name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
WithTop.coe_untop₀_of_ne_top | Mathlib.Algebra.Order.WithTop.Untop0 | [
"WithTop.untop₀",
"congrArg",
"Exists",
"Ne",
"WithTop.ne_top_iff_exists",
"WithTop.some",
"Exists.casesOn",
"WithTop.top",
"congr",
"True",
"eq_self",
"Iff.mp",
"of_eq_true",
"Top.top",
"Eq.symm",
"Eq",
"Eq.trans",
"WithTop",
"Zero"
] | true |
NumberField.InfinitePlace.instMulActionAlgEquiv._proof_3 | Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | [
"AlgEquiv.instEquivLike",
"MulOne.toOne",
"NumberField.InfinitePlace.instMulActionAlgEquiv._proof_1",
"instHSMul",
"AlgEquiv.symm",
"Monoid.toMulOneClass",
"NumberField.InfinitePlace.comap",
"Algebra",
"AlgEquivClass.toAlgHomClass",
"DivInvMonoid.toMonoid",
"SMul.mk",
"Field.toSemifield",
"G... | false |
Lean.instInhabitedTSyntax | Init.Prelude | [
"Lean.TSyntax",
"Inhabited.default",
"Lean.SyntaxNodeKinds",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Inhabited",
"Lean.instInhabitedSyntax",
"Inhabited.mk"
] | true |
Order.coheight_eq | Mathlib.Order.KrullDimension | [
"RelSeries.reverse",
"Preorder.toLT",
"instCompleteLinearOrderENat",
"Equiv.instEquivLike",
"RelSeries.last",
"ENat.instNatCast",
"iSup",
"SetRel.inv",
"setOf",
"Preorder.toLE",
"FiniteDimensionalOrder.match_1",
"Equiv.mk",
"Equiv",
"RelSeries.length",
"RelSeries.reverse_reverse",
"LE.... | true |
NormedAddGroupHom.opNorm_nonneg | Mathlib.Analysis.Normed.Group.Hom | [
"Norm.norm",
"Real.instLE",
"Real",
"NormedAddGroupHom",
"Lattice.toSemilatticeSup",
"SeminormedAddCommGroup",
"HMul.hMul",
"Real.instZero",
"PartialOrder.toPreorder",
"le_csInf",
"setOf",
"Preorder.toLE",
"Membership.mem",
"_private.Mathlib.Analysis.Normed.Group.Hom.0.NormedAddGroupHom.op... | true |
connectedSpace_iff_connectedComponent | Mathlib.Topology.Connected.Basic | [
"Eq.mpr",
"congrArg",
"Set.univ",
"ConnectedSpace.casesOn",
"PreconnectedSpace",
"PreconnectedSpace.mk",
"Exists",
"Set.eq_univ_of_univ_subset",
"ConnectedSpace.mk",
"id",
"connectedComponent",
"Nonempty.intro",
"isPreconnected_connectedComponent",
"TopologicalSpace",
"Iff",
"Exists.ca... | true |
AlgebraicGeometry.GeometricallyConnected.recOn | Mathlib.AlgebraicGeometry.Geometrically.Connected | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommRingCat",
"AlgebraicGeometry.GeometricallyConnected.mk",
"CommRingCat.instCategory",
"AlgebraicGe... | false |
Lean.Grind.CommRing.Poly.denoteAsIntModuleExpr._sunfold | Lean.Meta.Tactic.Grind.Arith.Linear.DenoteExpr | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.Grind.Arith.Linear.instMonadGetStructLinearM",
"Lean.Grind.CommRing.Poly",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Arith.Linear.LinearM.Context",
"Lean.Meta.Grind.State",
"ReaderT",
"... | false |
InnerProductSpace.Core.ne_zero_of_inner_self_ne_zero | Mathlib.Analysis.InnerProductSpace.Defs | [
"Inner.inner",
"AddCommGroup.toAddCommMonoid",
"NormedField.toField",
"mt",
"AddCommGroup",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"PreInnerProductSpace.Core",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Field.toSemifield",
"RCLike.toDenselyNormedFie... | true |
Stream'.get_append_left | Mathlib.Data.Stream.Init | [
"False",
"congrArg",
"False.elim",
"Eq.mp",
"Nat.not_lt_zero._simp_1",
"instOfNatNat",
"List.rec",
"Nat.add_lt_add_iff_right._simp_1",
"List.cons",
"Nat.casesAuxOn",
"GetElem.getElem",
"Stream'",
"List",
"instHAdd",
"Stream'.appendStream'",
"Stream'.get",
"HAdd.hAdd",
"Nat",
"LT.... | true |
List.lookup._sunfold | Init.Data.List.Basic | [
"List.filter.match_1",
"Option.some",
"List.lookup.match_1",
"Option.none",
"List",
"BEq.beq",
"Unit",
"List.lookup",
"Bool",
"Prod",
"BEq",
"Option"
] | false |
_private.Mathlib.Data.WSeq.Defs.0.Stream'.WSeq.length.match_1.eq_2 | Mathlib.Data.WSeq.Defs | [
"Stream'.Seq",
"Stream'.WSeq.length.match_1",
"Option.some",
"Prod.mk",
"Option.none",
"Unit",
