name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.PrettyPrinter.Delaborator.OmissionReason.string.sizeOf_spec | Lean.PrettyPrinter.Delaborator.Basic | [
"Lean.PrettyPrinter.Delaborator.OmissionReason",
"String",
"Lean.PrettyPrinter.Delaborator.OmissionReason._sizeOf_inst",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"String._sizeOf_inst",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.PrettyPrinter.Delaborator.Omi... | true |
Lean.Meta.Sym.Context.config._default | Lean.Meta.Sym.SymM | [
"id",
"Lean.Meta.Sym.Config.mk",
"Bool.true",
"Lean.Meta.Sym.Config"
] | false |
_private.Mathlib.RingTheory.Ideal.Maximal.0.Ideal.exists_le_prime_disjoint.match_1_1 | Mathlib.RingTheory.Ideal.Maximal | [
"Semiring.toModule",
"ChainCompletePartialOrder.instOfCompleteLattice",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"Exists",
"Submodule.instPartialOrder",
"LE.le",
"Ideal",
... | false |
MeasureTheory.ae_eq_trim_iff_of_aestronglyMeasurable | Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"MeasurableSpace.instLE",
"TopologicalSpace.MetrizableSpace",
"Filter.EventuallyEq.trans",
"MeasureTheory.Measure.trim",
"Filter.EventuallyEq",
"LE.le",
"MeasureTheory.AEStronglyMeasurable.stronglyMeasurable_mk",
"MeasureTheory.AEStronglyMeasurable.ae_e... | true |
Lean.Meta.mkHEq | Lean.Meta.AppBuilder | [
"Pure.pure",
"Lean.Meta.State",
"Lean.mkApp4",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Level",
"Lean.Meta.getLevel",
"Applicative.toPure",
"Lean.mkConst",
"List.cons",
"Lean.Core.CoreM",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"StateRefT'.instMonad",
"Monad.toBind",
"... | true |
String.Pos.instTransLe | Init.Data.String.OrderInstances | [
"String.Pos.instTransLe._proof_2",
"String",
"LE.le",
"Trans",
"String.Pos",
"String.instLEPos",
"Trans.mk"
] | true |
Submodule.mulRightMap | Mathlib.LinearAlgebra.Finsupp.LSum | [
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"instHSMul",
"instSMulOfMul",
"Pi.addCommMonoid",
"Finsupp.module",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"Submodule.mulRightMap._proof_1",
"MulOp... | true |
CategoryTheory.MonoidalClosed.uncurry_ihomUncurry | Mathlib.CategoryTheory.Monoidal.Closed.InternalCurrying | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.MonoidalClosed.uncurry",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.MonoidalClosed.uncurry_curry",
"Categor... | true |
CategoryTheory.LiftRightAdjoint.constructRightAdjoint | Mathlib.CategoryTheory.Adjunction.Lifting.Right | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.LiftRightAdjoint.constructRightAdjointObj",
"CategoryTheory.Functor.id",
"CategoryTheory.Limits.HasCoreflexiveEqualizers",
"CategoryTheor... | true |
TopCat.pathEquiv._proof_4 | Mathlib.Topology.Homotopy.TopCat.Path | [
"Real",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"ContinuousMapClass",
"Set.Elem",
"TopCat.str",
"Homeomorph.instEquivLike",
"TopCat.carrier",
"Homeomorph",
"TopCat.I",
"Real.pseudoMetricSpace",
"instTopologicalSpaceSubtype",
"Homeomorph.instContinuousMapClass",
"UniformSpace.... | false |
Bimod.AssociatorBimod.hom_inv_id | Mathlib.CategoryTheory.Monoidal.Bimod | [
"CategoryTheory.Limits.PreservesColimitsOfShape.preservesColimit",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"Bimod.AssociatorBimod.inv",
"CategoryTheory.Limits.PreservesColimitsOfSize",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"Bimo... | true |
