name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Finset.sum_mk | Mathlib.Algebra.BigOperators.Group.Finset.Defs | [
"Multiset.sum",
"Multiset.Nodup",
"Multiset.map",
"Multiset",
"AddCommMonoid",
"Finset.mk",
"Eq",
"Finset.sum",
"rfl"
] | true |
Std.Time.Millisecond.Offset.ofNat | Std.Time.Time.Unit.Millisecond | [
"Rat.instOfNat",
"instHDiv",
"Std.Time.Internal.UnitVal.ofInt",
"Rat",
"HDiv.hDiv",
"Int",
"Nat.cast",
"Nat",
"Std.Time.Millisecond.Offset",
"instNatCastInt",
"OfNat.ofNat",
"Rat.instDiv"
] | true |
AlgebraicGeometry.Scheme.emptyTo_base | Mathlib.AlgebraicGeometry.Limits | [
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommRingCat",
"TopCat.instCategory",
"ContinuousMap.mk",
"instTopologicalSpacePEmpty",
"CommRingCat.instCategory",
"AlgebraicGeometry.Scheme.emptyTo._proof_1",
"PEmpty",
"AlgebraicGeometry.LocallyRingedSpace.Hom... | true |
CategoryTheory.instDecidableEqPairwise.decEq._proof_6 | Mathlib.CategoryTheory.Category.Pairwise | [
"False",
"CategoryTheory.Pairwise.pair.noConfusion",
"CategoryTheory.Pairwise",
"eq_of_heq",
"HEq",
"Eq",
"CategoryTheory.Pairwise.pair",
"Not"
] | false |
Lean.Environment.contains | Lean.Environment | [
"Bool.true",
"Bool",
"Lean.Name",
"optParam",
"Option.isSome",
"Lean.Environment.findAsync?",
"Lean.AsyncConstantInfo",
"Lean.Environment"
] | true |
CauSeq.Completion.instNNRatCast | Mathlib.Algebra.Order.CauSeq.Completion | [
"NNRatCast",
"LinearOrder",
"CauSeq.Completion.Cauchy",
"IsStrictOrderedRing",
"CauSeq.Completion.ofRat",
"SemilatticeInf.toPartialOrder",
"DivisionRing.toDivisionSemiring",
"DistribLattice.toLattice",
"NNRatCast.mk",
"NNRat",
"DivisionRing.toRing",
"Field.toSemifield",
"Semifield.toDivision... | true |
AddOpposite.instAddRightCancelSemigroup._proof_1 | Mathlib.Algebra.Group.Opposite | [
"IsRightCancelAdd",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"AddLeftCancelSemigroup",
"AddOpposite",
"add_right_cancel",
"AddSemigroup.toAdd",
"AddLeftCancelSemigroup.toAddSemigroup",
"AddOpposite.instAddSemigroup",
"IsRightCancelAdd.mk",
"AddOpposite.instIsRightCancelAdd"
] | false |
Lean.Meta.Match.AltParamInfo.ctorIdx | Lean.Meta.Match.MatcherInfo | [
"Lean.Meta.Match.AltParamInfo",
"Nat"
] | false |
IO.Process.Stdio.ctorElimType | Init.System.IO | [
"cond",
"Nat.ble",
"IO.Process.Stdio.inherit",
"IO.Process.Stdio.null",
"PULift",
"IO.Process.Stdio",
"Nat",
"IO.Process.Stdio.piped"
] | false |
Representation.IntertwiningMap.coe_add | Mathlib.RepresentationTheory.Intertwining | [
"Monoid",
"Representation",
"Representation.IntertwiningMap.instAdd",
"Representation.IntertwiningMap.instFunLike",
"AddCommMonoid",
"instHAdd",
"Pi.instAdd",
"HAdd.hAdd",
"Semiring",
"Representation.IntertwiningMap",
"AddCommSemigroup.toAddCommMagma",
"Module",
"AddCommMonoid.toAddCommSemig... | true |
AddChar.zmod_add | Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality | [
"add_mul",
"Nat.instMulZeroClass",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"AddMonoidHom.instAddMonoidHomClass",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"ZMod.commRing",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddM... | true |
SemiNormedGrp₁.Hom._sizeOf_1 | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"NormedAddGroupHom",
"instSizeOfDefault",
"SemiNormedGrp₁",
"NormedAddGroupHom._sizeOf_inst",
"instOfNatNat",
"SemiNormedGrp₁.Hom",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SemiNormedGrp₁.carrier",
"SizeOf.sizeOf",
"SemiNormedGrp₁.str",
"SemiNormedGrp₁.Hom.rec",
"instAddNat",
"OfNat.ofNat",
"N... | false |
CategoryTheory.JointlyReflectIsomorphisms.mk._flat_ctor | Mathlib.CategoryTheory.Functor.ReflectsIso.Jointly | [
"CategoryTheory.JointlyReflectIsomorphisms",
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.map",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.obj",
