.hMul.{u1, u1, u1} › arg 2 of instHMul.{u1} › head", "why": "different leaves", "x": "Semigroup.toMul.{u1}", "y": "Monoid.toMul.{u1}", "xIn": "(Semigroup.toMul.{u1} #7 (Monoid.toSemigroup.{u1} #7 (MonoidWithZero.toMonoid.{u1} #7 #5)))", "yIn": "(Monoid.toMul.{u1} #7 (MonoidWithZero.toMonoid.{u1} #7 #5))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "GroupWithZero.div_eq_mul_inv", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G₀ body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "GroupWithZero.div_eq_mul_inv (proj of) ← GroupWithZero (type of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "GroupWithZero.div_eq_mul_inv (proj of) ← GroupWithZero (type of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "erasedDiffs": { "type": { "at": "∀ G₀ body › ∀ self body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "GroupWithZero.mul_inv_cancel", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G₀ body › ∀ self body › ∀ a body › ∀ a._@._internal._hyg.#0 body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "GroupWithZero.mul_inv_cancel (proj of) ← GroupWithZero (type of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "GroupWithZero.mul_inv_cancel (proj of) ← GroupWithZero (type of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "erasedDiffs": { "type": { "at": "∀ G₀ body › ∀ self body › ∀ a body › ∀ a._@._internal._hyg.#0 body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "GroupWithZero.zpow_succ'", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.GroupWithZero.Defs", "openai": "Mathlib.Algebra.GroupWithZero.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ G₀ body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2)))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "GroupWithZero.zpow_succ' (proj of) ← GroupWithZero (type of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of)", "openai": "GroupWithZero.zpow_succ' (proj of) ← GroupWithZero (type of) ← GroupWithZero.toDivisionMonoid (value of) ← CauSeq.inv (value of) ← CauSeq.Completion.instInvCauchy (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of)" }, "erasedDiffs": { "type": { "at": "∀ G₀ body › ∀ self body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2))))", "yIn": "(Monoid.toMul.{u0} #3 (MonoidWithZero.toMonoid.{u0} #3 (GroupWithZero.toMonoidWithZero.{u0} #3 #2)))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommSemiring.toNonUnitalCommSemiring", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#4 body › let __src._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#13 body › let __src._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#14 body › arg 2 of NonUnitalCommSemiring.mk.{u0} › arg 2 of NonUnitalSemiring.mk.{u0} › arg 3 of NonUnitalNonAssocSemiring.mk.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (CommMonoid.toMonoid.{u0} #3 #1)))", "yIn": "(Monoid.toMul.{u0} #3 (CommMonoid.toMonoid.{u0} #3 #1))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "CommSemiring.toNonUnitalCommSemiring (value of) ← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of)", "openai": "CommSemiring.toNonUnitalCommSemiring (value of) ← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of)" }, "erasedDiffs": { "value": { "at": "λ α body › λ inst._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#4 body › let __src._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#13 body › let __src._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#14 body › arg 2 of NonUnitalCommSemiring.mk.{u0} › arg 2 of NonUnitalSemiring.mk.{u0} › arg 3 of NonUnitalNonAssocSemiring.mk.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #3 (Monoid.toSemigroup.{u0} #3 (CommMonoid.toMonoid.{u0} #3 #1)))", "yIn": "(Monoid.toMul.{u0} #3 (CommMonoid.toMonoid.{u0} #3 #1))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonUnitalNonAssocRing.left_distrib", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 6 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #4 (AddMonoid.toAddSemigroup.{u0} #4 (SubNegMonoid.toAddMonoid.{u0} #4 (AddGroup.toSubNegMonoid.{u0} #4 (AddCommGroup.toAddGroup.{u0} #4 (NonUnitalNonAssocRing.toAddCommGroup.{u0} #4 #3))))))", "yIn": "(AddMonoid.toAdd.{u0} #4 (SubNegMonoid.toAddMonoid.{u0} #4 (AddGroup.toSubNegMonoid.{u0} #4 (AddCommGroup.toAddGroup.{u0} #4 (NonUnitalNonAssocRing.toAddCommGroup.{u0} #4 #3)))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonUnitalNonAssocRing.left_distrib (value of) ← NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of)", "openai": "NonUnitalNonAssocRing.left_distrib (value of) ← NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of)" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 6 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #4 (AddMonoid.toAddSemigroup.{u0} #4 (SubNegMonoid.toAddMonoid.{u0} #4 (AddGroup.toSubNegMonoid.{u0} #4 (AddCommGroup.toAddGroup.{u0} #4 (NonUnitalNonAssocRing.toAddCommGroup.{u0} #4 #3))))))", "yIn": "(AddMonoid.toAdd.{u0} #4 (SubNegMonoid.toAddMonoid.{u0} #4 (AddGroup.toSubNegMonoid.{u0} #4 (AddCommGroup.toAddGroup.{u0} #4 (NonUnitalNonAssocRing.toAddCommGroup.{u0} #4 #3)))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonUnitalNonAssocRing.right_distrib", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 5 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #4 (AddMonoid.toAddSemigroup.{u0} #4 (SubNegMonoid.toAddMonoid.{u0} #4 (AddGroup.toSubNegMonoid.{u0} #4 (AddCommGroup.toAddGroup.{u0} #4 (NonUnitalNonAssocRing.toAddCommGroup.{u0} #4 #3))))))", "yIn": "(AddMonoid.toAdd.{u0} #4 (SubNegMonoid.toAddMonoid.{u0} #4 (AddGroup.toSubNegMonoid.{u0} #4 (AddCommGroup.toAddGroup.{u0} #4 (NonUnitalNonAssocRing.toAddCommGroup.{u0} #4 #3)))))" } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonUnitalNonAssocRing.right_distrib (value of) ← NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of)", "openai": "NonUnitalNonAssocRing.right_distrib (value of) ← NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of)" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ self body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 5 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #4 (AddMonoid.toAddSemigroup.{u0} #4 (SubNegMonoid.toAddMonoid.{u0} #4 (AddGroup.toSubNegMonoid.{u0} #4 (AddCommGroup.toAddGroup.{u0} #4 (NonUnitalNonAssocRing.toAddCommGroup.{u0} #4 #3))))))", "yIn": "(AddMonoid.toAdd.{u0} #4 (SubNegMonoid.toAddMonoid.{u0} #4 (AddGroup.toSubNegMonoid.{u0} #4 (AddCommGroup.toAddGroup.{u0} #4 (NonUnitalNonAssocRing.toAddCommGroup.{u0} #4 #3)))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommRing.toNonUnitalCommRing", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "value" ], "class": "definitional", "diffs": { "value": { "at": "λ α body › λ s body › arg 2 of NonUnitalCommRing.mk.{u0} › arg 2 of NonUnitalRing.mk.{u0} › arg 3 of NonUnitalNonAssocRing.mk.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #1 (Monoid.toSemigroup.{u0} #1 (Semiring.toMonoid.{u0} #1 (Ring.toSemiring.{u0} #1 (CommRing.toRing.{u0} #1 #0)))))", "yIn": "(Monoid.toMul.{u0} #1 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of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of) ← Real.rpow (value of)" }, "erasedDiffs": { "value": { "at": "λ α body › λ s body › arg 2 of NonUnitalCommRing.mk.{u0} › arg 2 of NonUnitalRing.mk.{u0} › arg 3 of NonUnitalNonAssocRing.mk.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #1 (Monoid.toSemigroup.{u0} #1 (Semiring.toMonoid.{u0} #1 (Ring.toSemiring.{u0} #1 (CommRing.toRing.{u0} #1 #0)))))", "yIn": "(Monoid.toMul.{u0} #1 (Semiring.toMonoid.{u0} #1 (Ring.toSemiring.{u0} #1 (CommRing.toRing.{u0} #1 #0))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "value", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "value" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommSemiring.toNonUnitalCommSemiring._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#4 body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (Semiring.toMonoid.{u0} #4 (CommSemiring.toSemiring.{u0} #4 (inferInstance.{(u0+1)} (CommSemiring.{u0} #4) #3)))))", "yIn": "(Monoid.toMul.{u0} #4 (Semiring.toMonoid.{u0} #4 (CommSemiring.toSemiring.{u0} #4 (inferInstance.{(u0+1)} (CommSemiring.{u0} #4) #3))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommSemiring.toNonUnitalCommSemiring._proof_1 (value of) ← CommSemiring.toNonUnitalCommSemiring (value of) ← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommSemiring.toNonUnitalCommSemiring._proof_1 (value of) ← CommSemiring.toNonUnitalCommSemiring (value of) ← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommSemiring.toNonUnitalCommSemiring._proof_2", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#4 body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 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← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommSemiring.toNonUnitalCommSemiring._proof_3", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#4 body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (Semiring.toMonoid.{u0} #2 (CommSemiring.toSemiring.{u0} #2 (inferInstance.{(u0+1)} (CommSemiring.{u0} #2) #1)))))", "yIn": "(Monoid.toMul.{u0} #2 (Semiring.toMonoid.{u0} #2 (CommSemiring.toSemiring.{u0} #2 (inferInstance.{(u0+1)} (CommSemiring.{u0} #2) #1))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommSemiring.toNonUnitalCommSemiring._proof_3 (value of) ← CommSemiring.toNonUnitalCommSemiring (value of) ← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommSemiring.toNonUnitalCommSemiring._proof_3 (value of) ← CommSemiring.toNonUnitalCommSemiring (value of) ← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommSemiring.toNonUnitalCommSemiring._proof_4", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#4 body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (Semiring.toMonoid.{u0} #2 (CommSemiring.toSemiring.{u0} #2 (inferInstance.{(u0+1)} (CommSemiring.{u0} #2) #1)))))", "yIn": "(Monoid.toMul.{u0} #2 (Semiring.toMonoid.{u0} #2 (CommSemiring.toSemiring.{u0} #2 (inferInstance.{(u0+1)} (CommSemiring.{u0} #2) #1))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommSemiring.toNonUnitalCommSemiring._proof_4 (value of) ← CommSemiring.toNonUnitalCommSemiring (value of) ← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommSemiring.toNonUnitalCommSemiring._proof_4 (value of) ← CommSemiring.toNonUnitalCommSemiring (value of) ← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommSemiring.toNonUnitalCommSemiring._proof_5", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ inst._@.Mathlib.Algebra.Ring.Defs.#1868672820._hygCtx._hyg.#4 body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (CommMonoid.toMonoid.{u0} #4 (inferInstance.{(u0+1)} (CommMonoid.{u0} #4) (CommSemiring.toCommMonoid.{u0} #4 #3)))))", "yIn": "(Monoid.toMul.{u0} #4 (CommMonoid.toMonoid.{u0} #4 (inferInstance.{(u0+1)} (CommMonoid.{u0} #4) (CommSemiring.toCommMonoid.{u0} #4 #3))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommSemiring.toNonUnitalCommSemiring._proof_5 (value of) ← CommSemiring.toNonUnitalCommSemiring (value of) ← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommSemiring.toNonUnitalCommSemiring._proof_5 (value of) ← CommSemiring.toNonUnitalCommSemiring (value of) ← starRingAut (value of) ← starRingEnd (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonUnitalNonAssocRing.mk", "kind": "ctor", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ 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Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "NonUnitalNonAssocRing.mk (ctor of) ← NonUnitalNonAssocRing (type of) ← NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ toAddCommGroup body › ∀ toMul body › ∀ left_distrib type › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 6 of HMul.hMul.{u0, u0, u0} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #5 (AddMonoid.toAddSemigroup.{u0} #5 (SubNegMonoid.toAddMonoid.{u0} #5 (AddGroup.toSubNegMonoid.{u0} #5 (AddCommGroup.toAddGroup.{u0} #5 #4)))))", "yIn": "(AddMonoid.toAdd.{u0} #5 (SubNegMonoid.toAddMonoid.{u0} #5 (AddGroup.toSubNegMonoid.{u0} #5 (AddCommGroup.toAddGroup.{u0} #5 #4))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "NonUnitalNonAssocRing.rec", "kind": "rec", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type", "recursor rules" ], "class": "definitional", "diffs": { "type": { "at": "∀ α body › ∀ motive body › ∀ mk type › ∀ toAddCommGroup body › ∀ toMul body › ∀ left_distrib type › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u1+1)} › arg 6 of HMul.hMul.{u1, u1, u1} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #6 (AddMonoid.toAddSemigroup.{u1} #6 (SubNegMonoid.toAddMonoid.{u1} #6 (AddGroup.toSubNegMonoid.{u1} #6 (AddCommGroup.toAddGroup.{u1} #6 #4)))))", "yIn": "(AddMonoid.toAdd.{u1} #6 (SubNegMonoid.toAddMonoid.{u1} #6 (AddGroup.toSubNegMonoid.{u1} #6 (AddCommGroup.toAddGroup.{u1} #6 #4))))" }, "rules": { "x": [ [ "NonUnitalNonAssocRing.mk", 6 ] ], "y": [ [ "NonUnitalNonAssocRing.mk", 6 ] ] } }, "inErasedClosure": { "anthropic": true, "openai": true }, "reachedVia": { "anthropic": "NonUnitalNonAssocRing.rec (rec of) ← NonUnitalNonAssocRing (type of) ← NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "NonUnitalNonAssocRing.rec (rec of) ← NonUnitalNonAssocRing (type of) ← NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "erasedDiffs": { "type": { "at": "∀ α body › ∀ motive body › ∀ mk type › ∀ toAddCommGroup body › ∀ toMul body › ∀ left_distrib type › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u1+1)} › arg 6 of HMul.hMul.