Batteries.RBNode.Path.Balanced.ins | Batteries.Data.RBMap.Alter | [
"_private.Batteries.Data.RBMap.Alter.0.Batteries.RBNode.Path.Balanced.ins.match_1_5",
"Batteries.RBNode",
"Batteries.RBNode.Path",
"_private.Batteries.Data.RBMap.Alter.0.Batteries.RBNode.Path.Balanced.ins.match_1_1",
"Batteries.RBNode.RedRed.setBlack",
"Batteries.RBNode.balance2",
"Exists",
"Batteries... | true |
Ideal.snd_comp_quotientInfEquivQuotientProd | Mathlib.RingTheory.Ideal.Quotient.Operations | [
"CommRing",
"Semiring.toModule",
"Ideal.Quotient.ringHom_ext",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"Prod.instMul",
"Prod.instAdd",
"RingEquiv.instEquivLike",
"Submodule.completeLattice",
"RingEquiv.instRingEquivClass",
"RingHom",
"inf_le_right",
"CompleteLattice.toConditionallyCo... | true |
CategoryTheory.Profunctor.ofHom._proof_4 | Mathlib.CategoryTheory.Profunctor.Basic | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.ProfunctorCore.Hom",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"CategoryTheory.Profunctor.ofHom._proof_2",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.category",
"Ca... | false |
Subsemiring.mem_centralizer_iff | Mathlib.Algebra.Ring.Subsemiring.Basic | [
"Subsemiring.instSetLike",
"HMul.hMul",
"Subsemiring.centralizer",
"Iff.rfl",
"Membership.mem",
"Subsemiring",
"instDistribOfSemiring",
"Iff",
"Distrib.toMul",
"Semiring",
"Semiring.toNonAssocSemiring",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"instHMul",
"Set"
] | true |
BitVec.extractLsb'_append_extractLsb' | Init.Data.BitVec.Lemmas | [
"BitVec.getElem_append._proof_2",
"Eq.mpr",
"Decidable.casesOn",
"dite_congr",
"BitVec.extractLsb'",
"congrArg",
"BitVec.instHAppendHAddNat",
"HSub.hSub",
"Decidable",
"BitVec.getElem_append",
"BitVec.getElem_extractLsb'",
"BitVec",
"BitVec.getLsbD_eq_getElem",
"BitVec.getLsbD",
"id",
... | true |
Std.Internal.List.getValue?_insertEntry | Std.Data.Internal.List.Associative | [
"congrArg",
"Std.Internal.List.getValue?_insertEntry_of_false",
"Bool.false_eq_true",
"Option.some",
"instDecidableEqBool",
"Std.Internal.List.insertEntry",
"ite_cond_eq_true",
"Bool.true",
"List",
"Std.Internal.List.getValue?_insertEntry_of_beq",
"BEq.beq",
"Bool.casesOn",
"Std.Internal.Lis... | true |
sSupHom.instSSupHomClass | Mathlib.Order.Hom.CompleteLattice | [
"sSupHom.instFunLike",
"SupSet",
"sSupHomClass",
"sSupHom",
"sSupHom.map_sSup'",
"sSupHomClass.mk"
] | true |
DFinsupp.Colex.decidableLE | Mathlib.Data.DFinsupp.Lex | [
"Colex",
"DFinsupp.Colex.partialOrder",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"DecidableLE",
"DFinsupp.Lex.decidableLE",
"DFinsupp",
"OrderDual",
"OrderDual.instLinearOrder",
"instDistribLatticeOfLinearOrder",
... | true |
VectorFourier.norm_fourierIntegral_le_integral_norm | Mathlib.Analysis.Fourier.FourierTransform | [
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"Real.instLE",
"Real",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"VectorFourier.four... | true |
Ideal.Quotient.algebraMap_quotient_of_ramificationIdx_neZero | Mathlib.NumberTheory.RamificationInertia.Basic | [
"Ideal.Quotient.commSemiring",
"Nat.instMulZeroClass",
"CommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"Algebra",
"RingHom",
"Ideal.Quotient.algebraQuotientOfRamificationIdxNeZero",
"Ideal",
"HasQuotient.Quotient",
"Ideal.Quotient.ring",
"Ideal.instIsTwoSide... | true |
QuotientAddGroup.equivIcoMod._proof_2 | Mathlib.Algebra.Order.ToIntervalMod | [
