name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
AlgHom.snd_prod | Mathlib.Algebra.Algebra.Prod | [
"AlgHom.snd",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"Prod.instSemiring",
"AlgHom.ext",
"Prod.algebra",
"CommSemiring",
"Semiring",
"Eq.refl",
"Prod",
"AlgHom.comp",
"Eq",
"DFunLike.coe",
"AlgHom.prod"
] | true |
List.length_eraseP_le | Init.Data.List.Erase | [
"List.Sublist.length_le",
"List.eraseP_sublist",
"LE.le",
"instLENat",
"List",
"Nat",
"Bool",
"List.eraseP",
"List.length"
] | true |
_private.Mathlib.NumberTheory.Divisors.0.Int.mul_mem_one_two_three_iff._simp_1_4 | Mathlib.NumberTheory.Divisors | [
"False",
"One",
"eq_false",
"One.toOfNat1",
"Zero.toOfNat0",
"NeZero",
"one_ne_zero",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
Filter.filter_eq | Mathlib.Order.Filter.Defs | [
"Set.univ",
"Membership.mem",
"Filter.sets",
"Filter.mk",
"HasSubset.Subset",
"_private.Mathlib.Order.Filter.Defs.0.Filter.filter_eq.match_1_1",
"Set.instInter",
"Inter.inter",
"Eq",
"Set.instMembership",
"Filter",
"rfl",
"Set.instHasSubset",
"Set"
] | true |
_private.Mathlib.Data.Finset.Defs.0.Finset.instAsymmSSubset._proof_1 | Mathlib.Data.Finset.Defs | [
"Finset",
"PartialOrder.toPreorder",
"HasSSubset.SSubset",
"instAsymmLt",
"Finset.partialOrder",
"Std.Asymm",
"Finset.instHasSSubset"
] | false |
Finset.gcd_eq_of_dvd_sub | Mathlib.Algebra.GCDMonoid.Finset | [
"Eq.mpr",
"False",
"CommRing",
"Dvd.dvd",
"CommRing.toNonUnitalCommRing",
"Finset.mem_insert_self",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Finset",
"NormalizedGCDMonoid",
"gcd_assoc",
"semigroupDvd",
"HSub.hSub",
"MonoidWithZeroHom.funLike",
"Classical.propDecidable",
"CommSemiring... | true |
Turing.PartrecToTM2.Γ'.consₗ.elim | Mathlib.Computability.TuringMachine.ToPartrec | [
"PULift.up",
"Turing.PartrecToTM2.Γ'.ctorIdx",
"Turing.PartrecToTM2.Γ'",
"Turing.PartrecToTM2.Γ'.consₗ",
"Turing.PartrecToTM2.Γ'.ctorElim",
"Nat",
"Eq.symm",
"Eq"
] | false |
CategoryTheory.MorphismProperty.FunctorsInverting.hom_ext | Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.NatTrans.ext",
"CategoryTheory.MorphismProperty.IsInvertedBy",
"CategoryTheory.... | true |
QuadraticAlgebra.instNonUnitalNonAssocSemiring._proof_6 | Mathlib.Algebra.QuadraticAlgebra.Defs | [
"add_mul",
"Distrib.leftDistribClass",
"QuadraticAlgebra.re",
"_private.Mathlib.Algebra.QuadraticAlgebra.Defs.0.QuadraticAlgebra.instNonUnitalNonAssocSemiring._abel_5",
"Eq.mpr",
"QuadraticAlgebra.ext",
"HMul.hMul",
"QuadraticAlgebra.instMul",
"QuadraticAlgebra",
"AddMonoid.toAddSemigroup",
"con... | false |
_private.Mathlib.Analysis.SpecialFunctions.Complex.Log.0.Complex.expOpenPartialHomeomorph._simp_1 | Mathlib.Analysis.SpecialFunctions.Complex.Log | [
"Real",
"Real.instArchimedean",
"Real.pi",
"HMul.hMul",
"Complex.im",
"Nat.instAtLeastTwoHAddOfNat",
"Membership.mem",
"Ne",
"instOfNatNat",
"Real.two_pi_pos",
"Real.instAddCommGroup",
"Nat.instNeZeroSucc",
"Nat",
"Real.instMul",
"Real.instNeg",
"toIocMod",
"propext",
"Complex.exp"... | false |
lowerBounds_Icc | Mathlib.Order.Bounds.Basic | [
"lowerBounds",
"Preorder.toLE",
"LE.le",
"isGLB_Icc",
"Set.Icc",
"Set.Iic",
"Eq",
"IsGLB.lowerBounds_eq",
"Preorder",
"Set"
] | true |
HopfAlgCat.instMonoidalCategoryStruct._proof_2 | Mathlib.Algebra.Category.HopfAlgCat.Monoidal | [
"IsScalarTower.to_smulCommClass'",
"CommRing",
"HopfAlgebraStruct.toBialgebra",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Algebra.toModule",
"Algebra.id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSe... | false |
spectrum.map_star | Mathlib.Algebra.Algebra.Spectrum.Basic | [
"Set.ext",
"Eq.mpr",
"Set.star",
"Algebra.algebraMap",
"spectrum",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"InvolutiveStar",
"HSub.hSub",
"IsUnit",
"Algebra",
"RingHom",
"Algebra.toSMul",
"Membership.mem",