"Stream'.Seq1",
"Eq.refl",
"Eq",
"Option"
] | true |
finprod_le_finprod' | Mathlib.Algebra.BigOperators.Finprod | [
"_private.Mathlib.Algebra.BigOperators.Finprod.0.finprod_le_finprod'._proof_1_1",
"Set.Finite.union",
"Eq.mpr",
"MulOne.toOne",
"Finset.prod_le_prod'",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Set.instUnion",
"PartialOrder",... | true |
Equiv.asEmbedding_range | Mathlib.Logic.Embedding.Set | [
"Set.ext",
"Equiv.apply_symm_apply",
"Subtype.coe_prop",
"Equiv.instEquivLike",
"congrArg",
"_private.Mathlib.Logic.Embedding.Set.0.Equiv.asEmbedding_range.match_1_1",
"setOf",
"Membership.mem",
"Eq.rec",
"Equiv",
"Subtype",
"Function.Embedding",
"Subtype.mk",
"Equiv.asEmbedding",
"True"... | true |
SMul.comp.eq_1 | Mathlib.Algebra.Group.Action.Defs | [
"SMul.comp",
"SMul",
"SMul.mk",
"SMul.comp.smul",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.Opposite.0.CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.exists_epi | Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.Opposite | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Functor",
"_private.Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.Opposite.0.CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.generator._proof_1",
"CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits",
"Opposite"... | true |
_private.Lean.Elab.PreDefinition.WF.Eqns.0.Lean.Elab.WF.copyPrivateUnfoldTheorem._sparseCasesOn_1 | Lean.Elab.PreDefinition.WF.Eqns | [
"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 |
Lean.Elab.Term.expandSuffices | Lean.Elab.BuiltinNotation | [
"Pure.pure",
"cond",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.SourceInfo",
"Lean.Syntax.node5",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Array.mkArray0",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMon... | true |
Mathlib.Meta.FunProp.LambdaTheoremType.comp | Mathlib.Tactic.FunProp.Theorems | [
"Mathlib.Meta.FunProp.LambdaTheoremType",
"Mathlib.Meta.FunProp.LambdaTheoremType.comp"
] | true |
Set.iUnion_dite | Mathlib.Data.Set.Lattice | [
"Set.instUnion",
"iSup_dite",
"dite",
"DecidablePred",
"CompleteBooleanAlgebra.toCompleteLattice",
"Union.union",
"Eq",
"Set.iUnion",
"Not",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
"Set.instCompleteAtomicBooleanAlgebra",
"Set"
] | true |
Lean.Elab.Command.MacroExpandedSnapshot.mk.noConfusion | Lean.Elab.Command | [
"Lean.Language.DynamicSnapshot",
"Lean.Syntax",
"Lean.Elab.Command.MacroExpandedSnapshot.mk",
"id",
"Lean.Language.SnapshotTask",
"Array",
"Lean.Elab.Command.MacroExpandedSnapshot",
"Lean.Elab.Command.MacroExpandedSnapshot.noConfusion",
"Nat",
"Lean.Language.Snapshot",
"Bool",
"Lean.Name",
"... | false |
Nat.castAddMonoidHom | Mathlib.Data.Nat.Cast.Basic | [
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"AddMonoidHom.mk",
"AddMonoidWithOne.toNatCast",
"ZeroHom.mk",
"Nat.cast",
"Nat.cast_add",
"AddZero.toZero",
"Nat",
"Nat.cast_zero",
"AddMonoidWithOne.toAddMonoid",
"AddMonoidHom",
"AddMonoidWithOne"
] | true |
Std.DTreeMap.Internal.Impl.updateCell._proof_37 | Std.Data.DTreeMap.Internal.Model | [
"HSub.hSub",
"Std.DTreeMap.Internal.Impl.balance",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.updateCell._proof_32",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"instHSub",
"HAd... | false |
Polynomial.isPrimitiveRoot_of_mahlerMeasure_eq_one | Mathlib.NumberTheory.MahlerMeasure | [
"Real",
"Complex.commRing",
"IsDomain.of_isSimpleRing",
"Complex.instNormedField",
"IsPrimitiveRoot.exists_pos",
"Complex.instZero",
"NormedDivisionRing.toDivisionRing",
"Membership.mem",
"Exists",
"Multiset",
"Ne",
"instOfNatNat",
"Int",
"Polynomial.pow_eq_one_of_mahlerMeasure_eq_one",
... | true |
RegularExpression.matches'_pow | Mathlib.Computability.RegularExpressions | [
"RegularExpression",
"RegularExpression.instPowNat",
"Nat.brecOn",