"CategoryTheory.JointlyReflectIsomorphisms.mk... | false |
ENNReal.sum_le_tsum | Mathlib.Topology.Algebra.InfiniteSum.ENNReal | [
"ENNReal.instCanonicallyOrderedAdd",
"zero_le",
"ENNReal.instAddCommMonoid",
"instIsBotZeroClass",
"Finset",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"ENNReal.summable",
"SummationFilter.instLeAtTopUnconditional",
"Ad... | true |
_private.Mathlib.Algebra.Order.Round.0.round_neg_two_inv._simp_1_1 | Mathlib.Algebra.Order.Round | [
"Int.cast",
"instHDiv",
"AddGroupWithOne.toAddGroup",
"LinearOrder",
"PartialOrder.toPreorder",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"IsStrictOrderedRing",
"Membership.mem",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DivisionRing.to... | false |
eVariationOn.comp_le_of_monotoneOn | Mathlib.Topology.EMetricSpace.BoundedVariation | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"le_rfl",
"ENNReal.instAddCommMonoid",
"CompletelyDistribLattice.toCompleteLattice",
"LinearOrder",
"_private.Mathlib.Topology.EMetricSpace.BoundedVariation.0.eVariationOn.comp_le_of_monotoneOn.match_1_1",
"PartialOrder.toPreorder",
"Monotone",
"Preorde... | true |
_private.Mathlib.Analysis.MeanInequalities.0.ENNReal.inner_le_weight_mul_Lp_of_nonneg._simp_1_1 | Mathlib.Analysis.MeanInequalities | [
"Finset",
"Finset.sum_eq_zero_iff_of_nonneg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddLeftMono",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"PartialOrder",
"LE.le",
"AddCommMonoid",
"AddZero.toZero",
"Finset.instSetLike",
"propext",
"AddZero.toAdd",
... | false |
Aesop.Frontend.TacticConfig.erasedRules | Aesop.Frontend.Tactic | [
"Aesop.Frontend.TacticConfig",
"Array",
"Aesop.Frontend.RuleExpr"
] | true |
EMetric.Closeds.edist_eq | Mathlib.Topology.MetricSpace.Closeds | [
"TopologicalSpace.Closeds.instSetLike",
"TopologicalSpace.Closeds.edist_eq",
"EMetricSpace.toPseudoEMetricSpace",
"EMetricSpace",
"EMetricSpace.toWeakEMetricSpace",
"SetLike.coe",
"WeakPseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniformSpace",
"Metric.hausdorffEDist",
"WeakEMetricSpace.toWe... | true |
_private.Mathlib.MeasureTheory.Measure.Haar.Unique.0.MeasureTheory.Measure.integral_isMulLeftInvariant_isMulRightInvariant_combo._simp_1_10 | Mathlib.MeasureTheory.Measure.Haar.Unique | [
"HMul.hMul",
"Monoid.toMulOneClass",
"DivInvMonoid.toZPow",
"Group",
"zpow_one_add",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Int",
"Group.toDivInvMonoid",
"instHAdd",
"MulOneClass.toMulOne",
"HPow.hPow",
"instOfNat",
"HAdd.hAdd",
"Int.instAdd",
"instHPow",
"OfNat.ofNat",
"Eq.symm... | false |
Std.Packages.LinearPreorderOfLEArgs.isGE_compare | Init.Data.Order.PackageFactories | [
"Std.Packages.LinearPreorderOfLEArgs",
"Ord",
"Std.Packages.LinearPreorderOfLEArgs.toPreorderOfLEArgs",
"LE.le",
"Ord.compare",
"LE",
"Std.Packages.PreorderOfLEArgs.decidableLE",
"Bool.true",
"Std.Packages.LinearPreorderOfLEArgs.le_total",
"DecidableLE",
"Iff",
"Bool",
"Ordering.isGE",
"Or... | true |
_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.zetaMul_prime_pow_nonneg._simp_1_3 | Mathlib.NumberTheory.LSeries.Nonvanishing | [
"le_refl",
"Preorder.toLE",
"LE.le",
"True",
"eq_true",
"Eq",
"Preorder"
] | false |
Lean.Language.Lean.HeaderProcessedState | Lean.Language.Lean.Types | [
"Lean.Language.Lean.HeaderProcessedState.mk"
] | true |
LLVM.Attribute.noConfusion | Lean.Compiler.IR.LLVMBindings | [
"LLVM.Attribute.casesOn",
"LLVM.Attribute",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"LLVM.Attribute.noConfusionType",
"Eq",
"USize",
"LLVM.Context"
] | false |
MoritaEquivalence.ofAlgEquiv | Mathlib.RingTheory.Morita.Basic | [
"MoritaEquivalence",
"AlgEquiv.symm",
"Algebra",
"ModuleCat.restrictScalarsEquivalenceOfRingEquiv",