"id",
"NonUnitalNonAssoc... | true |
LightCondensed.lanPresheafIso | Mathlib.Condensed.Discrete.Colimit | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Functor.mapCocone",
"Opposite",
"LightCondensed.lanPresheafIso._proof_2",
"SecondCountableTopology",
"Finite",
"FintypeCat",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.colimit.isColimit",
"CategoryTheory.Limits.coc... | true |
AlgebraicGeometry.instSubsingletonOverTerminalScheme | Mathlib.AlgebraicGeometry.Limits | [
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Limits.uniqueToTerminal",
"Quiver.Hom",
"congrArg",
"_private.Mathlib.AlgebraicGeometry.Limits.0.AlgebraicGeometry.instSubsingletonOverTerminalScheme.match_1",
"AlgebraicGeometry.Scheme.Over",
"Unique.instSubsingleto... | true |
CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π_assoc | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products | [
"CategoryTheory.Category.assoc",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.instHasProductOppositeOp",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Limits.opCoproductIsoProduct_hom_comp_π",
"CategoryTheory.Li... | true |
CategoryTheory.BasedFunctor.isHomLift_iff | Mathlib.CategoryTheory.FiberedCategory.BasedCategory | [
"CategoryTheory.BasedFunctor",
"CategoryTheory.BasedCategory.category",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.IsHomLift",
"CategoryTheory.BasedCategory.p",
"CategoryTheory.instCategoryObj",
"CategoryTheory.BasedCategory.obj",
"CategoryTheory.BasedFunctor.isH... | true |
Polynomial.eval₂AlgHom | Mathlib.Algebra.Polynomial.AlgebraMap | [
"Polynomial.eval₂AlgHom._proof_2",
"Polynomial.eval₂AlgHom._proof_1",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"Algebra",
"Commute",
"RingHom",
"Polynomial.eval₂RingHom'",
"Polynomial",
"instDistribOfSemiring",
"CommSemiring",
"Distrib.toMul",
"RingHomClass.toRingHom",
... | true |
_private.Lean.Compiler.LCNF.ExtractClosed.0.Lean.Compiler.LCNF.ExtractClosed.searchArrayLiteral.identifyChain._sparseCasesOn_6 | Lean.Compiler.LCNF.ExtractClosed | [
"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.Mathlib.RingTheory.Localization.Ideal.0.IsLocalization.surjective_quotientMap_of_maximal_of_localization._simp_1_2 | Mathlib.RingTheory.Localization.Ideal | [
"HMul.hMul",
"MulZeroClass.toMul",
"mul_eq_mul_left_iff",
"MulZeroClass",
"IsLeftCancelMulZero",
"propext",
"Zero.toOfNat0",
"Or",
"OfNat.ofNat",
"Eq",
"MulZeroClass.toZero",
"instHMul"
] | false |
ProbabilityTheory.HasSubgaussianMGF.sum_of_iIndepFun | Mathlib.Probability.Moments.SubGaussian | [
"Real",
"MeasureTheory.Measure",
"Finset.univ",
"congrArg",
"Subtype.val_injective",
"Finset",
"Membership.mem",
"Finset.sum_attach",
"Eq.mp",
"Subtype",
"NNReal",
"ProbabilityTheory.HasSubgaussianMGF.aemeasurable",
"ProbabilityTheory.iIndepFun",
"ProbabilityTheory.iIndepFun.precomp",
"N... | true |
CategoryTheory.Abelian.Ext.mk₀_addEquiv₀_apply | Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Abelian.Ext.instAddCommGroup",
"CategoryTheory.Abelian",
"instOfNatNat",
"CategoryTheory.HasExt",
"Nat",
"CategoryTheory.Abelian.Ext",
"AddEquiv",
"Ca... | true |
MonomialOrder.leadingCoeff_prod_of_regular | Mathlib.RingTheory.MvPolynomial.MonomialOrder | [
"Nat.instMulZeroClass",
"congrArg",
"CommSemiring.toSemiring",
"MonomialOrder.leadingCoeff",
"Finset",
"IsRegular",
"AddMonoidAlgebra.commSemiring",
"MonomialOrder.coeff_prod_sum_degree",
"Membership.mem",
"MonomialOrder",
"Finset.prod_congr",
"instDistribOfSemiring",
"MvPolynomial.coeff",
... | true |
CategoryTheory.MonObj.casesOn | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"CategoryTheory.MonoidalCategoryStruct.whiskerRight",
... | false |
Lean.Server.FileWorker.EditableDocumentCore.mk.inj | Lean.Server.FileWorker.Utils | [
"Lean.Server.Snapshots.Snapshot",