"Language.instSemiring",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"RegularExpression.matches'",
"Semiring.toMonoid",
"instHPow",
"Language",
"RegularExpression.matches'_pow._f",
"Eq"
] | true |
hasSum_fintype_support | Mathlib.Topology.Algebra.InfiniteSum.Defs | [
"Filter.instMembership",
"Iff.mpr",
"SummationFilter.eventually_mem_or_not_mem",
"Iff.of_eq",
"congrArg",
"Set.iInter",
"Compl.compl",
"Finset",
"Subtype.finite",
"Filter.Eventually",
"SummationFilter",
"setOf",
"Membership.mem",
"Subtype.fintype",
"Eq.rec",
"Filter.mp_mem",
"Eq.mp",... | true |
IsFractionRing.liftAlgHom | Mathlib.RingTheory.Localization.FractionRing | [
"CommRing",
"CommSemiring.toSemiring",
"IsFractionRing",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"Algebra",
"Algebra.toSMul",
"nonZeroDivisors",
"Field.toSemifield",
"CommRing.toCommSemiring",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"IsLocalization.liftAlgHom",
... | true |
_private.Mathlib.Algebra.Homology.Opposite.0.HomologicalComplex.instHasHomologyUnopOfOpposite._proof_1 | Mathlib.Algebra.Homology.Opposite | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.unop",
"Opposite",
"HomologicalComplex.HasHomology",
"HomologicalComplex",
"ComplexShape",
"HomologicalComplex.sc",
"CategoryTheory.ShortComplex.instHasHomologyUnopOfOpposite",
"CategoryTheory.Category.opposite",
"ComplexShape.symm",
... | false |
Lean.Meta.RefinedDiscrTree.LazyEntry.mk.inj | Mathlib.Lean.Meta.RefinedDiscrTree.Basic | [
"Lean.Meta.RefinedDiscrTree.ExprInfo",
"Lean.Meta.RefinedDiscrTree.StackEntry",
"Lean.MetavarContext",
"Lean.MVarId",
"Lean.Meta.RefinedDiscrTree.LazyEntry.mk",
"Lean.Meta.RefinedDiscrTree.Key",
"Array",
"List",
"And",
"Lean.Meta.RefinedDiscrTree.LazyEntry",
"And.intro",
"Lean.Meta.RefinedDisc... | true |
Differentiable.fun_add_iff_left._simp_1 | Mathlib.Analysis.Calculus.FDeriv.Add | [
"Differentiable",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"instHAdd",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"HAdd.hAdd",
"propext",
"NontriviallyNormedField",
"NormedAddCommGroup.toAddCommGroup",
"NontriviallyNormedFiel... | false |
_private.Mathlib.Order.Atoms.0.le_iff_atom_le_imp.match_1_1 | Mathlib.Order.Atoms | [
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"PartialOrder",
"LE.le",
"And.casesOn",
"And",
"And.intro",
"IsAtom",
"Set.instMembership",
"Set"
] | false |
Submodule.coe_toNonUnitalSubalgebra | Mathlib.Algebra.Algebra.NonUnitalSubalgebra | [
"Submodule",
"NonUnitalSubalgebra",
"HMul.hMul",
"CommSemiring.toSemiring",
"Membership.mem",
"Submodule.toNonUnitalSubalgebra",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"SetLike.coe",
"Distrib.toMul",
"Submodule.setLike",
"NonUnitalSubalgebra.instSetLike",
"NonUnitalNonA... | true |
CategoryTheory.conjugateEquiv_leftUnitor_hom | Mathlib.CategoryTheory.Adjunction.Mates | [
"CategoryTheory.Iso.inv_ext'",
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.conjugateEquiv_apply_app",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.rightUnitor",
... | true |
_private.Mathlib.Order.Interval.Set.OrdConnectedComponent.0.Set.dual_ordConnectedSection._simp_1_5 | Mathlib.Order.Interval.Set.OrdConnectedComponent | [
"Exists",
"Subtype.exists",
"Subtype",
"Subtype.mk",
"propext",
"Eq"
] | false |
Semigrp.str | Mathlib.Algebra.Category.Semigrp.Basic | [
"Semigroup",
"Semigrp",
"Semigrp.carrier"
] | true |
Num.succ'.eq_1 | Mathlib.Data.Num.Lemmas | [
"instOnePosNum",
"One.toOfNat1",
"Eq.refl",
"PosNum",
"OfNat.ofNat",
"Num.succ'",
"Eq",
"Num.zero"
] | true |
DirectSum.equivCongrLeft | Mathlib.Algebra.DirectSum.Basic | [
"Equiv.instEquivLike",
"instAddCommMonoidDirectSum",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Equiv",
"AddCommMonoid",
"AddZero.toZero",
"AddEquiv.mk",
"AddEquiv",
"DFinsupp",
"AddCommMonoid.toAddMonoid",
"AddCommSemigroup.toAddCommMagma",
"Equiv.symm",
"AddCommMonoid.toAddCo... | true |