{u1, u1, u1} › arg 4 of HAdd.hAdd.{u1, u1, u1} › arg 2 of instHAdd.{u1} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u1}", "y": "AddMonoid.toAdd.{u1}", "xIn": "(AddSemigroup.toAdd.{u1} #6 (AddMonoid.toAddSemigroup.{u1} #6 (SubNegMonoid.toAddMonoid.{u1} #6 (AddGroup.toSubNegMonoid.{u1} #6 (AddCommGroup.toAddGroup.{u1} #6 #4)))))", "yIn": "(AddMonoid.toAdd.{u1} #6 (SubNegMonoid.toAddMonoid.{u1} #6 (AddGroup.toSubNegMonoid.{u1} #6 (AddCommGroup.toAddGroup.{u1} #6 #4))))" } }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommRing.toNonUnitalCommRing._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ s body › ∀ a body › ∀ b body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 #2))))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 #2)))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommRing.toNonUnitalCommRing._proof_1 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommRing.toNonUnitalCommRing._proof_1 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommRing.toNonUnitalCommRing._proof_3", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ s body › ∀ n body › ∀ a body › arg 3 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 #2))))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 #2)))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommRing.toNonUnitalCommRing._proof_3 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommRing.toNonUnitalCommRing._proof_3 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommRing.toNonUnitalCommRing._proof_5", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ s body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #2 (AddMonoid.toAddSemigroup.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (Semiring.toAddCommMonoid.{u0} #2 (Ring.toSemiring.{u0} #2 (CommRing.toRing.{u0} #2 #1))))))", "yIn": "(AddMonoid.toAdd.{u0} #2 (AddCommMonoid.toAddMonoid.{u0} #2 (Semiring.toAddCommMonoid.{u0} #2 (Ring.toSemiring.{u0} #2 (CommRing.toRing.{u0} #2 #1)))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommRing.toNonUnitalCommRing._proof_5 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommRing.toNonUnitalCommRing._proof_5 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommRing.toNonUnitalCommRing._proof_6", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ s body › ∀ a body › ∀ b body › arg 2 of Eq.{(u0+1)} › arg 4 of HAdd.hAdd.{u0, u0, u0} › arg 2 of instHAdd.{u0} › head", "why": "different leaves", "x": "AddSemigroup.toAdd.{u0}", "y": "AddMonoid.toAdd.{u0}", "xIn": "(AddSemigroup.toAdd.{u0} #3 (AddMonoid.toAddSemigroup.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 #2))))))", "yIn": "(AddMonoid.toAdd.{u0} #3 (AddCommMonoid.toAddMonoid.{u0} #3 (Semiring.toAddCommMonoid.{u0} #3 (Ring.toSemiring.{u0} #3 (CommRing.toRing.{u0} #3 #2)))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommRing.toNonUnitalCommRing._proof_6 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommRing.toNonUnitalCommRing._proof_6 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommRing.toNonUnitalCommRing._proof_7", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ s body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (Semiring.toMonoid.{u0} #4 (Ring.toSemiring.{u0} #4 (CommRing.toRing.{u0} #4 #3)))))", "yIn": "(Monoid.toMul.{u0} #4 (Semiring.toMonoid.{u0} #4 (Ring.toSemiring.{u0} #4 (CommRing.toRing.{u0} #4 #3))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommRing.toNonUnitalCommRing._proof_7 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommRing.toNonUnitalCommRing._proof_7 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommRing.toNonUnitalCommRing._proof_8", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ s body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (Semiring.toMonoid.{u0} #4 (Ring.toSemiring.{u0} #4 (CommRing.toRing.{u0} #4 #3)))))", "yIn": "(Monoid.toMul.{u0} #4 (Semiring.toMonoid.{u0} #4 (Ring.toSemiring.{u0} #4 (CommRing.toRing.{u0} #4 #3))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommRing.toNonUnitalCommRing._proof_8 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommRing.toNonUnitalCommRing._proof_8 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul, AddMonoid.toAdd" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommRing.toNonUnitalCommRing._proof_9", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ s body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (Semiring.toMonoid.{u0} #2 (Ring.toSemiring.{u0} #2 (CommRing.toRing.{u0} #2 #1)))))", "yIn": "(Monoid.toMul.{u0} #2 (Semiring.toMonoid.{u0} #2 (Ring.toSemiring.{u0} #2 (CommRing.toRing.{u0} #2 #1))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommRing.toNonUnitalCommRing._proof_9 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommRing.toNonUnitalCommRing._proof_9 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommRing.toNonUnitalCommRing._proof_10", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ s body › ∀ a body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #2 (Monoid.toSemigroup.{u0} #2 (Semiring.toMonoid.{u0} #2 (Ring.toSemiring.{u0} #2 (CommRing.toRing.{u0} #2 #1)))))", "yIn": "(Monoid.toMul.{u0} #2 (Semiring.toMonoid.{u0} #2 (Ring.toSemiring.{u0} #2 (CommRing.toRing.{u0} #2 #1))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommRing.toNonUnitalCommRing._proof_10 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommRing.toNonUnitalCommRing._proof_10 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "CommRing.toNonUnitalCommRing._proof_11", "kind": "thm", "module": { "anthropic": "Mathlib.Algebra.Ring.Defs", "openai": "Mathlib.Algebra.Ring.Defs" }, "differs": [ "type" ], "class": "proof-reach", "diffs": { "type": { "at": "∀ α body › ∀ s body › ∀ a body › ∀ b body › ∀ c body › arg 2 of Eq.{(u0+1)} › arg 4 of HMul.hMul.{u0, u0, u0} › arg 2 of instHMul.{u0} › head", "why": "different leaves", "x": "Semigroup.toMul.{u0}", "y": "Monoid.toMul.{u0}", "xIn": "(Semigroup.toMul.{u0} #4 (Monoid.toSemigroup.{u0} #4 (Semiring.toMonoid.{u0} #4 (Ring.toSemiring.{u0} #4 (CommRing.toRing.{u0} #4 #3)))))", "yIn": "(Monoid.toMul.{u0} #4 (Semiring.toMonoid.{u0} #4 (Ring.toSemiring.{u0} #4 (CommRing.toRing.{u0} #4 #3))))" } }, "inErasedClosure": { "anthropic": false, "openai": false }, "reachedVia": { "anthropic": "CommRing.toNonUnitalCommRing._proof_11 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)", "openai": "CommRing.toNonUnitalCommRing._proof_11 (value of) ← CommRing.toNonUnitalCommRing (value of) ← Complex.instNonUnitalCommRing (type of) ← Complex.instStarRing (value of) ← Complex.instInv (value of) ← Complex.instDivInvMonoid (value of) ← Complex.exp' (value of) ← Complex.definition._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (type of) ← Complex.wrapped._@.Mathlib.Analysis.Complex.Exponential.#867311647._hygCtx._hyg.#2 (value of) ← Complex.exp (value of) ← Complex.cpow (value of) ← Complex.instPow (value of)" }, "cross": { "openaiTermReadInAnthropic": { "status": "names-absent", "part": "type", "detail": "Monoid.toMul" }, "anthropicTermReadInOpenAI": { "status": "defeq", "part": "type" }, "both": false }, "defeqBothWays": false, "kernel": "identified in OpenAI's environment only", "group": "monoid-hierarchy" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.lt", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.lt (value of) ← Real.instLT (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Sort 0))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.zero", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.zero (value of) ← Real.instZero (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "Real", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": 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Real.instMul (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.add", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.add (value of) ← Real.instAdd (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.one", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.one (value of) ← Real.instOne (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "Real", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8", "kind": "opaque", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.lt (value of) ← Real.instLT (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Sort 0)) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Sort 0)) Real.definition._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Data.Real.Basic.#1850581184._hygCtx._hyg.#8", "kind": "opaque", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": 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OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Subtype.{1} (∀ (x : Real), (∀ (y : Real), Sort 0)) (Eq.{1} (∀ (x : Real), (∀ (y : Real), Sort 0)) Real.definition._@.Mathlib.Data.Real.Basic.#702802587._hygCtx._hyg.#8))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Semifield.toDivisionSemiring", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Field.Defs" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Semifield.toDivisionSemiring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (K : Sort (u0+1)), (∀ (self : (Semifield.{u0} #0)), (DivisionSemiring.{u0} #1)))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "same", "part": "type" }, "both": false }, "kernel": "one side only, identified in the other environment", "group": "elsewhere-identified" }, { "name": "Monoid.toSemigroup", "kind": "def", "module": { "anthropic": "Mathlib.Algebra.Group.Defs" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Monoid.toSemigroup (value of) ← Rat.instField (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (M : Sort (u0+1)), (∀ (self : (Monoid.{u0} #0)), (Semigroup.{u0} #1)))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "not-defeq", "part": "value", "detail": "(kernel) application type mismatch\n (fun M [self : Monoid M] => self.1) = fun M self => { toMul := self.toMul, mul_assoc := ⋯ }\nargument has type\n (M : Type u_2) → Monoid M → Semigroup M\nbut function has type\n ((M : Type u_2) → [self : Monoid M] → One M) → Prop" }, "both": false }, "kernel": "one side only", "group": "monoid-hierarchy" }, { "name": "Real.wrapped._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8", "kind": "opaque", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.mul (value of) ← Real.instMul (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8", "kind": "opaque", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.add (value of) ← Real.instAdd (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Data.Real.Basic.#1279875089._hygCtx._hyg.#8", "kind": "opaque", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Data.Real.Basic.#1279875089._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.one (value of) ← Real.instOne (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Subtype.{1} Real (Eq.{1} Real Real.definition._@.Mathlib.Data.Real.Basic.#1279875089._hygCtx._hyg.#8))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.lt (value of) ← Real.instLT (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Sort 0))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (value of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.lt (value of) ← Real.instLT (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Sort 0)) Real.definition._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 Real.definition._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Data.Real.Basic.#1850581184._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Data.Real.Basic.#1850581184._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1850581184._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.zero (value of) ← Real.instZero (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "Real", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Data.Real.Basic.#702802587._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Data.Real.Basic.#702802587._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#702802587._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.le (value of) ← Real.instLE (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (x : Real), (∀ (y : Real), Sort 0))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#702802587._hygCtx._hyg.#8", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#702802587._hygCtx._hyg.#8 (value of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#702802587._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.le (value of) ← Real.instLE (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Eq.{1} (∀ (x : Real), (∀ (y : Real), Sort 0)) Real.definition._@.Mathlib.Data.Real.Basic.#702802587._hygCtx._hyg.#8 Real.definition._@.Mathlib.Data.Real.Basic.#702802587._hygCtx._hyg.#8)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.mul (value of) ← Real.instMul (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (value of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.mul (value of) ← Real.instMul (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8 Real.definition._@.Mathlib.Data.Real.Basic.