"Lean.Server.FileWorker.EditableDocumentCore.mk.noConfusion",
"Lean.Widget.InteractiveDiagnostic",
"Array",
"And",
"And.intro",
"Lean.Server.DocumentMeta",
"IO.Error",
"IO.Ref",
"Lean.Server.FileWorker.EditableDocumentCore.mk",
"Lean.Server.FileWorker.EditableDo... | true |
nonpos_of_add_le_right | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"Eq.mpr",
"le_of_add_le_add_left",
"congrArg",
"AddZeroClass.toAddZero",
"id",
"LE.le",
"LE",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"HAdd.hAdd",
"AddLeftReflectLE",
"AddZero.toAdd",
"Zero.toOfNat0",
"add_zero",
"OfNat.ofNat",
"Eq"
] | true |
Std.HashMap.getKey!_diff | Std.Data.HashMap.Lemmas | [
"Inhabited.default",
"Std.DHashMap.getKey!_diff",
"Membership.mem",
"Std.HashMap",
"LawfulHashable",
"SDiff.sdiff",
"Std.HashMap.getKey!",
"EquivBEq",
"Std.HashMap.instDecidableMem",
"Inhabited",
"Hashable",
"Std.HashMap.instSDiff",
"Std.HashMap.inner",
"BEq",
"Eq",
"Std.HashMap.instMe... | true |
Lean.Elab.Tactic.BVDecide.Frontend.Normalize.MatchKind.enumWithDefault.noConfusion | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic | [
"Lean.ConstructorVal",
"id",
"Array",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.MatchKind.enumWithDefault",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.MatchKind",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.MatchKind.noConfusion",
"Eq",
"Lean.InductiveVal"
] | false |
_private.Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer.0.SubMulAction.ofStabilizer._simp_2 | Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer | [
"Membership.mem",
"Set.instSingletonSet",
"Set.mem_singleton_iff",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Lean.Meta.Match.SimpH.0.Lean.Meta.Match.SimpH.substRHS.match_1 | Lean.Meta.Match.SimpH | [
"Lean.MVarId",
"Prod.mk",
"Lean.Meta.FVarSubst",
"Prod",
"Prod.casesOn"
] | false |
Vector.toList_ofFn | Init.Data.Vector.Lemmas | [
"congrArg",
"List.ofFn",
"List",
"Array.toList_ofFn",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Fin",
"Vector.toList",
"Eq",
"Vector.ofFn",
"Eq.trans"
] | true |
OpenPartialHomeomorph.continuousAt_iff_continuousAt_comp_right | Mathlib.Topology.OpenPartialHomeomorph.Continuity | [
"Eq.mpr",
"ContinuousWithinAt",
"congrArg",
"ContinuousAt",
"continuousWithinAt_univ",
"PartialEquiv.target",
"Set.univ",
"Iff.rfl",
"Function.comp",
"Membership.mem",
"id",
"OpenPartialHomeomorph.toFun'",
"OpenPartialHomeomorph.continuousWithinAt_iff_continuousWithinAt_comp_right",
"Topol... | true |
Combinatorics.Line.coe_injective | Mathlib.Combinatorics.HalesJewett | [
"Nontrivial",
"Eq.mpr",
"False",
"eq_false",
"Option.ctorIdx",
"congrArg",
"Combinatorics.Line.toFun",
"Combinatorics.Line.ext",
"False.elim",
"Option.casesOn",
"Option.getD",
"noConfusion_of_Nat",
"Option.some.injEq",
"Option.some",
"Exists",
"Eq.mp",
"id",
"exists_ne",
"Ne",
... | true |
Std.Http.Header.Name.casesOn | Std.Internal.Http.Data.Headers.Name | [
"Std.Http.Header.Name.mk",
"String",
"Std.Http.Internal.IsLowerCase",
"Std.Http.Header.IsValidHeaderName",
"Std.Http.Header.Name.rec",
"Std.Http.Header.Name"
] | false |
Lean.Doc.Parser.document.formatter | Lean.DocString.Formatter | [
"Pure.pure",
"Lean.PrettyPrinter.Formatter.instMonadTraverserFormatterM",
"Unit.unit",
"Lean.PrettyPrinter.Formatter",
"instForInOfForIn'",
"Lean.Syntax.getArgs",
"_private.Lean.DocString.Formatter.0.Lean.Doc.Parser.versoSyntaxToString",
"Lean.Syntax",
"ReaderT.instMonad",
"inferInstance",
"Lean... | true |
Equiv.setDiffEquiv | Mathlib.Logic.Equiv.Fintype | [
"Finset.univ",
"Equiv.setDiffEquiv._proof_2",
"Finset",
"Equiv.setDiffEquiv._proof_3",
"Equiv.setDiffEquiv._proof_6",
"Classical.propDecidable",
"Finset.instSDiff",
"Finset.map",
"Membership.mem",
"Set.Elem",
"Fintype.card",
"Equiv",
"Subtype",
"Nonempty.some",
"SDiff.sdiff",
"Iff",