Mathlib.Tactic.Widget.StringDiagram.AtomNode.atom | Mathlib.Tactic.Widget.StringDiagram | [
"Mathlib.Tactic.Widget.StringDiagram.AtomNode",
"Mathlib.Tactic.BicategoryLike.Atom"
] | true |
SimpleGraph.map_injective | Mathlib.Combinatorics.SimpleGraph.Maps | [
"Function.LeftInverse.injective",
"SimpleGraph.leftInverse_comap_map",
"Function.Embedding",
"SimpleGraph",
"SimpleGraph.comap",
"Function.Injective",
"Function.instFunLikeEmbedding",
"DFunLike.coe",
"SimpleGraph.map"
] | true |
ODE.FunSpace.compProj | Mathlib.Analysis.ODE.PicardLindelof | [
"Real",
"ODE.FunSpace",
"Set.projIcc",
"Set.Elem",
"NNReal",
"Set.Icc",
"ODE.FunSpace.compProj._proof_1",
"ODE.FunSpace.toFun",
"Real.instPreorder",
"Real.linearOrder",
"NormedAddCommGroup"
] | true |
Composition.recOnSingleAppend._unary._proof_3 | Mathlib.Combinatorics.Enumerative.Composition | [
"Nat.instMulZeroClass",
"List.sum",
"List",
"Nat",
"instAddNat",
"Eq",
"rfl",
"MulZeroClass.toZero"
] | false |
WithBot.add_right_cancel | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"IsRightCancelAdd",
"WithBot",
"Ne",
"Bot.bot",
"instHAdd",
"HAdd.hAdd",
"Iff.mp",
"WithBot.add_right_inj",
"WithBot.add",
"Eq",
"WithBot.bot",
"Add"
] | true |
MeasureTheory.Integrable.condExpKernel_ae | Mathlib.Probability.Kernel.Condexp | [
"MeasureTheory.ae",
"Nontrivial",
"Eq.mpr",
"StandardBorelSpace",
"ProbabilityTheory.IsZeroOrMarkovKernel.isFiniteKernel",
"ProbabilityTheory.Kernel.comap",
"MeasureTheory.Measure",
"congrArg",
"HEq.refl",
"Filter.Eventually",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.Integrable",
"... | true |
HomologicalComplex.restrictionMap._proof_2 | Mathlib.Algebra.Homology.Embedding.Restriction | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HomologicalComplex",
"ComplexShape",
"HomologicalComplex.restriction",
"True",
"eq_self",
"CategoryTheory.CategoryStruct... | false |
ArithmeticFunction.pow_one_eq_id | Mathlib.NumberTheory.ArithmeticFunction.Misc | [
"False",
"Nat.instMulZeroClass",
"ArithmeticFunction.ext",
"ArithmeticFunction.instFunLikeNat",
"Nat.instOne",
"congrArg",
"Nat.instMonoid",
"false_and",
"one_ne_zero._simp_1",
"instOfNatNat",
"Monoid.toPow",
"ArithmeticFunction.pow",
"And",
"ArithmeticFunction.id",
"HPow.hPow",
"Nat.i... | true |
ENNReal.coe_sub._simp_1 | Mathlib.Data.ENNReal.Operations | [
"ENNReal.ofNNReal",
"HSub.hSub",
"NNReal",
"instHSub",
"ENNReal.coe_sub",
"ENNReal",
"ENNReal.instSub",
"Eq.symm",
"Eq",
"NNReal.instSub"
] | false |
MeasureTheory.OuterMeasure.addCommMonoid._proof_1 | Mathlib.MeasureTheory.OuterMeasure.Operations | [
"NonUnitalNonAssocSemiring.nat_isScalarTower",
"instSMulOfMul",
"CommSemiring.toSemiring",
"IsScalarTower",
"AddMonoid.toNSMul",
"ENNReal.instCommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"ENNReal",
"NonUnita... | false |
Function.Surjective.sumMap | Mathlib.Data.Sum.Basic | [
"_private.Mathlib.Data.Sum.Basic.0.Function.Surjective.sumMap.match_1_1",
"Sum.map",
"Exists",
"Sum",
"Sum.inl",
"congr_arg",
"Sum.inr",
"_private.Mathlib.Data.Sum.Basic.0.Function.Surjective.sumMap.match_1_3",
"Exists.intro",
"Eq",
"Function.Surjective"
] | true |
Std.DTreeMap.Const.ofList_singleton | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.insert",
"Ordering",
"Std.DTreeMap.Const.ofList",
"Prod.mk",
"List.cons",
"Eq.refl",
"Std.DTreeMap.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Prod",
"Eq",
"List.nil"
] | true |
CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.symmetricCategory_braiding_inv_left | Mathlib.CategoryTheory.Monoidal.Arrow | [
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.instArrow",
"CategoryTheory.Functor.leibnizPushout._proof_1",
"CategoryTheor... | true |
dist_single_single | Mathlib.Topology.MetricSpace.Pseudo.Pi | [
"NNDist.nndist",
"Real",
"pseudoMetricSpacePi",
"congrArg",
"PseudoMetricSpace.toNNDist",
"SemilatticeSup.toMax",
"nndist_single_single",
"NNReal.instSemilatticeSup",