#4214226450._hygCtx._hyg.#8)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.add (value of) ← Real.instAdd (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 (value of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.add (value of) ← Real.instAdd (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 Real.definition._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Data.Real.Basic.#1279875089._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Data.Real.Basic.#1279875089._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1279875089._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.one (value of) ← Real.instOne (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "Real", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition.match_1._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition.match_1._@.Mathlib.Data.Real.Basic.#1138242547._hygCtx._hyg.#8 (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.lt (value of) ← Real.instLT (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (motive : (∀ (x._@.Mathlib.Data.Real.Basic.#1648546948._hygCtx.#16.Mathlib.Data.Real.Basic.#1648546948._hygCtx._hyg.#36 : Real), (∀ (x._@.Mathlib.Data.Real.Basic.#1648546948._hygCtx.#17.Mathlib.Data.Real.Basic.#1648546948._hygCtx._hyg.#39 : Real), Sort u0))), (∀ (x._@.Mathlib.Data.Real.Basic.#1648546948._hygCtx.#16.Mathlib.Data.Real.Basic.#1648546948._hygCtx._hyg.#36 : Real), (∀ (x._@.Mathlib.D…", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._proof_1._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "Real.definition._proof_1._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1175651576._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.lt (value of) ← Real.instLT (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (x._@.Mathlib.Data.Real.Basic.#485170892._hygCtx._hyg.#70 : (CauSeq.{0, 0} Rat Rat.instField Rat.linearOrder Rat.instIsStrictOrderedRing Rat (DivisionRing.toRing.{0} Rat Rat.instDivisionRing) (abs.{0} Rat Rat.instLattice Rat.addGroup))), (∀ (x._@.Mathlib.Data.Real.Basic.#485170892._hygCtx._hyg.#72 : (CauSeq.{0, 0} Rat Rat.instField Rat.linearOrder Rat.instIsStrictOrderedRing Rat (DivisionRing.t…", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.inv'", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), Real)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Bool.and.match_1", "kind": "def", "module": { "anthropic": "Init.Prelude" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Bool.and.match_1 (value of) ← Bool.and (value of) ← Rat.blt (value of) ← Rat.instLE (value of) ← Rat.linearOrder (value of) ← Real.instNatCast (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (motive : (∀ (x._@.Init.Prelude.#2579035302._hygCtx._hyg.#8 : Bool), Sort u0)), (∀ (x._@.Init.Prelude.#2579035302._hygCtx._hyg.#8 : Bool), (∀ (h_1 : (∀ (_ : Unit), (#2 Bool.false))), (∀ (h_2 : (∀ (_ : Unit), (#3 Bool.true))), (#3 #2)))))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "lean-core" }, { "name": "Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8", "kind": "opaque", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "OrderIso.setCongr", "kind": "def", "module": { "anthropic": "Mathlib.Order.Hom.Set" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "OrderIso.setCongr (value of) ← StrictMono.orderIsoOfSurjective (value of) ← Real.expOrderIso (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (α : Sort (u0+1)), (∀ (inst._@.Mathlib.Order.Hom.Set.#94027056._hygCtx._hyg.#5 : (Preorder.{u0} #0)), (∀ (s : (Set.{u0} #1)), (∀ (t : (Set.{u0} #2)), (∀ (h : (Eq.{(u0+1)} (Set.{u0} #3) #1 #0)), (OrderIso.{u0, u0} (Set.Elem.{u0} #4 #2) (Set.Elem.{u0} #4 #1) (Subtype.instLE.{u0} #4 (Preorder.toLE.{u0} #4 #3) (fun (x : #4) => (Membership.mem.{u0, u0} #5 (Set.{u0} #5) (Set.instMembership.{u0} #5) #…", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "names-absent", "part": "value", "detail": "OrderIso.setCongr._proof_1" }, "both": false }, "kernel": "one side only", "group": "renamed" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.sup", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.neg", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), Real)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), Real)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Equiv.setCongr", "kind": "def", "module": { "anthropic": "Mathlib.Logic.Equiv.Set" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Equiv.setCongr (value of) ← OrderIso.setCongr (value of) ← StrictMono.orderIsoOfSurjective (value of) ← Real.expOrderIso (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (α : Sort (u0+1)), (∀ (s : (Set.{u0} #0)), (∀ (t : (Set.{u0} #1)), (∀ (h : (Eq.{(u0+1)} (Set.{u0} #2) #1 #0)), (Equiv.{(u0+1), (u0+1)} (Set.Elem.{u0} #3 #2) (Set.Elem.{u0} #3 #1))))))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "shape", "detail": "universe parameters 1, here 2" }, "both": false }, "kernel": "one side only", "group": "renamed" }, { "name": "OrderIso.setCongr._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Order.Hom.Set" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "OrderIso.setCongr._proof_1 (value of) ← OrderIso.setCongr (value of) ← StrictMono.orderIsoOfSurjective (value of) ← Real.expOrderIso (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (α : Sort (u0+1)), (∀ (inst._@.Mathlib.Order.Hom.Set.#94027056._hygCtx._hyg.#5 : (Preorder.{u0} #0)), (∀ (s : (Set.{u0} #1)), (∀ (t : (Set.{u0} #2)), (∀ (h : (Eq.{(u0+1)} (Set.{u0} #3) #1 #0)), (∀ (a._@.Mathlib.Order.Hom.Set.#94027056._hygCtx._hyg.#30 : (Set.Elem.{u0} #4 #2)), (∀ (b._@.Mathlib.Order.Hom.Set.#94027056._hygCtx._hyg.#31 : (Set.Elem.{u0} #5 #3)), (Iff (LE.le.{u0} (Set.Elem.{u0} #6 …", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "renamed" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.inf", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8", "kind": "opaque", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8", "kind": "opaque", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) Real.definition._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition.match_1._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition.match_1._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#4277896327._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (motive : (∀ (x._@.Mathlib.Data.Real.Basic.#2237667927._hygCtx.#12.Mathlib.Data.Real.Basic.#2237667927._hygCtx._hyg.#24 : Real), Sort u0)), (∀ (x._@.Mathlib.Data.Real.Basic.#2237667927._hygCtx.#12.Mathlib.Data.Real.Basic.#2237667927._hygCtx._hyg.#24 : Real), (∀ (h_1 : (∀ (a : (CauSeq.Completion.Cauchy.{0, 0} Rat Rat.instField Rat.linearOrder Rat.instIsStrictOrderedRing Rat (DivisionRing.toRing.…", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Equiv.setCongr._proof_1", "kind": "thm", "module": { "anthropic": "Mathlib.Logic.Equiv.Set" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "Equiv.setCongr._proof_1 (value of) ← Equiv.setCongr (value of) ← OrderIso.setCongr (value of) ← StrictMono.orderIsoOfSurjective (value of) ← Real.expOrderIso (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (α : Sort (u0+1)), (∀ (s : (Set.{u0} #0)), (∀ (t : (Set.{u0} #1)), (∀ (h : (Eq.{(u0+1)} (Set.{u0} #2) #1 #0)), (Eq.{(u0+1)} (∀ (a._@._internal._hyg.#0 : #3), Sort 0) (fun (x : #3) => (Membership.mem.{u0, u0} #4 (Set.{u0} #4) (Set.instMembership.{u0} #4) #3 #0)) (fun (x : #3) => (Membership.mem.{u0, u0} #4 (Set.{u0} #4) (Set.instMembership.{u0} #4) #2 #0)))))))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "shape", "detail": "universe parameters 1, here 2" }, "both": false }, "kernel": "one side only", "group": "renamed" }, { "name": "Real.wrapped._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8", "kind": "opaque", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (value of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 Real.definition._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), Real)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 (value of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) Real.definition._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8 Real.definition._@.Mathlib.Data.Real.Basic.#2451848184._hygCtx._hyg.#8)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8", "kind": "def", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Data.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (value of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8 Real.definition._@.Mathlib.Data.Real.Basic.#1934218611._hygCtx._hyg.#8)", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._proof_1._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8", "kind": "thm", "module": { "anthropic": "Mathlib.Data.Real.Basic" }, "presentOnly": "anthropic", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "Real.definition._proof_1._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (value of) ← Real.definition._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (type of) ← Real.wrapped._@.Mathlib.Data.Real.Basic.#3793047190._hygCtx._hyg.#8 (value of) ← _private.Mathlib.Data.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.ClaimAt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.Claim", "type": "(IsAbsoluteValue.{0, 0} Rat (Ring.toSemiring.{0} Rat (DivisionRing.toRing.{0} Rat (Field.toDivisionRing.{0} Rat Rat.instField))) (SemilatticeInf.toPartialOrder.{0} Rat (Lattice.toSemilatticeInf.{0} Rat (DistribLattice.toLattice.{0} Rat (instDistribLatticeOfLinearOrder.{0} Rat Rat.linearOrder)))) Rat (Ring.toSemiring.{0} Rat (DivisionRing.toRing.{0} Rat (Field.toDivisionRing.{0} Rat Rat.instField))…", "cross": { "openaiTermReadInAnthropic": { "status": "not read" }, "anthropicTermReadInOpenAI": { "status": "absent" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.lt", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.lt (value of) ← Real.instLT (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Sort 0))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.zero", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.zero (value of) ← Real.instZero (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "Real", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.le", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.le (value of) ← Real.instLE (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (x : Real), (∀ (y : Real), Sort 0))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.mul", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.mul (value of) ← Real.instMul (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.add", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.add (value of) ← Real.instAdd (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.one", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.one (value of) ← Real.instOne (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "Real", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2", "kind": "opaque", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.lt (value of) ← Real.instLT (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Sort 0)) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Sort 0)) Real.definition._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#3335671075._hygCtx._hyg.#2", "kind": "opaque", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#3335671075._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.zero (value of) ← Real.instZero (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Subtype.{1} Real (Eq.{1} Real Real.definition._@.Mathlib.Basic.Real.Basic.#3335671075._hygCtx._hyg.#2))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2", "kind": "opaque", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.le (value of) ← Real.instLE (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Subtype.{1} (∀ (x : Real), (∀ (y : Real), Sort 0)) (Eq.{1} (∀ (x : Real), (∀ (y : Real), Sort 0)) Real.definition._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Monoid.toMul", "kind": "def", "module": { "openai": "Mathlib.Algebra.Group.Monoid" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Monoid.toMul (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (M : Sort (u0+1)), (∀ (self : (Monoid.{u0} #0)), (Mul.{u0} #1)))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "monoid-hierarchy" }, { "name": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2", "kind": "opaque", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.mul (value of) ← Real.instMul (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Monoid.mul_assoc", "kind": "thm", "module": { "openai": "Mathlib.Algebra.Group.Monoid" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Monoid.mul_assoc (proj of) ← Monoid (type of) ← Monoid.toNPow (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (M : Sort (u0+1)), (∀ (self : (Monoid.{u0} #0)), (∀ (a : #1), (∀ (b : #2), (∀ (c : #3), (Eq.{(u0+1)} #4 (HMul.hMul.{u0, u0, u0} #4 #4 #4 (instHMul.{u0} #4 (Monoid.toMul.{u0} #4 #3)) (HMul.hMul.{u0, u0, u0} #4 #4 #4 (instHMul.{u0} #4 (Monoid.toMul.{u0} #4 #3)) #2 #1) #0) (HMul.hMul.{u0, u0, u0} #4 #4 #4 (instHMul.{u0} #4 (Monoid.toMul.{u0} #4 #3)) #2 (HMul.hMul.{u0, u0, u0} #4 #4 #4 (instHMul.