"CommSemiring",
"AlgEquiv",
"AlgEquiv.toRingEquiv",
"MoritaEquivalence.ofAlgEquiv._proof_1",
"Ring.toSemiring",
"Ring",
"MoritaEquivalence.mk"
] | true |
_private.Mathlib.CategoryTheory.Monoidal.Free.Coherence.0.CategoryTheory.FreeMonoidalCategory._aux_Mathlib_CategoryTheory_Monoidal_Free_Coherence___macroRules__private_Mathlib_CategoryTheory_Monoidal_Free_Coherence_0_CategoryTheory_FreeMonoidalCategory_termF_1 | Mathlib.CategoryTheory.Monoidal.Free.Coherence | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr... | false |
WeierstrassCurve.Projective.nonsingular_some | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"one_pow",
"AddGroup.toSubtractionMonoid",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"MulOne.toOne",
"WeierstrassCurve.Projective.toAffine",
"Ma... | true |
_private.Lean.Compiler.LCNF.PropagateBorrow.0.Lean.Compiler.LCNF.Decl.analyzePropagatedBorrows.collectCode._sparseCasesOn_1 | Lean.Compiler.LCNF.PropagateBorrow | [
"Lean.Compiler.LCNF.Arg.ctorIdx",
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.Arg.fvar",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"Lean.Compiler.LCNF.Arg.rec",
"instOfNatNat",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Purity.pure",
"Na... | false |
Lean.Server.Watchdog.handleWorkspaceSymbol | Lean.Server.Watchdog | [
"Pure.pure",
"instBEqFloat",
"Lean.Lsp.Location.mk",
"Lean.Server.References.MatchedDefinition.range",
"instAlternativeOption",
"Lean.privateToUserName?",
"Lean.Name.toString",
"Lean.Lsp.WorkspaceSymbolParams.query",
"Lean.Lsp.SymbolInformation",
"instMonadReaderOfReaderTOfMonad",
"ReaderT",
"... | true |
Rat.ctorIdx | Init.Data.Rat.Basic | [
"Rat",
"Nat"
] | false |
Lean.Elab.Deriving.Context.noConfusionType | Lean.Elab.Deriving.Util | [
"Lean.Elab.Deriving.Context",
"Lean.Elab.Deriving.Context.casesOn",
"Array",
"Bool",
"Lean.Name",
"Eq",
"Lean.InductiveVal"
] | false |
MeasureTheory.lintegral_deriv_eq_volume_image_of_monotoneOn | Mathlib.MeasureTheory.Function.JacobianOneDim | [
"IsModuleTopology.toContinuousSMul",
"MeasureTheory.lintegral_const",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"Real",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"MeasurableSet",
"IsTopologicalRing.toIsTopologicalSemi... | true |
Function.bicompl.bifunctor | Mathlib.Control.Bifunctor | [
"Functor",
"Bifunctor.bimap",
"Bifunctor",
"Function.bicompl",
"Bifunctor.mk",
"Functor.map"
] | true |
AlgEquiv.mopMatrix_apply | Mathlib.Data.Matrix.Basic | [
"Matrix",
"MulOpposite.instAlgebra",
"MulOpposite",
"Algebra",
"Matrix.instAlgebra",
"CommSemiring",
"Fintype",
"AlgEquiv",
"Matrix.transpose",
"MulOpposite.instSemiring",
"Matrix.map",
"Semiring",
"Eq.refl",
"MulOpposite.unop",
"Matrix.semiring",
"AlgEquiv.mopMatrix",
"Eq",
"DFunL... | true |
QuasiIsoAt.quasiIso | Mathlib.Algebra.Homology.QuasiIso | [
"CategoryTheory.ShortComplex.QuasiIso",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.HasHomology",
"CategoryTheory.ShortComplex",
"HomologicalComplex",
"CategoryTheory.ShortComplex.instCategor... | true |
Path.Homotopy.transReflReparamAux_zero | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | [
"Real.instIsOrderedRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"Mathlib.Meta.NormNum.IsNat.to_isNNRat",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"instDecidableTrue",
"GroupWithZero.toDivInvMonoid",
"Set.Icc.instZero",
"DivIn... | true |
Finset.weightedVSub_empty | Mathlib.LinearAlgebra.AffineSpace.Combination | [
"Pi.Function.module",
"Semiring.toModule",
"Pi.addCommMonoid",
"Ring.toNonAssocRing",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Finset",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"NonUnitalNonAssocRing.toNonUn... | true |
WType.Natα.zero.elim | Mathlib.Data.W.Constructions | [