"NNReal",
"Ne",
"Pi.single",
"PseudoMetricSpace",
"Real.instMax",
"Fintype",
"Max.max",
"True",
"eq_self",
"of_eq_t... | true |
Std.Internal.List.containsKey_filter_not_contains_eq_false_left | Std.Data.Internal.List.Associative | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Bool.not",
"congrArg",
"List.contains",
"id",
"Std.Internal.List.containsKey_filter_not_contains",
"Bool.and",
"Sigma.fst",
"List",
"Std.Internal.List.containsKey",
"EquivBEq",
"Bool.false_and",
"List.filter",
"True",
"eq_self",
"Bool",
... | true |
FreeRing.coe_one | Mathlib.RingTheory.FreeCommRing | [
"FreeCommRing",
"AddGroupWithOne.toAddMonoidWithOne",
"instCommRingFreeCommRing",
"instRingFreeRing",
"AddMonoidWithOne.toOne",
"FreeRing",
"One.toOfNat1",
"CommRing.toRing",
"FreeRing.castFreeCommRing",
"OfNat.ofNat",
"Eq",
"Ring.toAddGroupWithOne",
"rfl"
] | true |
Computation.Results.mem | Mathlib.Data.Seq.Computation | [
"Membership.mem",
"Computation.Results",
"Computation",
"Computation.length",
"Nat",
"Computation.terminates_of_mem",
"Computation.instMembership",
"Eq",
"_private.Mathlib.Data.Seq.Computation.0.Computation.Results.mem.match_1_1"
] | true |
ShrinkingLemma.PartialRefinement._sizeOf_inst | Mathlib.Topology.ShrinkingLemma | [
"ShrinkingLemma.PartialRefinement",
"TopologicalSpace",
"SizeOf.mk",
"SizeOf",
"ShrinkingLemma.PartialRefinement._sizeOf_1",
"Set"
] | false |
not_bddAbove_univ._simp_2 | Mathlib.Order.Bounds.Basic | [
"False",
"eq_false",
"Set.univ",
"Preorder.toLE",
"not_bddAbove_univ",
"NoTopOrder",
"BddAbove",
"Eq",
"Preorder"
] | false |
Finset.addEnergy_univ_right | Mathlib.Combinatorics.Additive.Energy | [
"Eq.mpr",
"HMul.hMul",
"Finset.univ",
"Finset.addEnergy_comm",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Finset",
"Nat.instMonoid",
"AddMonoid.toAddZeroClass",
"Finset.addEnergy_univ_left",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Fintype.card",
"id",
"i... | true |
FP.FloatCfg.prec | Mathlib.Data.FP.Basic | [
"FP.FloatCfg",
"Nat"
] | true |
AlgebraicGeometry.Scheme.Cover.locallyDirectedPullbackCover._proof_10 | Mathlib.AlgebraicGeometry.Cover.Directed | [
"CategoryTheory.Limits.limit.π",
"Set.range_comp",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"Algebrai... | false |
starRingOfComm | Mathlib.Algebra.Star.Basic | [
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"starRingOfComm._proof_1",
"StarMul",
"starMulOfComm",
"StarRing.mk",
"MulOne.toMul",
"CommSemiring",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"StarRing",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"CommSemiring.toCommMonoid",
"... | true |
MulEquiv.hasEnoughRootsOfUnity | Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity | [
"isCyclic_of_surjective",
"Units.val",
"Eq.mpr",
"IsPrimitiveRoot.toRootsOfUnity",
"Nat.instMulZeroClass",
"MulEquiv.instEquivLike",
"Subgroup.instSubgroupClass",
"Monoid.toMulOneClass",
"congrArg",
"HasEnoughRootsOfUnity.prim",
"SubgroupClass.toGroup._proof_6",
"MulEquiv.instMulEquivClass",
... | true |
Std.Sat.AIG.RelabelNat.State.inv2 | Std.Sat.AIG.RelabelNat | [
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.RelabelNat.State.map",
"Std.Sat.AIG.RelabelNat.State.Inv2",
"Array",
"Nat",
"Std.Sat.AIG.RelabelNat.State",
"Hashable",
"DecidableEq"
] | true |
CategoryTheory.Discrete.monoidalFunctor_δ | Mathlib.CategoryTheory.Monoidal.Discrete | [
"Monoid",
"MonoidHom.instFunLike",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CategoryTheory.Functor.OplaxMonoidal.δ",
"MulOne.toMul",
"CategoryTheory.Discrete.mk",
"CategoryTheory.Functor.Monoidal.toOplaxMonoidal",
"CategoryTheor... | true |
_private.Mathlib.CategoryTheory.Bicategory.CatEnriched.0.CategoryTheory.CatEnriched.hComp_id._simp_1_2 | Mathlib.CategoryTheory.Bicategory.CatEnriched | [
"CategoryTheory.Cat.category",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CatEnriched.hComp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.CatEnriched.hComp_id_heq",