"Preorder.toLT",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"AddCommGroup.toAddGroup",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"Function.Periodic.lift",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMono... | false |
Lean.Compiler.LCNF.Check.Pure.State._sizeOf_inst | Lean.Compiler.LCNF.Check | [
"SizeOf.mk",
"Lean.Compiler.LCNF.Check.Pure.State",
"SizeOf",
"Lean.Compiler.LCNF.Check.Pure.State._sizeOf_1"
] | false |
_private.Mathlib.Topology.UniformSpace.Defs.0.isOpen_uniformity._simp_1_2 | Mathlib.Topology.UniformSpace.Defs | [
"Filter.instMembership",
"Filter.mem_comap_prodMk",
"setOf",
"Membership.mem",
"Prod.mk",
"Prod.fst",
"propext",
"Prod",
"Eq",
"Set.instMembership",
"Prod.snd",
"Filter",
"Filter.comap",
"Set"
] | false |
Std.Rcc.isSome_succMany?_of_lt_length_toList | Init.Data.Range.Polymorphic.Lemmas | [
"Option.isSome_filter",
"GetElem?.toGetElem",
"Std.Rcc.lower",
"Std.PRange.UpwardEnumerable",
"congrArg",
"Option.any",
"List.instGetElem?NatLtLength",
"Option.some",
"Eq.mp",
"LE.le",
"Option.isSome_of_any",
"Std.Rcc.getElem?_toList_eq",
"LE",
"GetElem.getElem",
"Bool.true",
"List",
... | true |
Multiset.rel_zero_right._simp_1 | Mathlib.Data.Multiset.ZeroCons | [
"Multiset",
"Multiset.Rel",
"propext",
"Zero.toOfNat0",
"Multiset.rel_zero_right",
"OfNat.ofNat",
"Eq",
"Multiset.instZero"
] | false |
_private.Batteries.Data.Array.Scan.0.Array.back?_scanr._simp_1_1 | Batteries.Data.Array.Scan | [
"List.getLast?",
"Array.toList",
"Array",
"Array.back?",
"Array.getLast?_toList",
"Eq.symm",
"Eq",
"Option"
] | false |
Batteries.RBNode.del._unsafe_rec | Batteries.Data.RBMap.Basic | [
"Batteries.RBNode",
"Batteries.RBNode.fold.match_1",
"Batteries.RBNode.del.match_1",
"Batteries.RBNode.balLeft",
"Batteries.RBNode.isBlack",
"Batteries.RBNode.balRight",
"Ordering",
"Batteries.RBNode.nil",
"Batteries.RBNode.del._unsafe_rec",
"Batteries.RBNode.append",
"Unit",
"Batteries.RBColo... | false |
SimpleGraph.Subgraph.Preconnected.casesOn | Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | [
"SimpleGraph.Subgraph",
"SimpleGraph.Preconnected",
"Set.Elem",
"SimpleGraph.Subgraph.Preconnected",
"SimpleGraph",
"SimpleGraph.Subgraph.Preconnected.rec",
"SimpleGraph.Subgraph.coe",
"SimpleGraph.Subgraph.verts",
"SimpleGraph.Subgraph.Preconnected.mk"
] | false |
ContinuousLinearMap.isBigOTVS_fun_comp | Mathlib.Analysis.Asymptotics.TVS | [
"NormedCommRing.toSeminormedCommRing",
"Asymptotics.IsBigOTVS",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"AddZeroClass.toAddZero... | true |
Lean.Meta.DefaultInstanceEntry.rec | Lean.Meta.Instances | [
"Lean.Meta.DefaultInstanceEntry.mk",
"Nat",
"Lean.Meta.DefaultInstanceEntry",
"Lean.Name"
] | false |
_private.Mathlib.Algebra.Polynomial.Inductions.0.Polynomial.natDegree_divX_eq_natDegree_tsub_one._simp_1_2 | Mathlib.Algebra.Polynomial.Inductions | [
"Polynomial.C",
"RingHom",
"Polynomial.divX_eq_zero_iff",
"instOfNatNat",
"Polynomial.divX",
"Polynomial",
"Polynomial.coeff",
"RingHom.instFunLike",
"Polynomial.semiring",
"Nat",
"propext",
"Semiring",
"Zero.toOfNat0",
"Polynomial.instZero",
"OfNat.ofNat",
"Semiring.toNonAssocSemiring... | false |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital.0._auto_129 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.Bicategory.hom_inv_whiskerRight_whiskerRight_assoc | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"Eq.mp",