... | true |
ContinuousAt.cexp | Mathlib.Analysis.SpecialFunctions.Exp | [
"NormedCommRing.toSeminormedCommRing",
"ContinuousAt",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"nhds",
"TopologicalSpace",
"Complex.exp",
"SeminormedCommRing.toSeminormedRing",
"Filter.Tendsto.cexp",
"SeminormedRing.toPseudoMetricSpace",
"NormedField.toNormedCommRing",
"... | true |
Lean.Elab.abortTermExceptionId | Lean.Elab.Exception | [
"Inhabited.default",
"Lean.instInhabitedInternalExceptionId",
"Lean.InternalExceptionId"
] | true |
Module.DirectLimit.congr_symm_apply_of | Mathlib.Algebra.Colimit.Module | [
"LinearMap.id",
"Eq.mpr",
"Module.DirectLimit.map_apply_of",
"LinearEquiv.symm",
"Module.DirectLimit.congr",
"congrArg",
"Module.DirectLimit.of",
"LinearMap.comp_assoc",
"Module.DirectLimit.module",
"LinearMap.instFunLike",
"Preorder.toLE",
"RingHomInvPair.triples₂",
"LinearEquiv.refl_toLine... | true |
apply_le_nnnorm_cfc_nnreal._auto_3 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
AddEquiv.coprodAssoc._proof_2 | Mathlib.GroupTheory.Coprod.Basic | [
"AddMonoid.Coprod.inst",
"AddMonoid.toAddZeroClass",
"AddMonoid.Coprod.hom_ext",
"AddMonoid.Coprod.inr",
"AddMonoidHom.id",
"AddZeroClass.toAddZero",
"AddMonoidHom.ext",
"AddMonoid.Coprod.lift",
"AddMonoid.Coprod.instAddZeroClass",
"AddMonoid",
"AddMonoid.Coprod.inl",
"Eq.refl",
"AddMonoid.C... | false |
CategoryTheory.Functor.FullyFaithful.mapAddGrp._proof_4 | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.Functor.FullyFaithful.preimage_map",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.AddGrp",
"CategoryTheory.Functor.FullyFaithful.mapAddMon",
"CategoryTheory.AddMon.instCategory",
"CategoryTheory.AddGrp.homMk'",
"Categ... | false |
FGModuleRepr.instCategory._aux_5 | Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall | [
"Quiver.mk",
"CommRing",
"Quiver.Hom",
"ModuleCat",
"FGModuleRepr",
"ModuleCat.isFG",
"CategoryTheory.InducedCategory.Hom",
"FGModuleCat.of",
"FGModuleRepr.instCategory._aux_1",
"FGModuleRepr.instAddCommGroupRepr",
"CategoryTheory.InducedCategory",
"FGModuleRepr.repr",
"FGModuleRepr.instFini... | false |
Lean.Core.mkSnapshot?._auto_1 | Lean.CoreM | [
"Lean.Syntax.node",
"Lean.Syntax.ident",
"Array.push",
"String.toRawSubstring",
"Lean.Syntax",
"Array.empty",
"Lean.Syntax.Preresolved",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom",
"List.nil"
] | false |
CategoryTheory.Functor.isDenseAt_iff | Mathlib.CategoryTheory.Functor.KanExtension.DenseAt | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.LeftExtension.mk",
"Iff.rfl",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.rightUnitor",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.isDenseAt",
"CategoryTheory.Functor.id",
"CategoryTheory.Limits.IsColimit",
"CategoryTheor... | true |
LipschitzWith.min_const | Mathlib.Topology.MetricSpace.Lipschitz | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Real",
"LipschitzWith",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"congrArg",
"zero_le._simp_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"Eq.mp",
"NNReal.instSemilatticeSup",
"LipschitzWi... | true |
IsClosed.isCompletelyPseudoMetrizableSpace | Mathlib.Topology.Metrizable.CompletelyMetrizable | [
"Membership.mem",
"Set.Elem",
"Subtype",
"Topology.IsClosedEmbedding.IsCompletelyPseudoMetrizableSpace",
"IsClosed",
"TopologicalSpace",
"TopologicalSpace.IsCompletelyPseudoMetrizableSpace",
"IsClosed.isClosedEmbedding_subtypeVal",
"instTopologicalSpaceSubtype",
"Subtype.val",
"Set.instMembershi... | true |
Std.DHashMap.Internal.exists_bucket' | Std.Data.DHashMap.Internal.Model | [
"Std.DHashMap.Internal.AssocList.toList",
"Std.DHashMap.Internal.mkIdx",
"Exists",
"Std.DHashMap.Internal.AssocList.nil",
"List.Perm",
"Std.DHashMap.Internal.exists_bucket_of_uset",
"LawfulHashable",