"PULift.up",
"WType.Natα",
"Nat",
"WType.Natα.ctorIdx",
"WType.Natα.zero",
"Eq.symm",
"Eq",
"WType.Natα.ctorElim"
] | false |
_private.Mathlib.LinearAlgebra.Coevaluation.0.contractLeft_assoc_coevaluation._simp_1_2 | Mathlib.LinearAlgebra.Coevaluation | [
"Finset.mem_univ",
"Finset.univ",
"Finset",
"Membership.mem",
"Fintype",
"Finset.instSetLike",
"True",
"eq_true",
"Eq",
"SetLike.instMembership"
] | false |
Mathlib.Meta.NormNum.Result.toNNRat'.match_1 | Mathlib.Tactic.NormNum.Result | [
"Mathlib.Meta.NormNum.Result'.ctorIdx",
"Mathlib.Meta.NormNum.Result'.isNNRat",
"Lean.Expr.const",
"Rat",
"Mathlib.Meta.NormNum.Result'.isNat",
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Mathlib.Meta.NormNum.Result.toNNRat'._sparseCasesOn_1",
"Ma... | false |
Polynomial.roots_C_mul_X_sub_C_of_IsUnit | Mathlib.Algebra.Polynomial.Roots | [
"Units.val",
"Eq.mpr",
"Polynomial.C",
"NonAssocSemiring.toAddCommMonoidWithOne",
"IsDomain",
"MulOne.toOne",
"Polynomial.instOne",
"Semigroup.toMul",
"CommRing",
"Polynomial.C_1",
"Polynomial.roots",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRi... | true |
Std.ExtDHashMap.get!_insertIfNew | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.get!",
"instDecidableNot",
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"Std.ExtDHashMap.instDecidableMem",
"cast",
"LawfulBEq",
"Membership.mem",
"instDecidableEqBool",
"Std.ExtDHashMap.inductionOn",
"Std.ExtDHashMap... | true |
LightProfinite.of | Mathlib.Topology.Category.LightProfinite.Basic | [
"SecondCountableTopology",
"TotallyDisconnectedSpace",
"LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology",
"CompactSpace",
"TopologicalSpace",
"TopCat.str",
"And",
"TopCat.carrier",
"T2Space",
"CompHausLike.of",
"TopCat",
"LightProfinite"
] | true |
Filter.frequently_imp_distrib | Mathlib.Order.Filter.Basic | [
"congrArg",
"Filter.frequently_or_distrib._simp_1",
"Filter.Eventually",
"_private.Mathlib.Order.Filter.Basic.0.Filter.frequently_imp_distrib._simp_1_1",
"Filter.not_eventually._simp_1",
"Filter.Frequently",
"iff_self",
"funext",
"Iff",
"congr",
"True",
"of_eq_true",
"congrFun'",
"Or",
"... | true |
Set.sumEquiv_apply | Mathlib.Order.Hom.Set | [
"Set.sumEquiv",
"Prod.instLE_mathlib",
"Sum",
"Prod.mk",
"Sum.inl",
"LE.le",
"RelIso",
"Set.instLE",
"Set.preimage",
"Sum.inr",
"RelIso.instFunLike",
"Eq.refl",
"Prod",
"Eq",
"DFunLike.coe",
"Set"
] | true |
BitVec.shiftLeft_add_distrib | Init.Data.BitVec.Lemmas | [
"instPowNat",
"Nat.shiftLeft_eq",
"Nat.mod_mul_mod",
"Nat.recAux",
"HMul.hMul",
"congrArg",
"HShiftLeft.hShiftLeft",
"BitVec.instAdd",
"BitVec",
"Nat.instMod",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.shiftLeft_add_distrib._simp_1_1",
"instHMod",
"BitVec.instHShiftLeftNat",
"instMulNat",... | true |
SaturatedAddSubmonoid._sizeOf_inst | Mathlib.Algebra.Group.Submonoid.Saturation | [
"SaturatedAddSubmonoid._sizeOf_1",
"AddZeroClass",
"SizeOf.mk",
"SizeOf",
"SaturatedAddSubmonoid"
] | false |
Std.DHashMap.Raw.Const.getD_filter' | Std.Data.DHashMap.RawLemmas | [
"Iff.mpr",
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Option.pfilter",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"Std.DHashMap.Raw",
"Option.getD",
"Option.some",
"LawfulBEq",
"Membership.mem",
"Option.pfilter_congr",
"Bool.true",
"Std.DHashMap.Raw.Const.g... | true |
_private.Mathlib.Tactic.Translate.Reorder.0.Mathlib.Tactic.Translate.decomposePerm._proof_17 | Mathlib.Tactic.Translate.Reorder | [
"Lean.RArray.leaf",
"False",
"of_decide_eq_true",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"List.length_cons",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Eq.mp",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",
"id",... | false |
Set.univ_disjoint._simp_1 | Mathlib.Data.Set.Disjoint | [