"CategoryTheory.Cat",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"Category... | false |
PerfectClosure.instCommRing._proof_5 | Mathlib.FieldTheory.PerfectClosure | [
"Distrib.leftDistribClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"Semigroup.toMul",
"CommRing",
"Nat.Prime",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"RingHomClass.toAddMonoidHomClass",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"AddMonoid.... | false |
CategoryTheory.preadditiveCoyoneda_obj | Mathlib.CategoryTheory.Preadditive.Yoneda.Basic | [
"CategoryTheory.Functor",
"Opposite",
"AddCommGrpCat.instCategory",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"MulOpposite",
"CategoryTheory.Functor.category",
"LinearMap.instFunLike",
"CategoryTheory.Functor.comp",
"AddCommGroup.toAddGroup",
"AddCommGrpCat.instC... | true |
Lean.Elab.Term.Do.mkReturn | Lean.Elab.Do.Legacy | [
"Lean.Syntax",
"Lean.Name.cmp",
"Lean.Elab.Term.Do.Code.return",
"Lean.Elab.Term.Do.VarSet",
"Lean.Elab.Term.Do.CodeBlock",
"Lean.Name",
"Std.TreeMap.instEmptyCollection",
"Lean.Elab.Term.Do.CodeBlock.mk",
"EmptyCollection.emptyCollection"
] | true |
_private.Mathlib.Analysis.Asymptotics.LinearGrowth.0.LinearGrowth.EReal.eventually_atTop_exists_nat_between.match_1_3 | Mathlib.Analysis.Asymptotics.LinearGrowth | [
"Real",
"Preorder.toLT",
"PartialOrder.toPreorder",
"Option.casesOn",
"EReal",
"Option.some",
"instTopEReal",
"Bot.bot",
"Option.none",
"LT.lt",
"instPartialOrderEReal",
"Top.top",
"instBotEReal",
"Real.toEReal",
"WithTop"
] | false |
CategoryTheory.Quotient.preadditive._proof_6 | Mathlib.CategoryTheory.Quotient.Preadditive | [
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Quotient",
"Quiver.Hom",
"CategoryTheory.Quotient.preadditive._proof_1",
"Zero.zero",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Quotient.category",
"CategoryTheory.Quotient.preadditive._proof_5",
"Add.mk",
"Neg.mk",
"CategoryTheory.... | false |
Lean.Meta.Match.Extension.Entry.name | Lean.Meta.Match.MatcherInfo | [
"Lean.Name",
"Lean.Meta.Match.Extension.Entry"
] | true |
CategoryTheory.Preadditive.instMonoNegHom | Mathlib.CategoryTheory.Preadditive.Basic | [
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Preadditive.comp_neg",
"Eq.mp",
"SubtractionMonoid.toSubNegZeroMonoid",
"CategoryTheory.cancel_mono",
"SubNegZeroMonoid.toNegZeroC... | true |
_private.Lean.Environment.0.Lean.Environment.AddConstAsyncResult.allRealizationsPromise | Lean.Environment | [
"Lean.NameMap",
"Lean.Environment.AddConstAsyncResult",
"_private.Lean.Environment.0.Lean.AsyncConst",
"IO.Promise"
] | true |
ModuleCat.HasColimit.coconePointSMul._proof_12 | Mathlib.Algebra.Category.ModuleCat.Colimits | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"ModuleCat",
"ModuleCat.smul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"ModuleCat.smul_naturality",
"LinearMap.instFunLik... | false |
GradedTensorProduct.algebraMap_def | Mathlib.LinearAlgebra.TensorProduct.Graded.Internal | [
"Int.instCommMonoid",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"GradedTensorProduct",
"CommRing",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"Additive",
"AddGroupWithOne.toAddMonoidWithOne",
"Algebra",
"RingHom",
"Units",
"GradedTensorProduct.tmu... | true |
Fin.fin_two_eq_of_eq_zero_iff | Init.Data.Fin.Lemmas | [
"Eq.mpr",
"instDecidableTrue",
"of_decide_eq_true",
"congrArg",
"instDecidableEqFin",
"id",
"Fin.instOfNat",
"forall_prop_decidable",
"instOfNatNat",
"iff_self",
"Bool.true",
"And",
"Iff",
"Nat.instNeZeroSucc",
"implies_congr",
"Nat",
"congr",
"True",
"eq_self",
"Bool",
"Eq.r... | true |
instGroupObjOppositeOpensCarrierOfPresheafSmoothSheaf._aux_4 | Mathlib.Geometry.Manifold.Sheaf.Smooth | [
"MulOne.toOne",
"Opposite",
"NormedSpace",
"instTopENat",
"Monoid.toMulOneClass",
"TopologicalSpace.Opens.instPartialOrder",