{u…", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "monoid-hierarchy" }, { "name": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2", "kind": "opaque", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.add (value of) ← Real.instAdd (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#6358291._hygCtx._hyg.#2", "kind": "opaque", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#6358291._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.one (value of) ← Real.instOne (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Subtype.{1} Real (Eq.{1} Real Real.definition._@.Mathlib.Basic.Real.Basic.#6358291._hygCtx._hyg.#2))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.lt (value of) ← Real.instLT (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Sort 0))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2", "kind": "thm", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (value of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.lt (value of) ← Real.instLT (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Sort 0)) Real.definition._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 Real.definition._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Basic.Real.Basic.#3335671075._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Basic.Real.Basic.#3335671075._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#3335671075._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.zero (value of) ← Real.instZero (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "Real", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.le (value of) ← Real.instLE (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (x : Real), (∀ (y : Real), Sort 0))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2", "kind": "thm", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2 (value of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.le (value of) ← Real.instLE (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Eq.{1} (∀ (x : Real), (∀ (y : Real), Sort 0)) Real.definition._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2 Real.definition._@.Mathlib.Basic.Real.Basic.#3158186288._hygCtx._hyg.#2)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.mul (value of) ← Real.instMul (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2", "kind": "thm", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (value of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.mul (value of) ← Real.instMul (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2 Real.definition._@.Mathlib.Basic.Real.Basic.#1745762101._hygCtx._hyg.#2)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.add (value of) ← Real.instAdd (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2", "kind": "thm", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 (value of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.add (value of) ← Real.instAdd (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 Real.definition._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Basic.Real.Basic.#6358291._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Basic.Real.Basic.#6358291._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#6358291._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.one (value of) ← Real.instOne (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "Real", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition.match_1._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition.match_1._@.Mathlib.Basic.Real.Basic.#2153608522._hygCtx._hyg.#2 (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.lt (value of) ← Real.instLT (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (motive : (∀ (x._@.Mathlib.Basic.Real.Basic.#2304872548._hygCtx.#16.Mathlib.Basic.Real.Basic.#2304872548._hygCtx._hyg.#36 : Real), (∀ (x._@.Mathlib.Basic.Real.Basic.#2304872548._hygCtx.#17.Mathlib.Basic.Real.Basic.#2304872548._hygCtx._hyg.#39 : Real), Sort u0))), (∀ (x._@.Mathlib.Basic.Real.Basic.#2304872548._hygCtx.#16.Mathlib.Basic.Real.Basic.#2304872548._hygCtx._hyg.#36 : Real), (∀ (x._@.Mat…", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._proof_1._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2", "kind": "thm", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "Real.definition._proof_1._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#2348678026._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.lt (value of) ← Real.instLT (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (x._@.Mathlib.Basic.Real.Basic.#2942375680._hygCtx._hyg.#70 : (CauSeq.{0, 0} Rat Rat.instField Rat.linearOrder Rat.instIsStrictOrderedRing Rat (DivisionRing.toRing.{0} Rat Rat.instDivisionRing) (abs.{0} Rat Rat.instLattice Rat.addGroup))), (∀ (x._@.Mathlib.Basic.Real.Basic.#2942375680._hygCtx._hyg.#72 : (CauSeq.{0, 0} Rat Rat.instField Rat.linearOrder Rat.instIsStrictOrderedRing Rat (DivisionRi…", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "AddMonoid.toAdd", "kind": "def", "module": { "openai": "Mathlib.Algebra.Group.Monoid" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "AddMonoid.toAdd (type of) ← Ring.mk (ctor of) ← Ring (type of) ← CauSeq.Completion.Cauchy (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (M : Sort (u0+1)), (∀ (self : (AddMonoid.{u0} #0)), (Add.{u0} #1)))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "monoid-hierarchy" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.inv'", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), Real)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "AddZeroClass.toZero", "kind": "def", "module": { "openai": "Mathlib.Algebra.Group.Monoid" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "AddZeroClass.toZero (value of) ← AddZeroClass.toAddZero (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (M : Sort (u0+1)), (∀ (self : (AddZeroClass.{u0} #0)), (Zero.{u0} #1)))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "monoid-hierarchy" }, { "name": "AddZeroClass.toAdd", "kind": "def", "module": { "openai": "Mathlib.Algebra.Group.Monoid" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "AddZeroClass.toAdd (value of) ← AddZeroClass.toAddZero (value of) ← Multiset.sum (value of) ← Finset.sum (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.visitedSpace (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (M : Sort (u0+1)), (∀ (self : (AddZeroClass.{u0} #0)), (Add.{u0} #1)))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "monoid-hierarchy" }, { "name": "AddMonoid.add_assoc", "kind": "thm", "module": { "openai": "Mathlib.Algebra.Group.Monoid" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "AddMonoid.add_assoc (proj of) ← AddMonoid (type of) ← AddCommMonoid.mk (value of) ← Rat.commRing (value of) ← Rat.instField (value of) ← Real.instNatCast (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (M : Sort (u0+1)), (∀ (self : (AddMonoid.{u0} #0)), (∀ (a : #1), (∀ (b : #2), (∀ (c : #3), (Eq.{(u0+1)} #4 (HAdd.hAdd.{u0, u0, u0} #4 #4 #4 (instHAdd.{u0} #4 (AddMonoid.toAdd.{u0} #4 #3)) (HAdd.hAdd.{u0, u0, u0} #4 #4 #4 (instHAdd.{u0} #4 (AddMonoid.toAdd.{u0} #4 #3)) #2 #1) #0) (HAdd.hAdd.{u0, u0, u0} #4 #4 #4 (instHAdd.{u0} #4 (AddMonoid.toAdd.{u0} #4 #3)) #2 (HAdd.hAdd.{u0, u0, u0} #4 #4 #4 …", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "monoid-hierarchy" }, { "name": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2", "kind": "opaque", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "MulOneClass.toOne", "kind": "def", "module": { "openai": "Mathlib.Algebra.Group.Monoid" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "MulOneClass.toOne (value of) ← MulOneClass.toMulOne (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (M : Sort (u0+1)), (∀ (self : (MulOneClass.{u0} #0)), (One.{u0} #1)))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "monoid-hierarchy" }, { "name": "MulOneClass.toMul", "kind": "def", "module": { "openai": "Mathlib.Algebra.Group.Monoid" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "MulOneClass.toMul (value of) ← MulOneClass.toMulOne (value of) ← DivInvMonoid.div' (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (M : Sort (u0+1)), (∀ (self : (MulOneClass.{u0} #0)), (Mul.{u0} #1)))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "monoid-hierarchy" }, { "name": "Set.orderIsoOfEq", "kind": "def", "module": { "openai": "Mathlib.Order.Hom.Set" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Set.orderIsoOfEq (value of) ← StrictMono.orderIsoOfSurjective (value of) ← Real.expOrderIso (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (α : Sort (u0+1)), (∀ (inst._@.Mathlib.Order.Hom.Set.#1858681105._hygCtx._hyg.#5 : (Preorder.{u0} #0)), (∀ (s : (Set.{u0} #1)), (∀ (t : (Set.{u0} #2)), (∀ (h : (Eq.{(u0+1)} (Set.{u0} #3) #1 #0)), (OrderIso.{u0, u0} (Set.Elem.{u0} #4 #2) (Set.Elem.{u0} #4 #1) (Subtype.instLE.{u0} #4 (Preorder.toLE.{u0} #4 #3) (fun (x : #4) => (Membership.mem.{u0, u0} #5 (Set.{u0} #5) (Set.instMembership.{u0} #5)…", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "renamed" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.sup", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.neg", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), Real)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), Real)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2", "kind": "thm", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Set.equivOfEq", "kind": "def", "module": { "openai": "Mathlib.Logic.Equiv.Set" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Set.equivOfEq (value of) ← Set.orderIsoOfEq (value of) ← StrictMono.orderIsoOfSurjective (value of) ← Real.expOrderIso (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (α : Sort (u0+1)), (∀ (s : (Set.{u0} #0)), (∀ (t : (Set.{u0} #1)), (∀ (h : (Eq.{(u0+1)} (Set.{u0} #2) #1 #0)), (Equiv.{(u0+1), (u0+1)} (Set.Elem.{u0} #3 #2) (Set.Elem.{u0} #3 #1))))))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "renamed" }, { "name": "Set.orderIsoOfEq._proof_1", "kind": "thm", "module": { "openai": "Mathlib.Order.Hom.Set" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "Set.orderIsoOfEq._proof_1 (value of) ← Set.orderIsoOfEq (value of) ← StrictMono.orderIsoOfSurjective (value of) ← Real.expOrderIso (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (α : Sort (u0+1)), (∀ (inst._@.Mathlib.Order.Hom.Set.#1858681105._hygCtx._hyg.#5 : (Preorder.{u0} #0)), (∀ (s : (Set.{u0} #1)), (∀ (t : (Set.{u0} #2)), (∀ (h : (Eq.{(u0+1)} (Set.{u0} #3) #1 #0)), (∀ (a._@.Mathlib.Order.Hom.Set.#1858681105._hygCtx._hyg.#30 : (Set.Elem.{u0} #4 #2)), (∀ (b._@.Mathlib.Order.Hom.Set.#1858681105._hygCtx._hyg.#31 : (Set.Elem.{u0} #5 #3)), (Iff (LE.le.{u0} (Set.Elem.{u…", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "renamed" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.inf", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2", "kind": "opaque", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2", "kind": "opaque", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) Real.definition._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition.match_1._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition.match_1._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#339334276._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inv' (value of) ← Real.instInv (value of) ← Real.instDivInvMonoid (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (motive : (∀ (x._@.Mathlib.Basic.Real.Basic.#958436427._hygCtx.#12.Mathlib.Basic.Real.Basic.#958436427._hygCtx._hyg.#24 : Real), Sort u0)), (∀ (x._@.Mathlib.Basic.Real.Basic.#958436427._hygCtx.#12.Mathlib.Basic.Real.Basic.#958436427._hygCtx._hyg.#24 : Real), (∀ (h_1 : (∀ (a : (CauSeq.Completion.Cauchy.{0, 0} Rat Rat.instField Rat.linearOrder Rat.instIsStrictOrderedRing Rat (DivisionRing.toRing.…", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Set.equivOfEq._proof_1", "kind": "thm", "module": { "openai": "Mathlib.Logic.Equiv.Set" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "Set.equivOfEq._proof_1 (value of) ← Set.equivOfEq (value of) ← Set.orderIsoOfEq (value of) ← StrictMono.orderIsoOfSurjective (value of) ← Real.expOrderIso (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (α : Sort (u0+1)), (∀ (s : (Set.{u0} #0)), (∀ (t : (Set.{u0} #1)), (∀ (h : (Eq.{(u0+1)} (Set.{u0} #2) #1 #0)), (Eq.{(u0+1)} (∀ (a._@._internal._hyg.#0 : #3), Sort 0) (fun (x : #3) => (Membership.mem.{u0, u0} #4 (Set.{u0} #4) (Set.instMembership.{u0} #4) #3 #0)) (fun (x : #3) => (Membership.mem.{u0, u0} #4 (Set.{u0} #4) (Set.instMembership.{u0} #4) #2 #0)))))))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "renamed" }, { "name": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2", "kind": "opaque", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.wrapped._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Subtype.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) (Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Nonneg", "kind": "def", "module": { "openai": "Mathlib.Algebra.Order.Nonneg.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Nonneg (value of) ← NNReal.instSemiring._aux_1 (value of) ← NNReal.instSemiring (value of) ← NNReal.powOrderIso (value of) ← NNReal.sqrt (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (α : Sort (u0+1)), (∀ (inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2956920048._hygCtx._hyg.