"Set.univ",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Set.instDistribLattice",
"Set.instBoundedOrder",
"BoundedOrder.toOrderBot",
"Set.univ_disjoint",
"propext",
"Set.instEmptyCollection",
"EmptyCollection.emptyColle... | false |
CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv_assoc | Mathlib.Algebra.Homology.HomotopyCategory.HomComplex | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"HomologicalComplex.... | true |
IsLocalization.Away.of_surjective | Mathlib.RingTheory.Localization.Away.Basic | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Submodule.pointwiseDistribMulAction",
"Submodule",
"RingHom.instRingHomClass",
"SetLike.mem_coe._simp_1",
"Submodule.instAddCommMonoidWithOne",
"MulOne.toOne",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssoc... | true |
_private.Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified.0.AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType._proof_1 | Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified | [
"AlgebraicGeometry.Scheme",
"CommRingCat.Hom.hom",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"Algebra.algebraMap",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCatego... | false |
_private.Init.Data.List.MapIdx.0.List.mapFinIdx_append._proof_1 | Init.Data.List.MapIdx | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.LinearCombo.coordinate_eva... | false |
isSpectralMap_id | Mathlib.Topology.Spectral.Hom | [
"IsSpectralMap",
"id",
"TopologicalSpace",
"continuous_id",
"IsSpectralMap.mk",
"IsOpen",
"IsCompact",
"Set"
] | true |
BitVec.lawful_divSubtractShift | Init.Data.BitVec.Bitblast | [
"BitVec.DivModState.Lawful.hrWidth",
"BitVec.DivModState.Poised",
"instPowNat",
"Eq.mpr",
"HMul.hMul",
"BitVec.DivModState.Lawful",
"BitVec.DivModState.Poised.toLawful",
"instDecidableLtBitVec",
"BitVec.DivModState.wr_lt_w",
"eq_false",
"BitVec.instOfNat",
"_private.Init.Data.BitVec.Bitblast.0... | true |
ENNReal.toNNReal_sInf | Mathlib.Data.ENNReal.Operations | [
"iInf",
"congrArg",
"setOf",
"Membership.mem",
"Eq.mp",
"Subtype",
"NNReal",
"Ne",
"ENNReal.toNNReal",
"Subtype.range_coe_subtype",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"ENNReal.toNNReal_iInf",
"NNReal.instConditionallyCompleteLinearOrderBot",
"_private.Mathli... | true |
isScalarTower_closedBall_ball_ball | Mathlib.Analysis.Normed.Module.Ball.Action | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"instSMulOfMul",
"IsScalarTower.right",
"smul_assoc",
"MulZeroClass.toMul",
"IsScalarTower",
"SemigroupWithZero.toMulZeroClass",
"instSMulElemClosedBallOfNatRealBall",
"SeminormedRing.toRing",
"Algebra.toSMul",
"Membership.mem",
"... | true |
InvolutiveNeg.noConfusion | Mathlib.Algebra.Group.Defs | [
"HEq.refl",
"InvolutiveNeg.noConfusionType",
"Neg",
"InvolutiveNeg",
"InvolutiveNeg.casesOn",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq",
"Neg.neg"
] | false |
Set.div_nonempty | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"instHDiv",
"HDiv.hDiv",
"Div",
"And",
"Iff",
"Set.Nonempty",
"Set.div",
"Set.image2_nonempty_iff",
"Set"
] | true |
_private.Mathlib.Algebra.Order.Field.Power.0.zpow_eq_one_iff_cases₀._simp_1_1 | Mathlib.Algebra.Order.Field.Power | [
"NegZeroClass.toNeg",
"LinearOrder",
"IsStrictOrderedRing",
"DivInvMonoid.toZPow",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DivisionRing.toDivInvMonoid",
"DistribLattice.toLattice",
"DivisionRing.toRing",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"SubNegZeroMonoid.toNegZe... | false |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.MethodSpecs.0.reduceMethod.match_1 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.MethodSpecs | [
"_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.MethodSpecs.0.reduceMethod._sparseCasesOn_1",
"Option.ctorIdx",
"Option.some",