"CategoryTheory.Bicategory.whiskerRight",
"id",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"Mathlib.Tactic.Reassoc.eq_whisker... | true |
Booleanisation.instBooleanAlgebra._proof_14 | Mathlib.Order.Booleanisation | [
"Booleanisation.instDistribLattice",
"Booleanisation.instCompl",
"Lattice.toSemilatticeSup",
"Compl.compl",
"PartialOrder.toPreorder",
"Booleanisation",
"Preorder.toLE",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"LE.le",
"Max.max",
"GeneralizedBooleanAlgebra",
"Booleanisation.instP... | false |
Finset.convexHull_eq | Mathlib.Analysis.Convex.Combination | [
"Set.Subset.antisymm",
"Eq.mpr",
"mul_nonneg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"le_refl",
"instHSMul",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"ChainCompletePartialOrder.instOfCompleteLattice",
"CommRing.toNonUnita... | true |
Submodule.prodEquivOfIsCompl_symm_apply_right | Mathlib.LinearAlgebra.Projection | [
"Iff.mpr",
"Submodule",
"LinearEquiv.symm",
"Submodule.prodEquivOfIsCompl",
"congrArg",
"LinearEquiv.symm_apply_eq",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Submodule.completeLattice",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Membership.mem",
"CompleteLatti... | true |
Mathlib.Tactic.Push.Head.noConfusionType | Mathlib.Tactic.Push.Attr | [
"Mathlib.Tactic.Push.Head.casesOn",
"Mathlib.Tactic.Push.Head",
"dite",
"Mathlib.Tactic.Push.Head.const.elim",
"Nat",
"Mathlib.Tactic.Push.Head.ctorIdx",
"Nat.decEq",
"Lean.Name",
"Mathlib.Tactic.Push.Head.forall.elim",
"Eq",
"Not",
"Mathlib.Tactic.Push.Head.lambda.elim"
] | false |
biInf_sigma | Mathlib.Data.Set.Sigma | [
"iInf",
"Membership.mem",
"CompleteLattice.toCompleteSemilatticeInf",
"OrderDual.instCompleteLattice",
"Set.sigma",
"biSup_sigma",
"Sigma.mk",
"CompleteSemilatticeInf.toInfSet",
"OrderDual",
"CompleteLattice",
"Eq",
"Set.instMembership",
"Sigma",
"Set"
] | true |
ArchimedeanClass.mem_closedBall_iff | Mathlib.Algebra.Order.Module.Archimedean | [
"Submodule",
"Ring.toNonAssocRing",
"IsOrderedRing",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"ArchimedeanClass.instLinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Semi... | true |
_private.Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis.0.AlgebraicIndependent.matroid_isBasis_iff._simp_1_2 | Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis | [
"CommRing",
"AlgebraicIndependent.matroid_indep_iff",
"AlgebraicIndepOn",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.toSMul",
"AlgebraicIndependent.matroid",
"Matroid.Indep",
"id",
"instDistribOfSemiring",
"FaithfulSMul",
"CommRing.toCommSemiring",
"NoZeroDivisors",
"Distrib.toMul",
... | false |
Pi.addMonoidHom._proof_2 | Mathlib.Algebra.Group.Pi.Lemmas | [
"AddMonoidHom.toAddHom",
"AddZeroClass.toAddZero",
"AddHom.map_add'",
"instHAdd",
"AddZeroClass",
"Pi.instAdd",
"HAdd.hAdd",
"Pi.addHom",
"AddZero.toAdd",
"AddMonoidHom",
"Eq",
"AddHom.toFun"
] | false |
ContinuousMap.mem_nhds_iff | Mathlib.Topology.CompactOpen | [
"Filter.instMembership",
"ContinuousMap.hasBasis_nhds",
"Filter.HasBasis.mem_iff",
"_private.Mathlib.Topology.CompactOpen.0.ContinuousMap.mem_nhds_iff._simp_1_1",
"congrArg",
"Set.iInter",
"ContinuousMap",
"Prod.forall._simp_1",
"setOf",
"Set.Finite",
"Membership.mem",
"Exists",
"nhds",
"P... | true |
IsMulCommutative.instNonAssocCommSemiring._proof_1 | Mathlib.Algebra.Ring.Defs | [
"HMul.hMul",
"NonUnitalNonAssocSemiring.toMul",