#4 : (Zero.{u0} #0)), (∀ (inst._@.Mathlib.Algebra.Order.Nonneg.Basic.#2956920048._hygCtx._hyg.#7 : (LE.{u0} #1)), Sort (max 1 (u0+1)))))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "nonneg" }, { "name": "Real.definition._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2", "kind": "thm", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (value of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 Real.definition._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), Real)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2", "kind": "thm", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 (value of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.neg (value of) ← Real.instNeg (value of) ← Real.commRing (value of) ← Real.instCommSemiring (value of) ← Real.semiring (value of) ← Real.instMonoid (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), Real) Real.definition._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2 Real.definition._@.Mathlib.Basic.Real.Basic.#4282658333._hygCtx._hyg.#2)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2", "kind": "def", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "definitional", "inErasedClosure": true, "reachedVia": "Real.definition._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real))", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2", "kind": "thm", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "_private.Mathlib.Basic.Real.Basic.#0.Real.wrapped._proof_1._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (value of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.inf (value of) ← Real.instMin (value of) ← Real.instDistribLattice (value of) ← Real.lattice (value of) ← Real.log (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(Eq.{1} (∀ (a._@._internal._hyg.#0 : Real), (∀ (a._@._internal._hyg.#0 : Real), Real)) Real.definition._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2 Real.definition._@.Mathlib.Basic.Real.Basic.#326038627._hygCtx._hyg.#2)", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" }, { "name": "Real.definition._proof_1._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2", "kind": "thm", "module": { "openai": "Mathlib.Basic.Real.Basic" }, "presentOnly": "openai", "class": "proof-reach", "inErasedClosure": false, "reachedVia": "Real.definition._proof_1._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (value of) ← Real.definition._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (type of) ← Real.wrapped._@.Mathlib.Basic.Real.Basic.#1259013419._hygCtx._hyg.#2 (value of) ← _private.Mathlib.Basic.Real.Basic.#0.Real.sup (value of) ← Real.instMax (value of) ← Real.toNNReal (value of) ← Real.sqrt (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeScale (value of) ← OAI.Algorithms.SubexponentialSAT.SqrtLog.Statement.runtimeBound (type of) ← OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.exact_count_and_sat", "type": "(IsAbsoluteValue.{0, 0} Rat (Ring.toSemiring.{0} Rat (DivisionRing.toRing.{0} Rat (Field.toDivisionRing.{0} Rat Rat.instField))) (SemilatticeInf.toPartialOrder.{0} Rat (Lattice.toSemilatticeInf.{0} Rat (DistribLattice.toLattice.{0} Rat (instDistribLatticeOfLinearOrder.{0} Rat Rat.linearOrder)))) Rat (Ring.toSemiring.{0} Rat (DivisionRing.toRing.{0} Rat (Field.toDivisionRing.{0} Rat Rat.instField))…", "cross": { "openaiTermReadInAnthropic": { "status": "absent" }, "anthropicTermReadInOpenAI": { "status": "not read" }, "both": false }, "kernel": "one side only", "group": "moved-file" } ], "surfaceOnly": [ { "name": "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.locatedInit", "kind": "def", "differs": [ "value (binder names, binder infos or metadata)" ], "diff": { "at": "λ machine body › λ input body › arg 3 of OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.mk", "why": "binder name or info", "x": "(fun (x._@.Bridge.OpenAIStatement.#208244618._hygCtx._hyg.#18 : (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.tapeCount #1))) => (OfNat.ofNat.{0} Int 0 (instOfNat 0)))", "y": "(fun (x._@.ComparatorChallenges.SubexponentialSAT.#208244618._hygCtx._hyg.#18 : (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.tapeCount #1))) => (OfNat.ofNat.{0} Int 0 (instOfNat 0)))", "xIn": "(OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.mk #1 (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.init #1 #0) (fun (x._@.Bridge.OpenAIStatement.#208244618._hygCtx._hyg.#18 : (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.tapeCount #1))) => (OfNat.ofNat.{0} Int 0 (instOf…", "yIn": "(OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.mk #1 (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.init #1 #0) (fun (x._@.ComparatorChallenges.SubexponentialSAT.#208244618._hygCtx._hyg.#18 : (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.tapeCount #1))) => (OfNat.ofNat.{…" } }, { "name": "OAI.Algorithms.SubexponentialSAT.SAT.count", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "at": "∀ V body", "why": "binder name or info", "x": "(∀ (inst._@.Bridge.OpenAIStatement.#2383784525._hygCtx._hyg.#3 : (DecidableEq.{(u0+1)} #0)), (∀ (inst._@.Bridge.OpenAIStatement.#2383784525._hygCtx._hyg.#6 : (Fintype.{u0} #1)), (∀ (F : (OAI.Algorithms.SubexponentialSAT.SAT.CNF.{u0} #2)), Nat)))", "y": "(∀ (inst._@.ComparatorChallenges.SubexponentialSAT.#2383784525._hygCtx._hyg.#3 : (DecidableEq.{(u0+1)} #0)), (∀ (inst._@.ComparatorChallenges.SubexponentialSAT.#2383784525._hygCtx._hyg.#6 : (Fintype.{u0} #1)), (∀ (F : (OAI.Algorithms.SubexponentialSAT.SAT.CNF.{u0} #2)), Nat)))", "xIn": null, "yIn": null } }, { "name": "OAI.Algorithms.SubexponentialSAT.BinaryArithmetic.toNat", "kind": "def", "differs": [ "value (binder names, binder infos or metadata)" ], "diff": { "at": "the root", "why": "binder name or info", "x": "(fun (x._@.Bridge.OpenAIStatement.#4180722028._hygCtx._hyg.#8 : (List.{0} Bool)) => (List.brecOn.{1, 0} Bool (fun (x._@.Bridge.OpenAIStatement.#4180722028._hygCtx._hyg.#8 : (List.{0} Bool)) => Nat) #0 OAI.Algorithms.SubexponentialSAT.BinaryArithmetic.toNat._f))", "y": "(fun (x._@.ComparatorChallenges.SubexponentialSAT.#4180722028._hygCtx._hyg.#8 : (List.{0} Bool)) => (List.brecOn.{1, 0} Bool (fun (x._@.ComparatorChallenges.SubexponentialSAT.#4180722028._hygCtx._hyg.#8 : (List.{0} Bool)) => Nat) #0 OAI.Algorithms.SubexponentialSAT.BinaryArithmetic.toNat._f))", "xIn": null, "yIn": null } }, { "name": "NPow.toPow", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "at": "∀ M body", "why": "binder name or info", "x": "(∀ (inst._@.Mathlib.Algebra.Group.Defs.#148871009._hygCtx._hyg.#4 : (NPow.{u0} #0)), (Pow.{u0, 0} #1 Nat))", "y": "(∀ (inst._@.Mathlib.Algebra.Group.Monoid.#148871009._hygCtx._hyg.#4 : (NPow.{u0} #0)), (Pow.{u0, 0} #1 Nat))", "xIn": null, "yIn": null } }, { "name": "Finset", "kind": "induct", "differs": [ "universe parameter names" ], "diff": { "x": [ "u_4" ], "y": [ "u_3" ] } }, { "name": "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.monitor", "kind": "def", "differs": [ "value (binder names, binder infos or metadata)" ], "diff": { "at": "λ machine body › λ c body › λ config body › arg 4 of Sum.elim.{0, 0, 1}", "why": "binder name or info", "x": "(fun (x._@.Bridge.OpenAIStatement.#71945438._hygCtx._hyg.#13 : Bool) => (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.mk #3 #1 (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.position #3 #2) (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.lower #3 #2) (OAI.Algorithms.SubexponentialSAT.Sq…", "y": "(fun (x._@.ComparatorChallenges.SubexponentialSAT.#71945438._hygCtx._hyg.#13 : Bool) => (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.mk #3 #1 (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.position #3 #2) (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.lower #3 #2) (OAI.Algorithms.Sube…", "xIn": "(Sum.elim.{0, 0, 1} Bool (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.stateCount #2)) (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg #2) (fun (x._@.Bridge.OpenAIStatement.#71945438._hygCtx._hyg.#13 : Bool) => (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.mk #3 #1 (OAI.Algor…", "yIn": "(Sum.elim.{0, 0, 1} Bool (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.stateCount #2)) (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg #2) (fun (x._@.ComparatorChallenges.SubexponentialSAT.#71945438._hygCtx._hyg.#13 : Bool) => (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.LocatedCfg.mk …" } }, { "name": "OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.step", "kind": "def", "differs": [ "value (binder names, binder infos or metadata)" ], "diff": { "at": "λ machine body › λ c body › arg 2 of OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.step.match_5.{1}", "why": "binder name or info", "x": "(fun (x._@.Bridge.OpenAIStatement.#2479753423._hygCtx._hyg.#10 : (Sum.{0, 0} Bool (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.stateCount #1)))) => (Option.{0} (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.Cfg #2)))", "y": "(fun (x._@.ComparatorChallenges.SubexponentialSAT.#2479753423._hygCtx._hyg.#10 : (Sum.{0, 0} Bool (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.stateCount #1)))) => (Option.{0} (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.Cfg #2)))", "xIn": "(OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.step.match_5.{1} #1 (fun (x._@.Bridge.OpenAIStatement.#2479753423._hygCtx._hyg.#10 : (Sum.{0, 0} Bool (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.stateCount #1)))) => (Option.{0} (OAI.Algorithms.SubexponentialSAT.Computation.Primitiv…", "yIn": "(OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.step.match_5.{1} #1 (fun (x._@.ComparatorChallenges.SubexponentialSAT.#2479753423._hygCtx._hyg.#10 : (Sum.{0, 0} Bool (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.stateCount #1)))) => (Option.{0} (OAI.Algorithms.SubexponentialSAT.Comp…" } }, { "name": "Fintype", "kind": "induct", "differs": [ "universe parameter names" ], "diff": { "x": [ "u_4" ], "y": [ "u_3" ] } }, { "name": "OAI.Algorithms.SubexponentialSAT.SAT.satisfyingAssignments", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "at": "∀ V body", "why": "binder name or info", "x": "(∀ (inst._@.Bridge.OpenAIStatement.#2258046685._hygCtx._hyg.#3 : (DecidableEq.{(u0+1)} #0)), (∀ (inst._@.Bridge.OpenAIStatement.#2258046685._hygCtx._hyg.#6 : (Fintype.{u0} #1)), (∀ (F : (OAI.Algorithms.SubexponentialSAT.SAT.CNF.{u0} #2)), (Finset.{u0} (OAI.Algorithms.SubexponentialSAT.SAT.Assignment.{u0} #3)))))", "y": "(∀ (inst._@.ComparatorChallenges.SubexponentialSAT.#2258046685._hygCtx._hyg.#3 : (DecidableEq.{(u0+1)} #0)), (∀ (inst._@.ComparatorChallenges.SubexponentialSAT.#2258046685._hygCtx._hyg.#6 : (Fintype.{u0} #1)), (∀ (F : (OAI.Algorithms.SubexponentialSAT.SAT.CNF.{u0} #2)), (Finset.{u0} (OAI.Algorithms.SubexponentialSAT.SA…", "xIn": null, "yIn": null } }, { "name": "Fintype.mk", "kind": "ctor", "differs": [ "universe parameter names" ], "diff": { "x": [ "u_4" ], "y": [ "u_3" ] } }, { "name": "Finset.mk", "kind": "ctor", "differs": [ "universe parameter names" ], "diff": { "x": [ "u_4" ], "y": [ "u_3" ] } }, { "name": "OAI.Algorithms.SubexponentialSAT.BinaryArithmetic.toNat._f", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "at": "the root", "why": "binder name or info", "x": "(∀ (x._@.Bridge.OpenAIStatement.#4180722028._hygCtx._hyg.#8 : (List.{0} Bool)), (∀ (f : (List.below.{1, 0} Bool (fun (x._@.Bridge.OpenAIStatement.#4180722028._hygCtx._hyg.#8 : (List.{0} Bool)) => Nat) #0)), Nat))", "y": "(∀ (x._@.ComparatorChallenges.SubexponentialSAT.#4180722028._hygCtx._hyg.#8 : (List.{0} Bool)), (∀ (f : (List.below.{1, 0} Bool (fun (x._@.ComparatorChallenges.SubexponentialSAT.#4180722028._hygCtx._hyg.#8 : (List.{0} Bool)) => Nat) #0)), Nat))", "xIn": null, "yIn": null } }, { "name": "Rat.linearOrder", "kind": "def", "differs": [ "value (binder names, binder infos or metadata)" ], "diff": { "at": "arg 2 of LinearOrder.mk.{0} › arg 2 of PartialOrder.mk.{0} › arg 4 of Preorder.mk.{0}", "why": "binder name or info", "x": "(fun (x._@.Mathlib.Algebra.Order.Ring.Unbundled.Rat.#1059403224._hygCtx._hyg.#30 : Rat) => (Rat.le_refl #0))", "y": "(fun (x._@.Mathlib.Algebra.Order.Ring.Unbundled.Rat.#1059403224._hygCtx._hyg.#27 : Rat) => (Rat.le_refl #0))", "xIn": "(Preorder.mk.{0} Rat Rat.instLE Rat.instLT (fun (x._@.Mathlib.Algebra.Order.Ring.Unbundled.Rat.#1059403224._hygCtx._hyg.#30 : Rat) => (Rat.le_refl #0)) (fun (x._@.Mathlib.Algebra.Order.Ring.Unbundled.Rat.#1059403224._hygCtx._hyg.#35 : Rat) => (fun (x._@.Mathlib.Algebra.Order.Ring.Unbundled.Rat.#1059403224._hygCtx._hyg.…", "yIn": "(Preorder.mk.{0} Rat Rat.instLE Rat.instLT (fun (x._@.Mathlib.Algebra.Order.Ring.Unbundled.Rat.#1059403224._hygCtx._hyg.#27 : Rat) => (Rat.le_refl #0)) (fun (x._@.Mathlib.Algebra.Order.Ring.Unbundled.Rat.#1059403224._hygCtx._hyg.#32 : Rat) => (fun (x._@.Mathlib.Algebra.Order.Ring.Unbundled.Rat.#1059403224._hygCtx._hyg.…" } }, { "name": "Finset.univ", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "at": "∀ α body", "why": "binder name or info", "x": "(∀ (inst._@.Mathlib.Data.Fintype.Defs.#694412596._hygCtx._hyg.#5 : (Fintype.{u0} #0)), (Finset.{u0} #1))", "y": "(∀ (inst._@.Mathlib.Data.Fintype.Defs.