"Lean.Meta.Simp.Result",
"Nat.hasNotBit",
"Option"
] | false |
CategoryTheory.locallySmall_self | Mathlib.CategoryTheory.EssentiallySmall | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.LocallySmall",
"inferInstance",
"UnivLE.small",
"UnivLE.self",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.LocallySmall.mk",
"Small",
"CategoryTheory.Category"
] | true |
Hindman.FS.add | Mathlib.Combinatorics.Hindman | [
"Eq.mpr",
"Hindman.FS.tail",
"congrArg",
"add_assoc",
"Stream'.drop",
"Membership.mem",
"Exists",
"id",
"instOfNatNat",
"AddSemigroup",
"Stream'",
"instHAdd",
"AddSemigroup.toAdd",
"Exists.casesOn",
"HAdd.hAdd",
"Nat",
"Hindman.FS.rec",
"Exists.intro",
"instAddNat",
"Hindman.FS... | true |
Quaternion.instCStarRingReal | Mathlib.Analysis.Quaternion | [
"Norm.norm",
"NonUnitalNormedRing.toNorm",
"Real",
"HMul.hMul",
"Real.instZero",
"CStarRing.mk",
"NormedDivisionRing.toNorm",
"NormedDivisionRing.toNormMulClass",
"NormedDivisionRing.toNormedRing",
"NormedRing.toNonUnitalNormedRing",
"NonUnitalRing.toNonUnitalNonAssocRing",
"NonUnitalNonAssocR... | true |
_private.Mathlib.LinearAlgebra.Matrix.SesquilinearForm.0.mem_pairSelfAdjointMatricesSubmodule._simp_1_4 | Mathlib.LinearAlgebra.Matrix.SesquilinearForm | [
"Pi.Function.module",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"LinearMap.IsAdjointPair",
"CommRing.toNonUnitalCommRing",
"Matrix.module",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Matr... | false |
Lean.Grind.EqMatch | Init.Grind.Util | [
"Eq"
] | true |
LieAdmissibleRing.ext_iff | Mathlib.Algebra.NonAssoc.LieAdmissible.Defs | [
"LieAdmissibleRing.ext",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocRing.toMul",
"Zero.zero",
"HEq.refl",
"AddMonoid.toZero",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"Eq.casesOn",
"Add.add",
"Int",
"LieAdmissibleRing.toNonUnitalNonAssocRing",
"And.casesOn",
"S... | true |
CategoryTheory.SubobjectRepresentableBy._root.CategoryTheory.Classifier.SubobjectRepresentableBy.isTerminalΩ₀ | Mathlib.CategoryTheory.Subobject.Classifier.Defs | [
"CategoryTheory.Subobject.underlying",
"CategoryTheory.Limits.IsTerminal",
"PartialOrder.toPreorder",
"CategoryTheory.SubobjectRepresentableBy",
"Preorder.smallCategory",
"CategoryTheory.instPartialOrderSubobject",
"CategoryTheory.Limits.HasPullbacks",
"CategoryTheory.Functor.obj",
"CategoryTheory.S... | false |
AdjoinRoot.instDistribMulActionOfIsScalarTower._proof_4 | Mathlib.RingTheory.AdjoinRoot | [
"Monoid",
"AdjoinRoot.instSMulAdjoinRoot",
"Polynomial.distribMulAction",
"CommRing",
"instHSMul",
"AdjoinRoot.instDistribMulActionOfIsScalarTower._proof_2",
"Semiring.toModule",
"instSMulOfMul",
"AdjoinRoot",
"AddMonoid.toAddSemigroup",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSM... | false |
List.kunion_kerase | Mathlib.Data.List.Sigma | [
"List.brecOn",
"List.kunion",
"List.kerase",
"List",
"Eq",
"Sigma",
"List.kunion_kerase._f",
"DecidableEq"
] | true |
unitOfInvertible._proof_1 | Mathlib.Algebra.Group.Invertible.Basic | [
"Monoid",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Invertible.invOf",
"MulOne.toMul",
"MulOneClass.toMulOne",
"True",
"eq_self",
"Invertible",
"of_eq_true",
"One.toOfNat1",
"congrFun'",
"mul_invOf_self'",
"OfNat.ofNat",
"Eq",
"Eq.trans",
"instHMul"
] | false |
CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_obj_map | Mathlib.CategoryTheory.Limits.Constructions.Filtered | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finset",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"Membership.mem",
"CategoryTheory.Limits.Pi.π",
"Subtype",
"Preorder.smallCategory",
"CategoryTheory.Limits.ProductsFromFiniteCo... | true |
IsAntichain.image_embedding | Mathlib.Order.Antichain | [
"IsAntichain.image_relEmbedding",
"LE.le",
"LE",
"IsAntichain",
"Set.image",