"IsMulCommutative",
"NonUnitalNonAssocCommSemiring.mul_comm",
"IsMulCommutative.instNonUnitalNonAssocCommSemiring",
"NonAssocSemiring",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocS... | false |
sub_one_div_inv_le_two | Mathlib.Algebra.Order.Field.Basic | [
"Iff.mpr",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"DivInvMonoid.toInv",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"GroupWithZero.toDivi... | true |
Lean.Linter.MissingDocs.checkSyntaxCat._regBuiltin.Lean.Linter.MissingDocs.checkSyntaxCat_1 | Lean.Linter.MissingDocs | [
"Lean.Linter.MissingDocs.addBuiltinHandler",
"IO",
"Lean.Linter.MissingDocs.checkSyntaxCat",
"Unit",
"Lean.Name.mkStr4",
"Lean.Linter.MissingDocs.SimpleHandler.toHandler"
] | false |
Lean.Doc.PostponedName.casesOn | Lean.Elab.DocString.Builtin.Postponed | [
"Lean.Doc.PostponedName",
"Lean.Doc.PostponedName.mk",
"Lean.Name",
"Lean.Doc.PostponedName.rec"
] | false |
NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne | [
"IsModuleTopology.toContinuousSMul",
"NormedCommRing.toNormedRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Set.Ioi",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"trivial",
"NormedRing.toRing... | true |
Std.DHashMap.Raw.Const.get_map' | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Eq.mpr",
"congrArg",
"Std.DHashMap.Raw.mem_of_mem_map",
"Std.DHashMap.Raw.Const.get",
"Std.DHashMap.Internal.Raw₀.getKey",
"Std.DHashMap.Raw",
"Membership.mem",
"id",
"Std.DHashMap.Internal.Raw.get_eq._proof_2",
"instOfN... | true |
List.getElem?_iterate | Mathlib.Data.List.Iterate | [
"List.iterate",
"List.instGetElem?NatLtLength",
"Option.some",
"Nat.brecOn",
"Nat.iterate",
"List",
"Nat",
"LT.lt",
"instLTNat",
"GetElem?.getElem?",
"Eq",
"List.length",
"Option",
"List.getElem?_iterate._f"
] | true |
Finset.traverse.eq_1 | Mathlib.Data.Finset.Functor | [
"Multiset.toFinset",
"CommApplicative",
"Finset",
"Multiset.traverse",
"Multiset",
"Finset.val",
"Applicative",
"Applicative.toFunctor",
"Eq.refl",
"Finset.traverse",
"Eq",
"Functor.map",
"DecidableEq"
] | true |
MeasureTheory.FiniteMeasure.instModuleNNReal | Mathlib.MeasureTheory.Measure.FiniteMeasure | [
"MeasureTheory.FiniteMeasure",
"ENNReal.instModuleNNReal",
"MeasureTheory.Measure",
"Semiring.toModule",
"instSMulOfMul",
"MeasureTheory.FiniteMeasure.instModuleNNReal._proof_2",
"CommSemiring.toSemiring",
"MeasureTheory.FiniteMeasure.instModuleNNReal._proof_4",
"MeasureTheory.FiniteMeasure.instAddC... | true |
CoeFun.recOn | Init.Coe | [
"CoeFun.mk",
"CoeFun.rec",
"CoeFun"
] | false |
Lean.Compiler.LCNF.Decl.isTemplateLike | Lean.Compiler.LCNF.Basic | [
"Pure.pure",
"Bool.not",
"Lean.Compiler.LCNF.Decl.toSignature",
"Lean.Core.instMonadEnvCoreM",
"Lean.Compiler.LCNF.Decl",
"IO.RealWorld",
"Bool.and",
"EIO",
"instDecidableEqBool",
"Lean.Compiler.LCNF.Purity",
"instMonadEIO",
"Applicative.toPure",
"Lean.Compiler.hasSpecializeAttribute",
"Le... | true |
IsLocalExtr.comp_continuous | Mathlib.Topology.Order.LocalExtr | [
"ContinuousAt",
"IsLocalExtr",
"Function.comp",
"nhds",
"IsExtrFilter.comp_tendsto",
"TopologicalSpace",
"Preorder"
] | true |
Matroid.IsBasis.subset_closure | Mathlib.Combinatorics.Matroid.Closure | [
"Eq.mpr",
"Matroid.closure_subset_closure_iff_subset_closure",
"Matroid.IsBasis.subset_ground",
"congrArg",
"id",
"Set.instReflSubset",
"HasSubset.Subset",
"subset_refl",
"propext",
"Matroid.closure",
"Matroid.IsBasis",
"Eq.symm",
"Eq",