#694412596._hygCtx._hyg.#4 : (Fintype.{u0} #0)), (Finset.{u0} #1))", "xIn": null, "yIn": null } }, { "name": "NPow", "kind": "induct", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "NPow.npow", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "Monoid", "kind": "induct", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "IsAbsoluteValue.abs_isAbsoluteValue", "kind": "thm", "differs": [ "universe parameter names", "type (binder names, binder infos or metadata)" ], "diff": { "x": [ "u_5" ], "y": [ "u_4" ] } }, { "name": "Finset.rec", "kind": "rec", "differs": [ "universe parameter names" ], "diff": { "x": [ "u", "u_4" ], "y": [ "u", "u_3" ] } }, { "name": "Finset.nodup", "kind": "thm", "differs": [ "universe parameter names" ], "diff": { "x": [ "u_4" ], "y": [ "u_3" ] } }, { "name": "Finset.val", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u_4" ], "y": [ "u_3" ] } }, { "name": "OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.headDisplacement", "kind": "def", "differs": [ "value (binder names, binder infos or metadata)" ], "diff": { "at": "the root", "why": "binder name or info", "x": "(fun (x._@.Bridge.OpenAIStatement.#3464488531._hygCtx._hyg.#11 : (Turing.TM0.Stmt.{0} (Option.{0} Bool))) => (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.headDisplacement.match_1.{1} (fun (x._@.Bridge.OpenAIStatement.#3464488531._hygCtx.#11.Bridge.OpenAIStatement.#3464488531._hygCtx._hyg.#23 : (Turing.TM0.Stmt.{0} (O…", "y": "(fun (x._@.ComparatorChallenges.SubexponentialSAT.#3464488531._hygCtx._hyg.#11 : (Turing.TM0.Stmt.{0} (Option.{0} Bool))) => (OAI.Algorithms.SubexponentialSAT.SqrtLogSpace.headDisplacement.match_1.{1} (fun (x._@.ComparatorChallenges.SubexponentialSAT.#3464488531._hygCtx.#11.ComparatorChallenges.SubexponentialSAT.#34644…", "xIn": null, "yIn": null } }, { "name": "OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.step.match_5", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "at": "∀ machine body › ∀ motive type", "why": "binder name or info", "x": "(∀ (x._@.Bridge.OpenAIStatement.#2479753423._hygCtx._hyg.#10 : (Sum.{0, 0} Bool (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.stateCount #0)))), Sort u0)", "y": "(∀ (x._@.ComparatorChallenges.SubexponentialSAT.#2479753423._hygCtx._hyg.#10 : (Sum.{0, 0} Bool (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.stateCount #0)))), Sort u0)", "xIn": null, "yIn": null } }, { "name": "OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.step.match_3", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "at": "∀ machine body › ∀ motive type", "why": "binder name or info", "x": "(∀ (x._@.Bridge.OpenAIStatement.#2479753423._hygCtx._hyg.#41 : (Sum.{0, 0} Bool (Prod.{0, 0} (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.stateCount #0)) (Turing.TM0.Stmt.{0} (Option.{0} Bool))))), Sort u0)", "y": "(∀ (x._@.ComparatorChallenges.SubexponentialSAT.#2479753423._hygCtx._hyg.#41 : (Sum.{0, 0} Bool (Prod.{0, 0} (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.stateCount #0)) (Turing.TM0.Stmt.{0} (Option.{0} Bool))))), Sort u0)", "xIn": null, "yIn": null } }, { "name": "OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.step.match_1", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "at": "∀ motive type", "why": "binder name or info", "x": "(∀ (action._@.Bridge.OpenAIStatement.#2479753423._hygCtx._hyg.#80 : (Turing.TM0.Stmt.{0} (Option.{0} Bool))), Sort u0)", "y": "(∀ (action._@.ComparatorChallenges.SubexponentialSAT.#2479753423._hygCtx._hyg.#80 : (Turing.TM0.Stmt.{0} (Option.{0} Bool))), Sort u0)", "xIn": null, "yIn": null } }, { "name": "OAI.Algorithms.SubexponentialSAT.Encoding.encodeList", "kind": "def", "differs": [ "value (binder names, binder infos or metadata)" ], "diff": { "at": "λ α body › λ enc body", "why": "binder name or info", "x": "(fun (x._@.Bridge.OpenAIStatement.#664205651._hygCtx._hyg.#12 : (List.{u0} #1)) => (List.brecOn.{1, u0} #2 (fun (x._@.Bridge.OpenAIStatement.#664205651._hygCtx._hyg.#12 : (List.{u0} #2)) => (List.{0} Bool)) #0 (OAI.Algorithms.SubexponentialSAT.Encoding.encodeList._f.{u0} #2 #1)))", "y": "(fun (x._@.ComparatorChallenges.SubexponentialSAT.#664205651._hygCtx._hyg.#12 : (List.{u0} #1)) => (List.brecOn.{1, u0} #2 (fun (x._@.ComparatorChallenges.SubexponentialSAT.#664205651._hygCtx._hyg.#12 : (List.{u0} #2)) => (List.{0} Bool)) #0 (OAI.Algorithms.SubexponentialSAT.Encoding.encodeList._f.{u0} #2 #1)))", "xIn": null, "yIn": null } }, { "name": "OAI.Algorithms.SubexponentialSAT.Encoding.cnfNumbers", "kind": "def", "differs": [ "value (binder names, binder infos or metadata)" ], "diff": { "at": "λ n body › λ F body › arg 3 of Finset.sort.{0}", "why": "binder name or info", "x": "(fun (x1._@.Bridge.OpenAIStatement.#2102840263._hygCtx._hyg.#24 : (List.{0} Nat)) => (fun (x2._@.Bridge.OpenAIStatement.#2102840263._hygCtx._hyg.#24 : (List.{0} Nat)) => (LE.le.{0} (List.{0} Nat) (List.LE'.{0} Nat Nat.instLinearOrder) #1 #0)))", "y": "(fun (x1._@.ComparatorChallenges.SubexponentialSAT.#2102840263._hygCtx._hyg.#24 : (List.{0} Nat)) => (fun (x2._@.ComparatorChallenges.SubexponentialSAT.#2102840263._hygCtx._hyg.#24 : (List.{0} Nat)) => (LE.le.{0} (List.{0} Nat) (List.LE'.{0} Nat Nat.instLinearOrder) #1 #0)))", "xIn": "(Finset.sort.{0} (List.{0} Nat) (Finset.image.{0, 0} (OAI.Algorithms.SubexponentialSAT.SAT.Clause.{0} (Fin #1)) (List.{0} Nat) (fun (a : (List.{0} Nat)) => (fun (b : (List.{0} Nat)) => (instDecidableEqList.{0} Nat instDecidableEqNat #1 #0))) (OAI.Algorithms.SubexponentialSAT.Encoding.clauseNumbers #1) #0) (fun (x1._@.B…", "yIn": "(Finset.sort.{0} (List.{0} Nat) (Finset.image.{0, 0} (OAI.Algorithms.SubexponentialSAT.SAT.Clause.{0} (Fin #1)) (List.{0} Nat) (fun (a : (List.{0} Nat)) => (fun (b : (List.{0} Nat)) => (instDecidableEqList.{0} Nat 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(x._@.Mathlib.Data.Multiset.Defs.#3805720009._hygCtx._hyg.#12 : (List.{u0} #0)), (∀ (x._@.Mathlib.Data.Multiset.Defs.#3805720009._hygCtx._hyg.#14 : (List.{u0} #1)), (∀ (p : (Setoid.r.{(u0+1)} (List.{u0} #2) (List.isSetoid.{u0} #2) #1 #0)), (Eq.{1} Sort 0 (List.Nodup.{u0} #3 #2) (List.Nodup.{u0} #3 #1)))))", "xIn": null, "yIn": null } }, { "name": "IsAbsoluteValue.mk", "kind": "ctor", "differs": [ "universe parameter names", "type (binder names, binder infos or metadata)" ], "diff": { "x": [ "u_5", "u_6" ], "y": [ "u_4", "u_5" ] } }, { "name": "IsAbsoluteValue.rec", "kind": "rec", "differs": [ "universe parameter names", "type (binder names, binder infos or metadata)", "recursor rules (binder names)" ], "diff": { "x": [ "u", "u_5", "u_6" ], "y": [ "u", "u_4", "u_5" ] } }, { "name": "IsAbsoluteValue.abv_mul'", "kind": "thm", "differs": [ "universe parameter names", "type (binder names, binder infos or metadata)" ], "diff": { "x": [ "u_5", "u_6" ], "y": [ "u_4", "u_5" ] } }, { "name": "IsAbsoluteValue.abv_add'", "kind": "thm", "differs": [ "universe parameter names", "type (binder names, binder infos or metadata)" ], "diff": { "x": [ "u_5", "u_6" ], "y": [ "u_4", "u_5" ] } }, { "name": "IsAbsoluteValue.abv_nonneg'", "kind": "thm", "differs": [ "universe parameter names", "type (binder names, binder infos or metadata)" ], "diff": { "x": [ "u_5", "u_6" ], "y": [ "u_4", "u_5" ] } }, { "name": "IsAbsoluteValue.abv_eq_zero'", "kind": "thm", "differs": [ "universe parameter names", "type (binder names, binder infos or metadata)" ], "diff": { "x": [ "u_5", "u_6" ], "y": [ "u_4", "u_5" ] } }, { "name": "AddCommGroup", "kind": "induct", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "CommMonoid", "kind": "induct", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "SubNegMonoid.toAddMonoid", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "AddGroup.toSubNegMonoid", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "CommMonoid.toMonoid", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "SubNegMonoid.toNeg", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "SubNegMonoid.toSub", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "SubNegMonoid.toZSMul", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "ZPow.mk", "kind": "ctor", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "ZPow", "kind": "induct", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "ZPow.toPow", "kind": "def", "differs": [ "type 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"SubtractionMonoid.toSubNegMonoid", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "AddSemigroup.mk", "kind": "ctor", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "NSMul.mk", "kind": "ctor", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "ZSMul.mk", "kind": "ctor", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "Complex.ofReal", "kind": "def", "differs": [ "reducibility hints" ], "diff": { "x": "regular 3", "y": "regular 2" } }, { "name": "DivInvMonoid", "kind": "induct", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "DivInvMonoid.div'", "kind": "def", "differs": [ "universe parameter names", "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "zpowRec", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "at": "∀ G body", "why": "binder name or info", "x": "(∀ (inst._@.Mathlib.Algebra.Group.Defs.#3242858790._hygCtx._hyg.#3 : (One.{u0} #0)), (∀ (inst._@.Mathlib.Algebra.Group.Defs.#3242858790._hygCtx._hyg.#6 : (Mul.{u0} #1)), (∀ (inst._@.Mathlib.Algebra.Group.Defs.#3242858790._hygCtx._hyg.#9 : (Inv.{u0} #2)), (∀ (npow : (optParam.{(u0+1)} (∀ (a._@._internal._hyg.#0 : Nat), …", "y": "(∀ (inst._@.Mathlib.Algebra.Group.DivInvMonoid.#3242858790._hygCtx._hyg.#3 : (One.{u0} #0)), (∀ (inst._@.Mathlib.Algebra.Group.DivInvMonoid.#3242858790._hygCtx._hyg.#6 : (Mul.{u0} #1)), (∀ (inst._@.Mathlib.Algebra.Group.DivInvMonoid.#3242858790._hygCtx._hyg.#9 : (Inv.{u0} #2)), (∀ (npow : (optParam.{(u0+1)} (∀ (a._@._i…", "xIn": null, "yIn": null } }, { "name": "Real.decidableEq", "kind": "def", "differs": [ "reducibility hints" ], "diff": 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"why": "binder name or info", "x": "(∀ (inst._@.Mathlib.Algebra.Group.Defs.#148871010._hygCtx._hyg.#4 : (ZSMul.{u0} #0)), (SMul.{0, u0} Int #1))", "y": "(∀ (inst._@.Mathlib.Algebra.Group.DivInvMonoid.#148871009._hygCtx._hyg.#4 : (ZSMul.{u0} #0)), (SMul.{0, u0} Int #1))", "xIn": null, "yIn": null } }, { "name": "Semigroup.mk", "kind": "ctor", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "AddMonoid", "kind": "induct", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "ZPow.rec", "kind": "rec", "differs": [ "universe parameter names" ], "diff": { "x": [ "u_1", "u" ], "y": [ "u", "u_2" ] } }, { "name": "ZPow.zpow", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "Semigroup.rec", "kind": "rec", "differs": [ "universe parameter names" ], "diff": { "x": [ "u_1", "u" ], "y": [ "u", "u_2" ] } }, { "name": "Semigroup.mul_assoc", 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"Real.commRing._proof_10", "kind": "thm", "differs": [ "type (binder names, binder infos or metadata)" ], "diff": { "at": "∀ x body › arg 2 of Eq.{1} › arg 4 of HPow.hPow.{0, 0, 0} › arg 3 of instHPow.{0, 0} › arg 2 of NPow.toPow.{0} › arg 2 of NPow.mk.{0} › arg 3 of npowRec.{0} › arg 2 of Mul.mk.{0}", "why": "binder name or info", "x": "(fun (x1._@.Mathlib.Data.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (fun (x2._@.Mathlib.Data.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMul) #1 #0)))", "y": "(fun (x1._@.Mathlib.Basic.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (fun (x2._@.Mathlib.Basic.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMul) #1 #0)))", "xIn": "(Mul.mk.{0} Real (fun (x1._@.Mathlib.Data.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (fun (x2._@.Mathlib.Data.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => 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(x1._@.Mathlib.Basic.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (fun (x2._@.Mathlib.Basic.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMul) #1 #0)))", "xIn": "(Mul.mk.{0} Real (fun (x1._@.Mathlib.Data.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (fun (x2._@.Mathlib.Data.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMul) #1 #0))))", "yIn": "(Mul.mk.{0} Real (fun (x1._@.Mathlib.Basic.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (fun (x2._@.Mathlib.Basic.Real.Basic.#2614265405._hygCtx._hyg.#81 : Real) => (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMul) #1 #0))))" } }, { "name": "Real.instSub", "kind": "def", "differs": [ "reducibility hints" ], "diff": { "x": "regular 3", "y": "regular 2" } }, { "name": "zsmulRec", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, 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(Finset.…", "yIn": "(Exists.{0} (Membership.mem.{u0, u0} #4 (Finset.{u0} #4) (SetLike.instMembership.{u0, u0} (Finset.{u0} #4) #4 (Finset.instSetLike.{u0} #4)) #3 #0) (fun (x._@.Mathlib.Data.Finset.Defs.#4269110057._hygCtx._hyg.#65 : (Membership.mem.{u0, u0} #4 (Finset.{u0} #4) (SetLike.instMembership.{u0, u0} (Finset.{u0} #4) #4 (Finset.…" } }, { "name": "Multiset.decidableForallMultiset", "kind": "def", "differs": [ "type (binder names, binder infos or metadata)", "value (binder names, binder infos or metadata)" ], "diff": { "at": "∀ α body › ∀ m body › ∀ p body", "why": "binder name or info", "x": "(∀ (inst._@.Mathlib.Data.Multiset.Defs.