"OrderEmbedding",
"DFunLike.coe",
"instFunLikeOrderEmbedding",
"Set"
] | true |
LinearMap.toSpanSingleton_zero | Mathlib.LinearAlgebra.Span.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"smul_zero",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"LinearMap",
"AddC... | true |
Lean.Elab.Term.MatchAltView.noConfusionType | Lean.Elab.MatchAltView | [
"Lean.TSyntax",
"Lean.Elab.Term.MatchAltView",
"Lean.Elab.Term.MatchAltView.casesOn",
"Lean.SyntaxNodeKinds",
"Lean.Syntax",
"Array",
"HEq",
"Eq"
] | false |
EuclideanGeometry.Sphere.finrank_orthRadius | Mathlib.Geometry.Euclidean.Sphere.OrthRadius | [
"Iff.mpr",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Submodule",
"Real",
"outParam",
"Real.instRCLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"Submodule.addCommMonoid",
"vsub_ne_zero",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"AffineSubspace.mk'",
"Eucl... | true |
LinearMap.toAddMonoidHom'._proof_1 | Mathlib.Algebra.Module.LinearMap.Defs | [
"LinearMap.toAddMonoidHom",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"AddMonoidHom.instAddCommMonoid",
"AddMonoidHom.ext",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"LinearMap.addMonoid",
"Semiring",
"Zero.toOfNat0",
"Eq.refl",
"AddCommMonoid.toAddMonoid",
"... | false |
_private.Mathlib.Data.EReal.Basic.0.Mathlib.Meta.Positivity.evalERealToReal._sparseCasesOn_1 | Mathlib.Data.EReal.Basic | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
ruzsaSzemerediNumber.congr_simp | Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | [
"instSubsingletonDecidable",
"Decidable",
"Pi.instSubsingleton",
"Fintype",
"Nat",
"ruzsaSzemerediNumber",
"Eq.ndrec",
"Eq.refl",
"Subsingleton.elim",
"Eq",
"DecidableEq"
] | true |
HahnSeries.zero_le_orderTop_iff | Mathlib.RingTheory.HahnSeries.Basic | [
"HahnSeries.support",
"Iff.mpr",
"HahnSeries.order",
"instReflLe",
"WithTop.instPreorder",
"congrArg",
"le_top._simp_2",
"HahnSeries.orderTop",
"PartialOrder.toPreorder",
"Classical.propDecidable",
"Preorder.toLE",
"Std.le_refl._simp_1",
"PartialOrder",
"HahnSeries.instZero",
"Ne",
"LE... | true |
CategoryTheory.FunctorToTypes.prodMk_snd | Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.category",
"TypeCat.instFunLikeFun",
"CategoryTheory.FunctorToTypes.binaryProductIso_inv_comp_snd_apply",
"UnivLE.small",
"Prod.mk",
"CategoryTheory.Limits.WalkingPai... | true |
Lean.Parser.scientificLit.parenthesizer | Lean.Parser.Extra | [
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.scientificLitKind",
"Lean.PrettyPrinter.Parenthesizer",
"Bool.true",
"Lean.PrettyPrinter.Parenthesizer.withAntiquot.parenthesizer",
"Bool.false",
"Lean.PrettyPrinter.Parenthesizer.scientificLitNoAntiquot.parenthesizer"
] | true |
Matrix.compl_zero_eq_of_one_sub_one | Mathlib.Combinatorics.SimpleGraph.AdjMatrix | [
"AddGroup.toSubtractionMonoid",
"One",
"Equiv.instEquivLike",
"SimpleGraph.Top.adjDecidable",
"congrArg",
"Matrix",
"Matrix.of",
"HSub.hSub",
"SimpleGraph.completeGraph",
"Equiv",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
... | true |
_private.Mathlib.Tactic.ComputeDegree.0.Mathlib.Tactic.ComputeDegree.twoHeadsArgs.match_14 | Mathlib.Tactic.ComputeDegree | [
"Lean.Expr",
"Prod.mk",
"Lean.Name",
"Prod",
"Prod.casesOn"
] | false |
Lean.Meta.simpEq._sparseCasesOn_8 | Mathlib.Lean.Meta.Simp | [
"Lean.Name.rec",
"Nat.ne_of_beq_eq_false",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Nat.land",
"Nat",
"Bool",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",
"Bool.false"
] | false |
_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.isAltWildcard | Lean.Elab.Tactic.Induction | [
"Option.instBEq",
"_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.getAltName?",
"Option.some",
"Lean.Syntax",
"BEq.beq",
"Bool",
"Lean.Name",