"Array.toList",
"Array",
"And.casesOn",
"GetElem.getElem",
"instHAppendOfAppend",
"List",
... | true |
PrimeMultiset.prod_sup | Mathlib.Data.PNat.Factors | [
"Eq.mpr",
"instSemilatticeSupPrimeMultiset",
"congrArg",
"SemilatticeSup.toMax",
"PrimeMultiset.prod",
"id",
"PNat.lcm",
"Max.max",
"PNat.factorMultiset_lcm",
"Eq.refl",
"PNat.factorMultiset",
"PrimeMultiset.factorMultiset_prod",
"PNat.prod_factorMultiset",
"Eq.symm",
"Eq",
"PrimeMulti... | true |
MeasureTheory.Measure.restrict_zero | Mathlib.MeasureTheory.Measure.Restrict | [
"MeasureTheory.Measure",
"Semiring.toModule",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"LinearMap.map_zero",
"MeasureTheory.Measure.restrict",
"Algebra.id",
"ENNReal.instCommSemiring",
"MeasureTheory.Measure.instZero",
"MeasurableSpace",
"MeasureTheory.Measure.instAddCommMonoid",
"ENN... | true |
ModelWithCorners.t1Space | Mathlib.Geometry.Manifold.IsManifold.Basic | [
"NormedSpace",
"NormedAddCommGroup.toMetricSpace",
"EMetricSpace.metrizableSpace",
"PseudoMetricSpace.toUniformSpace",
"ModelWithCorners.toFun'",
"Topology.IsClosedEmbedding.toIsEmbedding",
"TopologicalSpace",
"ModelWithCorners",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"T2Space.t1Space",
"... | true |
LinearMap.IsSymmetric.toMatrix_eigenvectorBasis | Mathlib.Analysis.InnerProductSpace.Spectrum | [
"LinearIsometryEquiv.instEquivLike",
"NormedCommRing.toNormedRing",
"Finsupp.instFunLike",
"Eq.mpr",
"Pi.Function.module",
"Finsupp.smulZeroClass",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"S... | true |
Lean.Parser.Tactic.anyGoals | Init.Tactics | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.const",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | true |
WittVector.polyOfInterest | Mathlib.RingTheory.WittVector.MulCoeff | [
"wittPolynomial",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Nat.Prime",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.algebra",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"... | true |
Lean.PersistentHashMap.Zipper.consCollision.noConfusion | Lean.Data.Iterators.Producers.PersistentHashMap | [
"Subarray",
"Lean.PersistentHashMap.Zipper",
"Lean.PersistentHashMap.Zipper.noConfusion",
"id",
"heq_of_eq",
"Std.Slice.Internal.SubarrayData",
"Nat",
"Std.Slice.size",
"Eq.refl",
"Subarray.instSliceSizeSubarrayData",
"HEq",
"Eq",
"Lean.PersistentHashMap.Zipper.consCollision"
] | false |
_private.Lean.Level.0.Lean.Level.addOffsetAux.match_1 | Lean.Level | [
"instOfNatNat",
"Lean.Level",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
_private.Init.Data.Array.Range.0.Array.mk_add_mem_zipIdx_iff_getElem?._simp_1_2 | Init.Data.Array.Range | [
"and_left_comm",
"And",
"propext",
"Eq"
] | false |
TwoSidedIdeal.mem_mk | Mathlib.RingTheory.TwoSidedIdeal.Basic | [
"NonUnitalNonAssocRing",
"RingCon.instFunLikeForallProp",
"TwoSidedIdeal",
"Iff.rfl",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"RingCon",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Iff",
"Distrib.toMul",
"TwoSidedIdeal.setLike",
"NonUnitalNonA... | true |
Lean.MetavarDecl | Lean.MetavarContext | [
"Lean.MetavarDecl.mk"
] | true |
Std.Internal.List.containsKey_maxKeyD | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"Ord",
"Std.TransOrd",
"Std.OrientedOrd.opposite",
"Std.TransOrd.opposite",
"Std.Internal.List.containsKey_minKeyD",
"inferInstance",
"Ord.compare",
"Bool.true",
"Std.Internal.List.maxKeyD",
"List",
"Std.Internal.List.containsKey",
"List.isEmpty",
"Ord.opp... | true |
NonemptyFinLinOrd.instLargeCategory._proof_9 | Mathlib.Order.Category.NonemptyFinLinOrd | [
"Quiver.mk",
"CategoryTheory.CategoryStruct.mk",
"CategoryTheory.InducedCategory.instCategory._proof_6",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Category.assoc._autoParam",
"LinOrd",
"autoParam",
"LinOrd.instCategory",