#2960937607._hygCtx._hyg.#10 : (∀ (a : #2), (Decidable (#1 #0)))), (Decidable (∀ (a : #3), (∀ (a._@._internal._hyg.#0 : (Membership.mem.{u0, u0} #4 (Multiset.{u0} #4) (Multiset.instMembership.{u0} #4) #3 #0)), (#3 #1)))))", "y": "(∀ (inst._@.Mathlib.Data.Multiset.Defs.#2960937607._hygCtx._hyg.#9 : (∀ (a : #2), (Decidable (#1 #0)))), (Decidable (∀ (a 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"u_2" ] } }, { "name": "NSMul.rec", "kind": "rec", "differs": [ "universe parameter names" ], "diff": { "x": [ "u_1", "u" ], "y": [ "u", "u_2" ] } }, { "name": "NSMul.nsmul", "kind": "def", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "Complex.instZero", "kind": "def", "differs": [ "reducibility hints" ], "diff": { "x": "regular 4", "y": "regular 3" } }, { "name": "Complex.instOne", "kind": "def", "differs": [ "reducibility hints" ], "diff": { "x": "regular 4", "y": "regular 3" } }, { "name": "Complex.instMul", "kind": "def", "differs": [ "reducibility hints" ], "diff": { "x": "regular 3", "y": "regular 2" } }, { "name": "MulOneClass", "kind": "induct", "differs": [ "universe parameter names" ], "diff": { "x": [ "u" ], "y": [ "u_2" ] } }, { "name": "Real.leTotal_R", "kind": "thm", "differs": [ "type (binder names, binder infos or metadata)" ], "diff": { "at": "arg 2 of Std.Total.{1}", "why": "binder name or info", "x": "(fun 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"Finset.decidableExistsAndFinset._proof_1", "kind": "thm", "differs": [ "type (binder names, binder infos or metadata)" ], "diff": { "at": "∀ α body › ∀ s body › ∀ p body › arg 1 of Iff › arg 2 of Exists.{(u0+1)} › λ a body › arg 2 of Exists.{0}", "why": "binder name or info", "x": "(fun (x._@.Mathlib.Data.Finset.Defs.#4269110057._hygCtx._hyg.#66 : (Membership.mem.{u0, u0} #3 (Finset.{u0} #3) (SetLike.instMembership.{u0, u0} (Finset.{u0} #3) #3 (Finset.instSetLike.{u0} #3)) #2 #0)) => (#2 #1))", "y": "(fun (x._@.Mathlib.Data.Finset.Defs.#4269110057._hygCtx._hyg.#65 : (Membership.mem.{u0, u0} #3 (Finset.{u0} #3) (SetLike.instMembership.{u0, u0} (Finset.{u0} #3) #3 (Finset.instSetLike.{u0} #3)) #2 #0)) => (#2 #1))", "xIn": "(Exists.{0} (Membership.mem.{u0, u0} #3 (Finset.{u0} #3) (SetLike.instMembership.{u0, u0} (Finset.{u0} #3) #3 (Finset.instSetLike.{u0} #3)) #2 #0) (fun (x._@.Mathlib.Data.Finset.Defs.#4269110057._hygCtx._hyg.#66 : (Membership.mem.{u0, u0} #3 (Finset.{u0} #3) 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{ "x": [ "u_1", "u" ], "y": [ "u", "u_2" ] } } ] }, "chain": { "note": "the headline factored: the same text on the two sides, then the declared change (theorem → def ClaimAt + def Claim) on each side", "challengeAcrossSides": { "statementTerm": { "kernelEqual": true, "surfaceEqual": true, "erasedEqual": true, "kernelDiff": null, "surfaceDiff": null, "nodes": [ 335, 335 ] }, "identical": false, "identicalModuloProofs": false, "surfaceIdentical": false, "constants": { "anthropic": { "full": 2634, "erased": 2042 }, "openai": { "full": 2640, "erased": 2048 }, "common": 2585 }, "presentOnly": { "anthropic": 49, "openai": 55 }, "kernelDiffer": 308, "surfaceOnly": 201, "erased": { "presentOnly": { "anthropic": 37, "openai": 43 }, "differ": 225 }, "differences": [ { "name": "Real.instLT", "class": "definitional", "differs": [ "value" ] }, { "name": "Real.instZero", "class": "definitional", "differs": [ "value" ] }, { "name": "Real.instLE", "class": "definitional", "differs": [ "value" ] }, { 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"Semiring.mul_zero", "class": "definitional", "differs": [ "type" ] }, { "name": "Semiring.left_distrib", "class": "definitional", "differs": [ "type" ] }, { "name": "Real.commRing", "class": "definitional", "differs": [ "value" ] }, { "name": "CauSeq.instLTAbs", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.Completion.instZeroCauchy", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "Bool.not", "class": "definitional", "differs": [ "value" ] }, { "name": "Semiring.toNonAssocSemiring", "class": "definitional", "differs": [ "value" ] }, { "name": "DivisionSemiring.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "DivisionSemiring.div_eq_mul_inv", "class": "definitional", "differs": [ "type" ] }, { "name": "DivisionSemiring.mul_inv_cancel", "class": "definitional", "differs": [ "type" ] }, { "name": "DivisionSemiring.nnqsmul_def", "class": "definitional", "differs": [ "type" ] }, { "name": "DivisionSemiring.zpow_succ'", "class": "definitional", "differs": [ "type" ] }, { "name": "Semifield.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "AddMonoid.toAddSemigroup", "class": "definitional", "differs": [ "value" ] }, { "name": "CauSeq.ofEq", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.instAdd", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.instNeg", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.instSub._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "AddCommGroup.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "CommMonoid.mk", "class": "definitional", "differs": [ "type" ] }, { "name": "CommMonoid.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "Bool.and", "class": "definitional", "differs": [ "value" ] }, { "name": "SubtractionMonoid.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "SubtractionMonoid.neg_add_rev", "class": "definitional", "differs": [ "type" ] }, { "name": "SubtractionMonoid.neg_eq_of_add", "class": "definitional", "differs": [ "type" ] }, { "name": "SubNegMonoid.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "SubNegMonoid.sub_eq_add_neg", "class": "definitional", "differs": [ "type" ] }, { "name": "SubNegMonoid.zsmul_succ'", "class": "definitional", "differs": [ "type" ] }, { "name": "AddGroupWithOne.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "IsCauSeq.const", "class": "proof-reach", "differs": [ "type" ] }, { "name": "DivInvMonoid.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "DivInvMonoid.div_eq_mul_inv", "class": "definitional", "differs": [ "type" ] }, { "name": "DivInvMonoid.zpow_succ'", "class": "definitional", "differs": [ "type" ] }, { "name": "MulOneClass.toMulOne", "class": "definitional", "differs": [ "value" ] }, { "name": "Monoid.toMulOneClass", "class": "definitional", "differs": [ "value" ] }, { "name": "StrictMono.orderIsoOfSurjective", "class": "definitional", "differs": [ "value" ] }, { "name": "Real.instMax", "class": "definitional", "differs": [ "value" ] }, { "name": "AddZeroClass.mk", "class": "definitional", "differs": [ "kernel facts", "type" ] }, { "name": "AddMonoid.zero_add", "class": "definitional", "differs": [ "type" ] }, { "name": "AddMonoid.add_zero", "class": "definitional", "differs": [ "type" ] }, { "name": "AddCancelCommMonoid.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "AddCancelCommMonoid.toIsLeftCancelAdd", "class": "definitional", "differs": [ "type" ] }, { "name": "CauSeq.Completion.instMulCauchy", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CommSemiring.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "CommSemiring.mul_comm", "class": "definitional", "differs": [ "type" ] }, { "name": "Real.instNeg", "class": "definitional", "differs": [ "value" ] }, { "name": "CauSeq.Completion.instIntCastCauchy", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.Completion.instAddCauchy", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.Completion.instOneCauchy", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.Pos", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.instLTAbs._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CauSeq.Completion.ofRat", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "AddCommMonoidWithOne.mk", "class": "definitional", "differs": [ "type" ] }, { "name": "NonAssocSemiring.natCast_succ", "class": "definitional", "differs": [ "type" ] }, { "name": "NonAssocSemiring.mk", "class": "definitional", "differs": [ "type" ] }, { "name": "NonUnitalNonAssocSemiring.mk", "class": "definitional", "differs": [ "type" ] }, { "name": "NonUnitalNonAssocSemiring.toDistrib", "class": "definitional", "differs": [ "value" ] }, { "name": "CauSeq.ofEq._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CauSeq.instAdd._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CauSeq.instNeg._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "AddMonoid.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "AddMonoid.nsmul_succ", "class": "definitional", "differs": [ "type" ] }, { "name": "AddMonoid.toNSMul", "class": "definitional", "differs": [ "value" ] }, { "name": "CommMonoidWithZero.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "CommMonoidWithZero.zero_mul", "class": "definitional", "differs": [ "type" ] }, { "name": "CommMonoidWithZero.mul_zero", "class": "definitional", "differs": [ "type" ] }, { "name": "AddMonoidWithOne.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "AddMonoidWithOne.natCast_succ", "class": "definitional", "differs": [ "type" ] }, { "name": "MulOneClass.mk", "class": "definitional", "differs": [ "kernel facts", "type" ] }, { "name": "Real.instMin", "class": "definitional", "differs": [ "value" ] }, { "name": "NNReal.instSemiring", "class": "definitional", "differs": [ "value" ] }, { "name": "AddZeroClass.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "AddZeroClass.zero_add", "class": "definitional", "differs": [ "type" ] }, { "name": "AddZeroClass.add_zero", "class": "definitional", "differs": [ "type" ] }, { "name": "CauSeq.instMul", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.mul_equiv_mul", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CauSeq.instIntCast", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.add_equiv_add", "class": "proof-reach", "differs": [ "type" ] }, { "name": "AddCommMonoid.toAddCommSemigroup", "class": "definitional", "differs": [ "value" ] }, { "name": "AddCommMonoidWithOne.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "AddCommMonoidWithOne.add_comm", "class": "definitional", "differs": [ "type" ] }, { "name": "NonAssocSemiring.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "NonUnitalNonAssocSemiring.left_distrib", "class": "definitional", "differs": [ "type" ] }, { "name": "NonUnitalNonAssocSemiring.right_distrib", "class": "definitional", "differs": [ "type" ] }, { "name": "SubtractionCommMonoid.mk", "class": "definitional", "differs": [ "type" ] }, { "name": "NonUnitalNonAssocSemiring.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "MulOneClass.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "MulOneClass.mul_one", "class": "definitional", "differs": [ "type" ] }, { "name": "MulOneClass.one_mul", "class": "definitional", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._aux_1", "class": "definitional", "differs": [ "value" ] }, { "name": "NNReal.instSemiring._proof_4", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._proof_5", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._aux_6", "class": "definitional", "differs": [ "value" ] }, { "name": "NNReal.instSemiring._proof_9", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._proof_10", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._aux_11", "class": "definitional", "differs": [ "value" ] }, { "name": "NNReal.instSemiring._proof_14", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._proof_15", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._aux_16", "class": "definitional", "differs": [ "value" ] }, { "name": "NNReal.instSemiring._proof_19", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._proof_20", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._proof_21", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._proof_22", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._proof_23", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._proof_26", "class": "proof-reach", "differs": [ "type" ] }, { "name": "NNReal.instSemiring._proof_27", "class": "proof-reach", "differs": [ "type" ] }, { "name": "MulZeroOneClass.toMulZeroClass", "class": "definitional", "differs": [ "value" ] }, { "name": "MonoidWithZero.toMulZeroOneClass", "class": "definitional", "differs": [ "value" ] }, { "name": "CauSeq.instMul._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "SubtractionCommMonoid.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "SubtractionCommMonoid.add_comm", "class": "definitional", "differs": [ "type" ] }, { "name": "CauSeq.Completion.instInvCauchy", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "Nonneg.add._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Nonneg.nsmul", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "Nonneg.mul._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Nonneg.pow", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "MulZeroOneClass.zero_mul", "class": "definitional", "differs": [ "type" ] }, { "name": "MulZeroOneClass.mul_zero", "class": "definitional", "differs": [ "type" ] }, { "name": "MulZeroOneClass.mk", "class": "definitional", "differs": [ "type" ] }, { "name": "MonoidWithZero.zero_mul", "class": "definitional", "differs": [ "type" ] }, { "name": "MonoidWithZero.mul_zero", "class": "definitional", "differs": [ "type" ] }, { "name": "MonoidWithZero.mk", "class": "definitional", "differs": [ "type" ] }, { "name": "Multiset.instAddCancelCommMonoid", "class": "definitional", "differs": [ "value" ] }, { "name": "CauSeq.lim", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "Real.instField", "class": "definitional", "differs": [ "value" ] }, { "name": "NonAssocSemiring.toMulZeroOneClass", "class": "definitional", "differs": [ "value" ] }, { "name": "Real.sinOrderIso", "class": "definitional", "differs": [ "value" ] }, { "name": "CauSeq.instZero", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.inv", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.Completion.instInvCauchy._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Nonneg.semilatticeSup._aux_1", "class": "proof-internal", "differs": [ "value" ] }, { "name": "Nonneg.nsmul._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Nonneg.pow._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "MonoidWithZero.