"Lean.Name.mkStr1",
"Lean.Name.instBEq",
"Option"
] | true |
Module.Presentation.tautologicalSolutionIsPresentationCore._proof_2 | Mathlib.Algebra.Module.Presentation.Tautological | [
"Equiv.instEquivLike",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"Module.Presentation.tautologicalSolution",
"Equiv",
"Module.Relations.Solution",
"LinearMap",
"Module.Presentation.tautologicalRelations",
"Module",
"Module.Relations.Solution.postcomp",
"RingHom.id",
"Semiring.toNonAssocS... | false |
Turing.PartrecToTM2.Λ'.ret.injEq | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.Cont'",
"Turing.PartrecToTM2.Λ'.ret.inj",
"Eq.propIntro",
"Turing.PartrecToTM2.Λ'",
"Turing.PartrecToTM2.Λ'.ret",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
Bind.recOn | Init.Prelude | [
"Bind.rec",
"Bind",
"Bind.mk"
] | false |
AffineSubspace.nonempty_iff_ne_bot | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"id",
"Ne",
"Bot.bot",
"AffineSubspace... | true |
CategoryTheory.Mon.mul_def | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.tensorμ",
"CategoryTheory.BraidedCategory",
"CategoryTheory.Mon.instMonObjTensorObj",
"CategoryTheory.Mon.X",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory... | true |
IsClosed.right_addCoset | Mathlib.Topology.Algebra.Group.Basic | [
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"SeparatelyContinuousAdd",
"AddZeroClass.toAddZero",
"AddOpposite",
"Set.vaddSet",
"HVAdd.hVAdd",
"isClosedMap_add_right",
"IsClosed",
"TopologicalSpace",
"AddAction.toAddSemigroupAction",
"AddGroup",
"AddSemigroupAction.toVAdd",
"Add... | true |
nsmul_right_inj | Mathlib.Algebra.Group.Torsion | [
"instHSMul",
"AddMonoid.toNSMul",
"Function.Injective.eq_iff",
"Ne",
"instOfNatNat",
"IsAddTorsionFree",
"Iff",
"Nat",
"AddMonoid",
"HSMul.hSMul",
"nsmul_right_injective",
"OfNat.ofNat",
"Eq"
] | true |
Std.DTreeMap.Internal.Impl.get!_erase | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.toListModel_erase",
"Eq.mpr",
"Inhabited.default",
"Std.Internal.List.DistinctKeys",
"instDecidableEqOrdering",
"Std.DTreeMap.Internal.Impl.get!_eq_getValueCast!",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"beqOfOr... | true |
IsAddUnit.smul_left | Mathlib.Algebra.Module.End | [
"instHSMul",
"AddMonoidHom.instAddMonoidHomClass",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"IsAddUnit",
"AddCommMonoid",
"AddZero.toZero",
"IsAddUnit.map",
"DistribSMul",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"AddCommMonoid.toAddMonoid",
"AddMo... | true |
FirstOrder.Language.Substructure.FG.map | Mathlib.ModelTheory.FinitelyGenerated | [
"Iff.mpr",
"Eq.mpr",
"ChainCompletePartialOrder.instOfCompleteLattice",
"congrArg",
"PartialOrder.toPreorder",
"FirstOrder.Language.Substructure.fg_def",
"Set.Finite",
"FirstOrder.Language.Substructure.instSetLike",
"Exists",
"id",
"FirstOrder.Language.Hom",
"Set.Finite.image",
"ChainComplet... | true |
OrderType | Mathlib.Order.Types.Defs | [
"LinOrd",
"OrderType.instSetoid",
"Quotient"
] | true |
Finset.mulOneClass._proof_1 | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"MulOne.toOne",
"Finset.coe_singleton",
"Finset",
"Set.instSingletonSet",
"MulOneClass.toMulOne",
"SetLike.coe",
"Finset.instSetLike",
"One.toOfNat1",
"MulOneClass",
"Finset.instSingleton",
"Singleton.singleton",
"OfNat.ofNat",
"Eq",
"Set"
] | false |
CategoryTheory.le_topology_of_closedSieves_isSheaf | Mathlib.CategoryTheory.Sites.Closed | [
"CategoryTheory.Presieve.IsSheaf",
"Eq.mpr",
"Opposite",
"CategoryTheory.Functor.closedSieves",
"congrArg",
"CategoryTheory.Presieve.IsSheafFor",
"Membership.mem",
"id",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Sieve",
"LE.le",
"CategoryTheory.Subfunctor.toFunctor",
"CategoryTheory.Fun... | true |
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