"Matroid",
"Set.instHasSubset",
"Matroid.IsBasis.... | true |
IsDiscrete.preimage' | Mathlib.Topology.DiscreteSubset | [
"Pure.pure",
"Iff.mpr",
"Filter.Tendsto.le_comap",
"le_refl",
"congrArg",
"inf_le_inf",
"Filter.instCompleteLatticeFilter",
"nhdsWithin",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"nhds",
"CompleteLattice.toConditionallyCompleteLattice",... | true |
_private.Mathlib.Data.Nat.GCD.Basic.0.Nat.coprime_iff_isRelPrime._simp_1_5 | Mathlib.Data.Nat.GCD.Basic | [
"MulOne.toOne",
"Dvd.dvd",
"Monoid.toMulOneClass",
"semigroupDvd",
"IsUnit",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"propext",
"Monoid.toSemigroup",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"CommMonoid",
"isUnit_iff_dvd_one"
] | false |
NonUnitalSubring.add_mem | Mathlib.RingTheory.NonUnitalSubring.Defs | [
"NonUnitalNonAssocRing",
"NonUnitalSubring.instSetLike",
"AddSubmonoidClass.toAddMemClass",
"NonUnitalSubringClass.toNonUnitalSubsemiringClass",
"AddMonoid.toAddZeroClass",
"NonUnitalSubring",
"Membership.mem",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonUnitalSubring... | true |
SSet.Truncated.HomotopyCategory₂._sizeOf_1 | Mathlib.AlgebraicTopology.Quasicategory.TwoTruncated | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"instSizeOfDefault",
"SSet.Truncated",
"SSet.Truncated.Quasicategory₂._proof_1",
"SSet.Truncated.HomotopyCategory₂.rec",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Opposite.op",
"Nat"... | false |
SimpleGraph.IsClique.mono | Mathlib.Combinatorics.SimpleGraph.Clique | [
"SimpleGraph.Adj",
"LE.le",
"SimpleGraph",
"Set.Pairwise.mono'",
"SimpleGraph.IsClique",
"SimpleGraph.instLE",
"Set"
] | true |
MonCat | Mathlib.Algebra.Category.MonCat.Basic | [
"MonCat.mk"
] | true |
Topology.CWComplex.instRelCWComplex._proof_3 | Mathlib.Topology.CWComplex.Classical.Basic | [
"Eq.mpr",
"Real",
"pseudoMetricSpacePi",
"Real.instZero",
"congrArg",
"Topology.CWComplex",
"Finset",
"Set.empty_union",
"Membership.mem",
"Exists",
"Set.instUnion",
"Topology.CWComplex.cell",
"id",
"Topology.CWComplex.map",
"Pi.instZero",
"Topology.CWComplex.mapsTo'",
"Fin.fintype",... | false |
WithTopology.instSemilatticeSup | Mathlib.Topology.WithTopology | [
"Preorder.toLT",
"WithTopology.ofTopology",
"WithTopology.instMax",
"WithTopology.ofTopology_injective",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"WithTopology.instLT",
"Function.Injective.semilatticeSup",
"WithTopology.instSemilatticeSup._proof_2",
"WithTopology.instS... | true |
Lean.Grind.CommRing.Poly.checkCoeffs._unsafe_rec | Lean.Meta.Tactic.Grind.Arith.CommRing.Poly | [
"bne",
"Lean.Grind.CommRing.Poly",
"Int.instDecidableEq",
"Bool.and",
"Int",
"instBEqOfDecidableEq",
"Lean.Grind.CommRing.Poly.checkCoeffs._unsafe_rec",
"Bool.true",
"instOfNat",
"Bool",
"OfNat.ofNat",
"Lean.Grind.CommRing.Mon",
"_private.Lean.Meta.Tactic.Grind.Arith.CommRing.Poly.0.Lean.Gri... | false |
EuclideanDomain.remainder | Mathlib.Algebra.EuclideanDomain.Defs | [
"EuclideanDomain"
] | true |
UInt64.lt_irrefl | Init.Data.UInt.Lemmas | [
"UInt64.not_lt._simp_1",
"UInt64",
"instLTUInt64",
"UInt64.le_refl._simp_1",
"LE.le",
"LT.lt",
"True",
"of_eq_true",
"instLEUInt64",
"Not",
"Eq.trans"
] | true |
RootPairing.Base.mk._flat_ctor | Mathlib.LinearAlgebra.RootSystem.Base | [
"NegZeroClass.toNeg",
"CommRing",
"CommSemiring.toSemiring",
"RootPairing.Base",
"AddCommGroup.toAddCommMonoid",