"TopologicalSpace.Opens.instChartedSpace",
"ContMDiffMap.const",
"PartialOrder.toPreorder",
"Group",
"TopologicalSpace.Opens",
"Membership.mem",
"Subtype",
"DivInvMo... | false |
spectralNorm.nontriviallyNormedField | Mathlib.Analysis.Normed.Unbundled.SpectralNorm | [
"spectralNorm.nontriviallyNormedField._proof_1",
"NormedCommRing.toSeminormedCommRing",
"CompleteSpace",
"PseudoMetricSpace.toUniformSpace",
"Algebra",
"NormedField.toField",
"Field.toDivisionRing",
"DivisionRing.toRing",
"Algebra.IsAlgebraic",
"Field.toSemifield",
"Field.toCommRing",
"NormedF... | true |
_private.Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas.0.iteratedDeriv_neg._simp_1_1 | Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | [
"NormedSpace",
"Set.univ",
"iteratedDerivWithin",
"Nat",
"iteratedDerivWithin_univ",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"iteratedDeriv",
"Eq.symm",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Eq",
"NormedAddCommGroup"
] | false |
CategoryTheory.Comonad.mk.noConfusion | Mathlib.CategoryTheory.Monad.Basic | [
"CategoryTheory.Comonad",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Comonad.right_counit._autoParam",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id... | false |
CategoryTheory.GrothendieckTopology.instWEqualsLocallyBijectiveTypeFun | Mathlib.CategoryTheory.Sites.LocallyBijective | [
"CategoryTheory.Limits.Types.hasColimitsOfShape",
"CategoryTheory.GrothendieckTopology.instPreservesSheafificationForgetOfPreservesLimitsOfHasColimitsOfShapeOfPreservesColimitsOfShapeOppositeCoverOfHasLimitsOfShapeWalkingMulticospanOfReflectsIsomorphisms",
"CategoryTheory.instFaithfulForget",
"CategoryTheory.... | true |
_private.Init.Data.List.Impl.0.List.replaceTR.go.eq_def | Init.Data.List.Impl | [
"cond",
"List.brecOn",
"Eq.mpr",
"List.brecOn.go",
"List.brecOn.eq",
"Array.push",
"congrArg",
"id",
"List.rec",
"_private.Init.Data.List.Impl.0.List.takeWhileTR.go.match_1",
"List.cons",
"Array",
"_private.Init.Data.List.Impl.0.List.replaceTR.go",
"List",
"BEq.beq",
"PProd",
"PUnit"... | true |
Lean.Meta.Grind.Arith.Cutsat.EqCnstr.rec_2 | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.mul",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.coreToInt",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.core0",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.ofLeGe",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.neg",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.r... | false |
AlgebraicGeometry.Scheme.Pullback.t'._proof_1 | Mathlib.AlgebraicGeometry.Pullbacks | [
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"AlgebraicGeometry.Scheme.Pullback.v",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.Scheme.OpenCover",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.PreZeroHyperco... | false |
MulEquiv.toMonoidHom._proof_1 | Mathlib.Algebra.Group.Equiv.Defs | [
"HMul.hMul",
"MulEquiv.map_mul'",
"MulOne.toMul",
"MulEquiv.toEquiv",
"Equiv.toFun",
"MulOneClass.toMulOne",
"MulEquiv",
"MulOneClass",
"Eq",
"instHMul"
] | false |
OpenPartialHomeomorph.singletonChartedSpace_chartAt_eq | Mathlib.Geometry.Manifold.HasGroupoid | [
"chartAt",
"Set.univ",
"TopologicalSpace",
"OpenPartialHomeomorph.singletonChartedSpace",
"PartialEquiv.source",
"OpenPartialHomeomorph.toPartialEquiv",
"Eq",
"OpenPartialHomeomorph",
"rfl",
"Set"
] | true |
PresheafOfModules.colimitPresheafOfModules._proof_8 | Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits | [
"CategoryTheory.Functor",
"Opposite",
"HMul.hMul",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"MulZeroOneClass.toMulOneClass",
"RingCat",
"MulOneClass.toMulOne",
"RingHom.id._proof_2",
"RingCat.instCategory",
"CategoryTheory.Category.opposite",
"RingCat.instRingObjForgetRingHomCarri... | false |
ModuleCat.hom_add | Mathlib.Algebra.Category.ModuleCat.Basic | [