"NonemptyFinLinOrd.instLargeCategory._aux_1",
... | false |
Std.Tactic.BVDecide.LRAT.Internal.ReduceResult.reducedToEmpty | Std.Tactic.BVDecide.LRAT.Internal.Clause | [
"Std.Tactic.BVDecide.LRAT.Internal.ReduceResult",
"Std.Tactic.BVDecide.LRAT.Internal.ReduceResult.reducedToEmpty"
] | true |
setOf_minimal_antichain | Mathlib.Order.Antichain | [
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"PartialOrder",
"LE.le",
"IsAntichain.swap",
"IsAntichain",
"OrderDual.instPartialOrder",
"Maximal",
"OrderDual",
"Minimal",
"setOf_maximal_antichain"
] | true |
AddSubgroup.centralizer.eq_1 | Mathlib.GroupTheory.Subgroup.Centralizer | [
"Set.neg_mem_addCentralizer",
"AddSubgroup",
"AddSubgroup.centralizer",
"AddSubmonoid.centralizer",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Eq.refl",
"SubNegMonoid.toAddMonoid",
"AddSubgroup.mk",
"Eq",
"Set"
] | true |
IntermediateField.relrank_eq_of_inf_eq | Mathlib.FieldTheory.Relrank | [
"Cardinal",
"congrArg",
"IntermediateField",
"Subfield.relrank_eq_of_inf_eq",
"Algebra",
"Field.toDivisionRing",
"Subfield.instMin",
"CompleteLattice.toConditionallyCompleteLattice",
"id",
"SemilatticeInf.toMin",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiri... | true |
AddMonoidHom.coe_prod | Mathlib.Algebra.Group.Prod | [
"Prod.instAddZeroClass",
"AddZeroClass.toAddZero",
"AddZeroClass",
"Function.prod",
"AddMonoidHom.prod",
"AddMonoidHom",
"Prod",
"AddMonoidHom.instFunLike",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
CategoryTheory.ObjectProperty.limitsClosure.of_isoClosure | Mathlib.CategoryTheory.ObjectProperty.LimitsClosure | [
"CategoryTheory.Iso",
"CategoryTheory.ObjectProperty.limitsClosure",
"CategoryTheory.ObjectProperty.limitsClosure.of_isoClosure",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty",
"CategoryTheory.Category"
] | true |
Std.TreeMap.keyAtIdx? | Std.Data.TreeMap.Basic | [
"Std.TreeMap.inner",
"Std.DTreeMap.keyAtIdx?",
"Ordering",
"Nat",
"Std.TreeMap",
"Option"
] | true |
Matrix.conjTransposeRingEquiv_symm_apply | Mathlib.LinearAlgebra.Matrix.ConjTranspose | [
"Matrix.instStar",
"Matrix.add",
"Matrix.instMulOfFintypeOfAddCommMonoid",
"Matrix",
"MulOpposite",
"StarRingEquiv.symm",
"Distrib.toAdd",
"StarRingEquiv.instFunLike",
"StarAddMonoid.toInvolutiveStar",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"StarRing.toStarAddMonoid",
"MulOpposite.instAd... | true |
_private.Mathlib.Algebra.Order.Ring.WithTop.0.WithBot.instPosMulMono._simp_1 | Mathlib.Algebra.Order.Ring.WithTop | [
"OrderBot.toBot",
"OrderBot",
"Bot.bot",
"LE.le",
"LE",
"True",
"eq_true",
"Eq",
"bot_le"
] | false |
_private.Lean.Environment.0.Lean.importModulesCore.match_3 | Lean.Environment | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"_private.Lean.Environment.0.Lean.Kernel.Environment.Diagnostics.recordUnfold._sparseCasesOn_1",
"_private.Lean.Environment.0.Lean.ImportedModule",
"Option"
] | false |
CategoryTheory.Mon.instSymmetricCategory.eq_1 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.Mon.instSymmetricCategory._proof_3",
"CategoryTheory.Mon.mkIso'",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon.instSymmetricCategory._proof_11",
"CategoryTheory.BraidedCategory.mk",
"CategoryTheory.Mon.instSymmetricCategory._proof_1",
"CategoryTheory.Mon.monMonoidal",
"Catego... | true |
AddGroupNormClass.casesOn | Mathlib.Algebra.Order.Hom.Basic | [
"AddGroup.toSubtractionMonoid",
"AddGroupNormClass.mk",
"AddGroupSeminormClass",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"PartialOrder",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"AddGroupNormClass.rec",
"AddCommMonoid",
"AddZero.toZero",
"AddGrou... | false |
_private.Lean.Expr.0.Lean.Expr.getForallBody._sparseCasesOn_1 | Lean.Expr | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