"Finset",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"AddSubmonoid",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZ... | false |
lie_eq_smul | Mathlib.Algebra.Lie.OfAssociative | [
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Bracket.bracket",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"LieRingModule.toBracket",
"LieRingModule.ofAssociativeModule",
"Add... | true |
_private.Mathlib.Algebra.Homology.CochainComplexOpposite.0.CochainComplex.homotopyUnop._proof_5 | Mathlib.Algebra.Homology.CochainComplexOpposite | [
"Eq.mpr",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"neg_inj._simp_1",
"AddGroupWithOne.toAddMonoidWithOne",
"id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Int",
"NonUnitalNonAssocRing.toHasDistribNeg",
"AddMonoidWithOne.toOne",
"Int.instCommRi... | false |
CategoryTheory.Coyoneda.punitIso | Mathlib.CategoryTheory.Yoneda | [
"CategoryTheory.Coyoneda.punitIso._proof_3",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.coyoneda",
"CategoryTheory.Functor.category",
"TypeCat.instFunLikeFun",
"CategoryTheory.Functor.id",
"TypeCat.ofHom",
"CategoryTheory.Iso",
"CategoryTheory.Iso.mk",
"TypeCat.Fun",
"PUnit",
"Opp... | true |
_private.Lean.Meta.MatchUtil.0.Lean.Meta.matchHelper?.match_1 | Lean.Meta.MatchUtil | [
"Unit.unit",
"Option.ctorIdx",
"Nat.hasNotBit",
"Option.none",
"Unit",
"_private.Lean.Meta.MatchUtil.0.Lean.Meta.matchHelper?._sparseCasesOn_1",
"Option"
] | false |
List.getElem_cons_length | Init.Data.List.Lemmas | [
"List.getLast",
"Eq.mpr",
"List.getElem_cons_length._proof_1",
"congrArg",
"HEq.refl",
"HSub.hSub",
"Eq.casesOn",
"id",
"instSubNat",
"instOfNatNat",
"List.cons",
"GetElem.getElem",
"List",
"instHSub",
"Nat",
"List.cons_ne_nil",
"LT.lt",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"H... | true |
CategoryTheory.Functor.FullyFaithful.hasShift.map_zero_inv_app | Mathlib.CategoryTheory.Shift.Basic | [
"CategoryTheory.Functor.FullyFaithful.hasShift.zero",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.rightUnitor",
"CategoryTheory.... | true |
String.Pos.Raw.isValid.eq_def | Init.Data.String.Basic | [
"String.instLTRaw",
"String",
"String.getUTF8Byte",
"String.Pos.Raw",
"dite",
"String.rawEndPos",
"UInt8.IsUTF8FirstByte",
"instDecidableEqRaw",
"String.instDecidableLtRaw",
"LT.lt",
"String.Pos.Raw.isValid",
"Bool",
"Eq.refl",
"UInt8.instDecidableIsUTF8FirstByte",
"Decidable.decide",
... | true |
UInt64.lt_trans | Init.Data.UInt.Lemmas | [
"UInt64",
"instLTUInt64",
"instOfNatNat",
"BitVec.lt_trans",
"Nat",
"LT.lt",
"OfNat.ofNat",
"UInt64.toBitVec"
] | true |
_private.Mathlib.Computability.NFA.0.NFA.mem_evalFrom_iff_nonempty_path.match_1_7 | Mathlib.Computability.NFA | [
"NFA.Path.cons",
"NFA.step",
"NFA.Path.casesOn",
"HEq.refl",
"NFA.Path",
"NFA",
"Membership.mem",
"Nonempty.intro",
"NFA.Path.nil",
"List.cons",
"List",
"Nonempty.casesOn",
"eq_of_heq",
"Eq.ndrec",
"Nonempty",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"Set.instMembership",
"List.nil... | false |
Representation.Coinvariants.induction_on | Mathlib.RepresentationTheory.Coinvariants | [
"Monoid",
"Representation.Coinvariants.ker",
"CommRing",
"Representation",
"Submodule.Quotient.induction_on",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"AddCommGroup",
"LinearMap",
"Representation.Coinvariants",
"CommRing.toCommSemiring",
"Representa... | true |
CochainComplex.HomComplex.Cochain.rightUnshift_comp._proof_2 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift | [