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "MulZeroOneClass.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "CauSeq.instMaxAbs", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.sup_equiv_sup", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CauSeq.Completion.instNegCauchy", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.IsComplete", "class": "definitional", "differs": [ "type" ] }, { "name": "CauSeq.complete", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Real.instField._proof_5", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Real.instField._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Real.instField._proof_2", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.commRing", "class": "definitional", "differs": [ "value" ] }, { "name": "Complex.instDivInvMonoid", "class": "definitional", "differs": [ "value" ] }, { "name": "CauSeq.inv_aux", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CauSeq.instMinAbs", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.inf_equiv_inf", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Set.Ici.semilatticeSup._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CauSeq.instMaxAbs._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CauSeq.neg_equiv_neg", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CauSeq.IsComplete.mk", "class": "definitional", "differs": [ "type" ] }, { "name": "CauSeq.IsComplete.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "CauSeq.IsComplete.isComplete", "class": "definitional", "differs": [ "type" ] }, { "name": "CauSeq.Completion.instNNRatCast", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "CauSeq.Completion.instRatCast", "class": "definitional", "differs": [ "type", "value" ] }, { "name": "Complex.commRing._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.commRing._proof_9", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.commRing._proof_10", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.commRing._proof_13", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.instDivInvMonoid._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.instDivInvMonoid._proof_2", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.instDivInvMonoid._proof_3", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.instDivInvMonoid._proof_4", "class": "proof-reach", "differs": [ "type" ] }, { "name": "DivisionMonoid.mk", "class": "definitional", "differs": [ "type" ] }, { "name": "GroupWithZero.toDivisionMonoid._proof_2", "class": "proof-reach", "differs": [ "type" ] }, { "name": "GroupWithZero.toDivisionMonoid._proof_3", "class": "proof-reach", "differs": [ "type" ] }, { "name": "GroupWithZero.mk", "class": "definitional", "differs": [ "type" ] }, { "name": "CauSeq.instMinAbs._proof_1", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.addCommGroup", "class": "definitional", "differs": [ "value" ] }, { "name": "Complex.addGroupWithOne._proof_2", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.addGroupWithOne._proof_5", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.addGroupWithOne._proof_7", "class": "proof-reach", "differs": [ "type" ] }, { "name": "Complex.addGroupWithOne._proof_9", "class": "proof-reach", "differs": [ "type" ] }, { "name": "DivisionMonoid.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "DivisionMonoid.mul_inv_rev", "class": "definitional", "differs": [ "type" ] }, { "name": "DivisionMonoid.inv_eq_of_mul", "class": "definitional", "differs": [ "type" ] }, { "name": "GroupWithZero.rec", "class": "definitional", "differs": [ "type", "recursor rules" ] }, { "name": "GroupWithZero.div_eq_mul_inv", "class": "definitional", "differs": [ "type" ] }, { "name": "GroupWithZero.mul_inv_cancel", "class": "definitional", "differs": [ "type" ] }, { "name": "GroupWithZero.zpow_succ'", "class": "definitional", "differs": [ "type" ] }, { "name": "CommSemiring.toNonUnitalCommSemiring", "class": "definitional", "differs": [ "value" ] }, { "name": "NonUnitalNonAssocRing.left_distrib", "class": "definitional", "differs": [ "type" ] }, { "name": "NonUnitalNonAssocRing.right_distrib", "class": "definitional", "differs": [ "type" ] }, { "name": "CommRing.toNonUnitalCommRing", "class": "definitional", "differs": [ "value" ] }, { "name": "CommSemiring.toNonUnitalCommSemiring._proof_1", "class": "proof-reach", "differs": [ "type" ] 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"proof-reach", "differs": [ "type" ] }, { "name": "CommRing.toNonUnitalCommRing._proof_7", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CommRing.toNonUnitalCommRing._proof_8", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CommRing.toNonUnitalCommRing._proof_9", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CommRing.toNonUnitalCommRing._proof_10", "class": "proof-reach", "differs": [ "type" ] }, { "name": "CommRing.toNonUnitalCommRing._proof_11", "class": "proof-reach", "differs": [ "type" ] }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.lt", "class": "definitional", "differs": "present only on anthropic" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.zero", "class": "definitional", "differs": "present only on anthropic" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.le", "class": "definitional", "differs": "present only on anthropic" }, { "name": "_private.Mathlib.Data.Real.Basic.#0.Real.mul", "class": "definitional", 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"surfaceIdentical": false, "constants": { "claim": { "full": 2634, "erased": 2042 }, "challenge": { "full": 2634, "erased": 2042 }, "common": 2634 }, "presentOnly": { "claim": 0, "challenge": 0 }, "kernelDiffer": 0, "surfaceOnly": 18, "erased": { "presentOnly": { "claim": 0, "challenge": 0 }, "differ": 0 } }, "claimVsChallengeOpenAI": { "statementTerm": { "kernelEqual": true, "surfaceEqual": false, "erasedEqual": true, "kernelDiff": null, "surfaceDiff": { "at": "∀ k body", "why": "binder name or info", "x": "(∀ (a._@._internal._hyg.#0 : (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) #0)), (Exists.{1} OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine (fun (machine : OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine) => (Exists.{1} (Fin (OAI.Algorithms.SubexponentialSAT.Computation.…", "y": "(∀ (hk : (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) #0)), (Exists.{1} OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine (fun (machine : OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine) => (Exists.{1} (Fin (OAI.Algorithms.SubexponentialSAT.Computation.PrimitiveMachine.tap…", "xIn": null, "yIn": null }, "nodes": [ 335, 335 ] }, "identical": true, "identicalModuloProofs": true, "surfaceIdentical": false, "constants": { "claim": { "full": 2640, "erased": 2048 }, "challenge": { "full": 2640, "erased": 2048 }, "common": 2640 }, "presentOnly": { "claim": 0, "challenge": 0 }, "kernelDiffer": 0, "surfaceOnly": 18, "erased": { "presentOnly": { "claim": 0, "challenge": 0 }, "differ": 0 } } }, "classes": { "proof-internal": "the constant differs, but after proof erasure the two terms are the same (the kernel identifies proofs of one proposition)", "proof-reach": "in neither proof-erased closure: only proofs reach it (a theorem's statement, or a definition only a proof mentions), so it cannot change what the statement says", "definitional": "differs outside proofs, or is present on one side only inside the proof-erased closure: the statement's meaning may depend on it" }, "run": { "id": 40947568989, "url": "https://github.com/carlostoledo1891/cert-machine/actions/runs/40947568989", "commit": "787a9fd15076283880133c76f112873cdb13cd30", "branch": "eth-seam", "createdAt": "2026-10-29T20:16:37Z", "conclusion": "success", "jobs": [ { "name": "smoke (v4.34.1)", "conclusion": "success", "startedAt": "2026-10-29T20:16:41Z", "completedAt": "2026-10-29T20:17:07Z" }, { "name": "smoke (v4.33.1)", "conclusion": "success", "startedAt": "2026-10-29T20:16:40Z", "completedAt": "2026-10-29T20:17:02Z" }, { "name": "export (anthropic)", "conclusion": "success", "startedAt": "2026-10-29T20:17:10Z", "completedAt": "2026-10-29T20:21:06Z" }, { "name": "export (openai)", "conclusion": "success", "startedAt": "2026-10-29T20:17:10Z", "completedAt": "2026-10-29T20:22:13Z" }, { "name": "cross (openai, anthropic)", "conclusion": "success", "startedAt": "2026-10-29T20:22:16Z", "completedAt": "2026-10-29T20:26:31Z" }, { "name": "cross (anthropic, openai)", "conclusion": "success", "startedAt": "2026-10-29T20:22:16Z", "completedAt": "2026-10-29T20:25:37Z" } ] }, "steps": { "openai": { "env": [ "side: openai", "toolchain: leanprover/lean4:v4.34.1", "Lean (version 4.34.1, x86_64-unknown-linux-gnu, commit 5045d0056413266e57c625dcd7c365b10e377c52, Release)", "Lake version 5.0.0-src+5045d00 (Lean version 4.34.1)", "mathlib: d13f23b723b8a846827a245b89c10fc7d3f11612", "commit: 787a9fd15076283880133c76f112873cdb13cd30", "run: 40947568989 attempt 1" ], "buildExit": 0, "buildErrors": [], "sorryWarnings": [ "seam/ComparatorChallenges/SubexponentialSAT.lean" ], "exports": { "challenge": { "exit": 0, "seconds": 7, "maxRssKB": 7624384, "line": "SeamExport challenge: 2641 constants in the closure, 2049 after proof erasure, 0 missing, truncated false, erase errors 0" }, "claim": { "exit": 0, "seconds": 8, "maxRssKB": 7624700, "line": "SeamExport claim: 2642 constants in the closure, 2050 after proof erasure, 0 missing, truncated false, erase errors 0" } } }, "anthropic": { "env": [ "side: anthropic", "toolchain: leanprover/lean4:v4.33.1", "Lean (version 4.33.1, x86_64-unknown-linux-gnu, commit 819816b2e0a3bf405af45ae5c7af2491d8f5bee6, Release)", "Lake version 5.0.0-src+819816b (Lean version 4.33.1)", "mathlib: 0df444a360eaa60ab8c11dca51a86af692955474", "commit: 787a9fd15076283880133c76f112873cdb13cd30", "run: 40947568989 attempt 1" ], "buildExit": 0, "buildErrors": [], "sorryWarnings": [ "seam/ComparatorChallenges/SubexponentialSAT.lean", "bridge/BridgeChallenge.lean" ], "exports": { "challenge": { "exit": 0, "seconds": 7, "maxRssKB": 7513280, "line": "SeamExport challenge: 2635 constants in the closure, 2043 after proof erasure, 0 missing, truncated false, erase errors 0" }, "claim": { "exit": 0, "seconds": 7, "maxRssKB": 7513816, "line": "SeamExport claim: 2636 constants in the closure, 2044 after proof erasure, 0 missing, truncated false, erase errors 0" }, "bridge": { "exit": 0, "seconds": 4, "maxRssKB": 7497316, "line": "SeamExport bridge: 0 constants in the closure, 0 after proof erasure, 0 missing, truncated false, erase errors 0" } } } }, "logs": "corpus/eth-refutation/seam/runs/40947568989", "gaps": [ "The comparison is of terms, not of meanings: two different kernel terms can still denote the same proposition; DIFFERENT says only that the terms differ, and the classes say where.", "The kernel check across the sides is constant by constant: a foreign term is read with the LOCAL meaning of every constant it names. It identifies differences of instance paths and of compilation; it cannot identify two different inductive types (the Monoid constructors of the two Mathlibs), so ℝ's ring and field structures stay unidentified, and no single kernel has checked that the two statements are the same proposition.", "The groups are our reading of the diffs, by name patterns written after reading them (GROUPS in this tool); the kernel statuses and the diffs beside each difference are the evidence.", "Proof erasure trusts Meta.isProof on each subterm (Lean's elaborator-side type inference, not the kernel); an erase error is counted in each export header (eraseErrors) and keeps the subterm, which can only add differences, never hide one.", "The exports are written by our metaprogram running inside each Lean; a bug in it that is the same on both sides would hide nothing it serialises faithfully but could miss a field it does not serialise: the kernel-relevant fields written are kind, universe parameters, type, value, safety, mutual block, inductive/constructor/recursor counts and flags, and recursor rules.", "OpenAI's side is our project on OpenAI's toolchain and Mathlib (as corpus/eth-refutation/bridge/openai), not openai/math itself: the challenge module imports Mathlib alone, so the other dependencies of openai/math cannot reach its elaboration; the package option is autoImplicit false, as theirs." ] }