CategoryTheory.evaluationLeftAdjoint_map_app | Mathlib.CategoryTheory.Adjunction.Evaluation | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.evaluationLeftAdjoint._proof_2",
"CategoryTheory.evaluationLeftAdjoint._proof_4",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.Sigma.ι",
"CategoryTheory.Functor... | true |
Mathlib.Notation3.MatchState.getBinders | Mathlib.Util.Notation3 | [
"Lean.TSyntax",
"Mathlib.Notation3.MatchState",
"Option.getD",
"Lean.Name.mkStr3",
"List.toArray",
"List.cons",
"Array",
"Lean.SyntaxNodeKind",
"Mathlib.Notation3.MatchState.scopeState",
"List.nil"
] | true |
Std.Internal.IO.Async.System.UserId.toNat | Std.Internal.Async.System | [
"Nat",
"Std.Internal.IO.Async.System.UserId"
] | true |
Lean.Server.Reference.aliases._default | Lean.Server.References | [
"id",
"List.toArray",
"Array",
"Lean.Lsp.RefIdent",
"List.nil"
] | false |
BoxIntegral.unitPartition.box_upper | Mathlib.Analysis.BoxIntegral.UnitPartition | [
"Int.cast",
"Nat.instMulZeroClass",
"Real",
"instHDiv",
"Real.instDivInvMonoid",
"BoxIntegral.Box.upper",
"HDiv.hDiv",
"Int",
"Nat.cast",
"Real.instAdd",
"Real.instOne",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Real.instIntCast",
"DivInvMonoid.toDiv",
"One.toOfNat1",
"NeZero",
"OfNat.ofN... | true |
ContinuousLinearMap.toLinearMap₁₂ | Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap | [
"ContinuousLinearMap.toLinearMap₁₂._proof_2",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"ContinuousLinearMap.addCommMonoid",
"AddCommGroup.toAddGroup",
"RingHom",
"ContinuousLinearMap.precomp._proof_3",
"No... | true |
_private.Mathlib.FieldTheory.KummerExtension.0.exists_root_adjoin_eq_top_of_isCyclic.match_1_5 | Mathlib.FieldTheory.KummerExtension | [
"OrderDual.instLE",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Algebra",
"Subtype.casesOn",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"Equiv",
"Subtype",
"Subgroup",
"Bot.bot",
"Field.toSemifield",
"Subtype.mk",
... | false |
FreeSemigroup.noConfusion | Mathlib.Algebra.Free | [
"HEq.refl",
"FreeSemigroup.noConfusionType",
"List",
"eq_of_heq",
"Eq.ndrec",
"FreeSemigroup.casesOn",
"HEq",
"FreeSemigroup",
"Eq"
] | false |
_private.Mathlib.RingTheory.Ideal.Over.0.Ideal.Quotient.ker_stabilizerHom._simp_1_2 | Mathlib.RingTheory.Ideal.Over | [
"Semiring.toModule",
"AddGroupWithOne.toAddGroup",
"Ideal.Quotient.mk",
"HSub.hSub",
"RingHom",
"Membership.mem",
"Ideal.IsTwoSided",
"Ideal",
"SubNegMonoid.toSub",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Ideal.Quotient.eq",
"HasQuotient.Quotient",
"Ideal.Quotient.ring",
"RingHom.ins... | false |
Real.mk_zero | Mathlib.Data.Real.Basic | [
"Eq.mpr",
"Real",
"Real.instZero",
"abs",
"Real.ofCauchy_zero",
"congrArg",
"IsAbsoluteValue.abs_isAbsoluteValue",
"Rat",
"CauSeq.Completion.Cauchy",
"Rat.linearOrder",
"Real.ofCauchy",
"id",
"Rat.instLattice",
"Rat.instDivisionRing",
"DivisionRing.toRing",
"CauSeq.Completion.instZeroC... | true |
List.Perm.union | Batteries.Data.List.Perm | [
"List.Perm.union_right",
"LawfulBEq",
"List.Perm.union_left",
"List.Perm",
"List.Perm.trans",
"List",
"List.instUnionOfBEq_batteries",
"Union.union",
"BEq"
] | true |
OrderIso.map_ciInf | Mathlib.Order.ConditionallyCompleteLattice.Indexed | [
"iInf",
"PartialOrder.toPreorder",
"ConditionallyCompleteLattice",
"OrderIso.map_ciSup",
"Preorder.toLE",
"OrderIso",
"OrderIso.dual",
"instFunLikeOrderIso",
"OrderDual.instConditionallyCompleteLattice",
"BddBelow",
"Nonempty",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"Conditio... | true |
_private.Init.Data.String.Pattern.Basic.0.String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher.finitenessRelation._proof_1 | Init.Data.String.Pattern.Basic | [
"InvImage",
"String.Slice.Pattern.SearchStep",
"String.Slice",
"WellFoundedRelation.rel",
"Id",