"ModuleCat.instAddHom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instAdd",
"LinearMap",
"instHAdd",
"ModuleCat.isAddCommGroup",
"HAdd.hAdd",
"ModuleCat.moduleCategory",
"ModuleCat.carrier",
"CategoryTheory.Category.toCate... | true |
MonadControl.noConfusion | Init.Control.Basic | [
"MonadControl.casesOn",
"HEq.refl",
"MonadControl.noConfusionType",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq",
"MonadControl"
] | false |
IsCompact.diff | Mathlib.Topology.Compactness.Compact | [
"Iff.mpr",
"False",
"Compl.compl",
"Membership.mem",
"Set.instCompl",
"IsClosed",
"TopologicalSpace",
"SDiff.sdiff",
"IsCompact.inter_right",
"IsOpen",
"Set.instMembership",
"IsCompact",
"Set.instSDiff",
"isClosed_compl_iff",
"Set"
] | true |
Set.image_insert_eq | Mathlib.Data.Set.Image | [
"_private.Mathlib.Data.Set.Image.0.Set.image_insert_eq._proof_1_1",
"Insert.insert",
"Set.instInsert",
"Set.image",
"Eq",
"Set"
] | true |
Complex.not_continuousAt_Gamma_neg_nat | Mathlib.Analysis.SpecialFunctions.Gamma.Deriv | [
"Iff.mpr",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"False",
"T6Space.toT5Space",
"Nat.recAux",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"Complex.Gamma_add_one",
"AddMonoid.toAddSemigroup",
"IsTopologicalRing.toIsTopologicalSemiring",
"AddGr... | true |
Associates.mkMonoidHom_apply | Mathlib.Algebra.GroupWithZero.Associated | [
"Associates.mk",
"Associates.instCommMonoid",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Associates.mkMonoidHom",
"MulOneClass.toMulOne",
"Associates",
"CommMonoid.toMonoid",
"Eq",
"CommMonoid",
"DFunLike.coe",
"rfl"
] | true |
CategoryTheory.Triangulated.TStructure.natTransTruncLEOfLE.congr_simp | Mathlib.CategoryTheory.Triangulated.TStructure.TruncLEGT | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Triangulated.TStructure.natTransTruncLEOfLE",
"Int",
"Int.instAddMonoid",
"LE.le",
"CategoryTheor... | true |
alexandrovDiscrete_coinduced | Mathlib.Topology.AlexandrovDiscrete | [
"Eq.mpr",
"congrArg",
"Set.iInter",
"Membership.mem",
"id",
"AlexandrovDiscrete.mk",
"TopologicalSpace.coinduced",
"TopologicalSpace",
"AlexandrovDiscrete",
"Set.preimage",
"isOpen_coinduced",
"Set.preimage_sInter",
"propext",
"IsOpen",
"Eq",
"Set.sInter",
"Set.instMembership",
"is... | true |
DivisibleHull.instIsOrderedCancelAddMonoid | Mathlib.GroupTheory.DivisibleHull | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"PNat.val",
"Eq.mpr",
"add_lt_add_right",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Meta.NormNum.isNat_add",
"instHSMul",
"Preorder.toLT",
"Mathlib.Tactic.Ring.Common.mul_congr",
"HMul.hMul... | true |
Monoid.CoprodI.NeWord.inv_last | Mathlib.GroupTheory.CoprodI | [
"MulOne.toOne",
"Monoid.CoprodI.NeWord.inv",
"DivInvOneMonoid.toInvOneClass",
"Monoid.CoprodI.NeWord",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"DivInvMonoid.toMonoid",
"Ne",
"Monoid.CoprodI.NeWord.append",
"Group.toDivInvMono... | true |
Lean.Elab.Command.AssertExists.isDecl | Lean.Elab.AssertExists | [
"Lean.Elab.Command.AssertExists",
"Bool"
] | true |
Lean.PrettyPrinter.Delaborator.OmissionReason.string.noConfusion | Lean.PrettyPrinter.Delaborator.Basic | [
"Lean.PrettyPrinter.Delaborator.OmissionReason",
"Lean.PrettyPrinter.Delaborator.OmissionReason.noConfusion",
"String",
"id",
"Eq",
"Lean.PrettyPrinter.Delaborator.OmissionReason.string"
] | false |
Vector.get_ofFn | Batteries.Data.Vector.Lemmas | [
"Vector.get",
"Fin.isLt",
"Fin.val",
"Nat",
"Vector.getElem_ofFn",
"Fin",
"Eq",
"Vector.ofFn"
] | true |
Subgroup.QuotientDiff | Mathlib.GroupTheory.SchurZassenhaus | [
"Monoid.toMulOneClass",
"Subgroup.FiniteIndex",
"Subgroup.leftTransversals.diff",
"Subgroup.mul",
"Group",
"Membership.mem",
"Subgroup.QuotientDiff._proof_3",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"Subgroup.one",
"IsMulCommutative",
"MulOneClass.toMulOne",... | true |
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