"Std.IterM.internalState",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher",
"WellFoundedRelation.wf",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher.currPos",
"Std.IterM"... | false |
Std.Sat.CNF.sat_empty._simp_1 | Std.Sat.CNF.Basic | [
"Std.Sat.CNF.sat_empty",
"Std.Sat.CNF.empty",
"True",
"eq_true",
"Bool",
"Std.Sat.CNF.Sat",
"Eq"
] | false |
Lean.Core.State.messages | Lean.CoreM | [
"Lean.Core.State",
"Lean.MessageLog"
] | true |
List.reflBEq_iff | Init.Data.List.Lemmas | [
"BEq.rfl",
"congrArg",
"Bool.and_true",
"inferInstance",
"Eq.mp",
"ReflBEq.mk",
"List.cons",
"Bool.true",
"List.instReflBEq",
"List",
"BEq.beq",
"Iff",
"ReflBEq",
"True",
"Iff.intro",
"eq_self",
"Bool",
"of_eq_true",
"List.instBEq",
"congrFun'",
"BEq",
"Eq",
"Eq.trans",
... | true |
_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.not_isNonloop_iff_closure._simp_1_1 | Mathlib.Combinatorics.Matroid.Loop | [
"Matroid.E",
"Membership.mem",
"Set.instSingletonSet",
"And",
"propext",
"Matroid.closure",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Matroid",
"Matroid.isLoop_iff_closure_eq_loops_and_mem_ground",
"Matroid.IsLoop",
"Matroid.loops",
"Set"
] | false |
CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp_assoc | Mathlib.CategoryTheory.Limits.IsLimit | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.IsLimit.conePointsIsoOfNatIso_inv_comp",
"CategoryTheory.Functor.category",
"Eq.mp",
... | true |
Std.ExtTreeSet.mem_insertMany_list | Std.Data.ExtTreeSet.Lemmas | [
"instForInOfForIn'",
"List.contains",
"Membership.mem",
"Ordering",
"Std.ExtTreeSet.inner",
"inferInstance",
"Std.TransCmp",
"Id",
"Membership",
"Bool.true",
"List",
"Iff",
"List.instMembership",
"Std.LawfulBEqCmp",
"Std.ExtTreeMap.mem_insertManyIfNewUnit_list",
"Std.ExtTreeSet.instMem... | true |
Lean.Grind.AC.Seq.endsWithVar_k_var | Init.Grind.AC | [
"Eq.mpr",
"congrArg",
"Bool.eq_iff_iff",
"Nat.beq_eq",
"id",
"Nat.beq",
"instBEqOfDecidableEq",
"Lean.Grind.AC.Seq.endsWithVar_k",
"iff_self",
"Bool.true",
"BEq.beq",
"Iff",
"Nat",
"congr",
"True",
"propext",
"Bool",
"of_eq_true",
"Lean.Grind.AC.Seq.var",
"beq_iff_eq._simp_1",
... | true |
Aesop.SimpTheorems.foldSimpEntries | Aesop.Util.Basic | [
"Id.run",
"Id",
"Lean.Meta.SimpTheorems",
"Id.instMonad",
"Aesop.SimpTheorems.foldSimpEntriesM",
"Lean.Meta.SimpEntry"
] | true |
_private.Mathlib.Topology.Algebra.MetricSpace.Lipschitz.0.LocallyLipschitzOn.exists_lipschitzOnWith_of_compact.match_1_5 | Mathlib.Topology.Algebra.MetricSpace.Lipschitz | [
"Real",
"instHDiv",
"Real.instDivInvMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"HDiv.hDiv",
"upperBounds",
"Metric.ball",
"BddAbove",
"SDiff.sdiff",
"PseudoMetricSpace",
"Exists.casesOn",
"Exists.i... | false |
IntervalIntegrable.iff_comp_neg._auto_1 | Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Ideal.ramificationIdx_le_finrank | Mathlib.NumberTheory.RamificationInertia.Basic | [
"Iff.mpr",
"Eq.mpr",
"IsDedekindDomain.toIsDomain",
"Nat.instMulZeroClass",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Ideal.primesOver",
"instIsTorsionFreeO... | true |
LieAlgebra.Orthogonal.JD | Mathlib.Algebra.Lie.Classical | [
"Matrix.fromBlocks",
"CommRing",
"CommSemiring.toSemiring",
"Matrix",
"AddGroupWithOne.toAddMonoidWithOne",
"Sum",
"AddMonoidWithOne.toOne",
"CommRing.toCommSemiring",
"One.toOfNat1",
"Matrix.one",
"Zero.toOfNat0",
"CommRing.toRing",
"OfNat.ofNat",
"Matrix.zero",
"Ring.toAddGroupWithOne"... | true |
Nat.any._f | Init.Data.Nat.Fold | [
"_private.Init.Data.Nat.Fold.0.Nat.fold._proof_4",
"_private.Init.Data.Nat.Fold.0.Nat.any.match_1",
"instOfNatNat",
"Nat.below",
"Nat",
"LT.lt",
"_private.Init.Data.Nat.Fold.0.Nat.fold._proof_3",
"Decidable.byContradiction",
"Bool",
"Nat.decLt",
"Bool.or",
"instLTNat",
"OfNat.ofNat",
"Bool... | false |
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