"_private.Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift.0.CochainComplex.HomComplex.Cochain.rightUnshift_comp._proof_1",
"Int",
"instHAdd",
"HAdd.hAdd",
"Int.instAdd",
"Eq"
] | false |
CentroidHom.coe_neg | Mathlib.Algebra.Ring.CentroidHom | [
"NonUnitalNonAssocRing",
"NegZeroClass.toNeg",
"Pi.instNeg",
"NonUnitalNonAssocRing.toAddCommGroup",
"CentroidHom.instNeg",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"... | true |
Subtype.coe_eq_iff | Mathlib.Data.Subtype | [
"_private.Mathlib.Data.Subtype.0.Subtype.coe_eq_iff._proof_1_3",
"Exists",
"Subtype",
"Subtype.mk",
"Iff",
"Subtype.val",
"Eq"
] | true |
Std.Roo.size | Init.Data.Range.Polymorphic.Iterators | [
"Std.PRange.UpwardEnumerable",
"Std.Roo.upper",
"Std.Roo.lower",
"instOfNatNat",
"Std.PRange.UpwardEnumerable.succ?",
"Unit",
"Nat",
"Std.Rxo.HasSize",
"Std.Roc.size.match_1",
"OfNat.ofNat",
"Std.Rxo.HasSize.size",
"Std.Roo",
"Option"
] | true |
_private.Mathlib.Topology.UniformSpace.Cauchy.0.UniformSpace.secondCountable_of_separable._simp_3 | Mathlib.Topology.UniformSpace.Cauchy | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
Equiv.distribMulAction._proof_2 | Mathlib.Algebra.GroupWithZero.Action.TransferInstance | [
"Monoid",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Equiv.addZeroClass",
"AddZeroClass.toAddZero",
"Equiv",
"Equiv.distribSMul",
"DistribSMul.toSMulZeroClass",
"AddZero.toZero",
"AddMonoid",
"DistribMulAction",
"Zero.toOfNat0",
"HSMul.hSMul",
"SMulZeroCl... | false |
DistLat.instConcreteCategoryLatticeHomCarrier._proof_4 | Mathlib.Order.Category.DistLat | [
"DistLat.Hom.hom'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"DistLat.str",
"DistribLattice.toLattice",
"id",
"DistLat.instCategory",
"LatticeHom",
"CategoryTheory.CategoryStruct.comp",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"LatticeHom.instFunLike",
"Eq",
"D... | false |
Finsupp.embDomain_zero | Mathlib.Data.Finsupp.Defs | [
"Function.Embedding",
"Finsupp.embDomain",
"Zero.toOfNat0",
"Finsupp.instZero",
"OfNat.ofNat",
"Eq",
"Finsupp",
"rfl",
"Zero"
] | true |
CategoryTheory.CatCommSq.iso | Mathlib.CategoryTheory.CatCommSq | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso",
"CategoryTheory.CatCommSq",
"CategoryTheory.Category"
] | true |
TemperedDistribution.instLineDeriv | Mathlib.Analysis.Distribution.TemperedDistribution | [
"instInnerProductSpaceRealComplex",
"TemperedDistribution.instLineDeriv._proof_1",
"InnerProductSpace.toNormedSpace",
"TemperedDistribution.instLineDeriv._proof_4",
"Real",
"PointwiseConvergenceCLM",
"Complex.instNormedAddCommGroup",
"NormedSpace",
"SchwartzMap.instModule",
"UniformConvergenceCLM.... | true |
CategoryTheory.effectiveEpiFamily_of_effectiveEpi_epi_comp | Mathlib.CategoryTheory.EffectiveEpi.Comp | [
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.EffectiveEpiFamilyStruct",
"CategoryTheory.effectiveEpiFamilyStructOfComp",
"Nonempty.intro",
"CategoryTheory.EffectiveEpiFamily.mk",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategor... | true |
_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.eqImp | Lean.Compiler.LCNF.Basic | [
"Lean.instBEqFVarId",
"Lean.Compiler.LCNF.Arg",
"_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.eqImp",
"Lean.Expr.instBEq",
"Lean.Compiler.LCNF.instBEqArg",
"Array.instBEq",
"Lean.Expr",
"ptrEq",
"Lean.Compiler.LCNF.FunDecl",
"Bool.and",
"Lean.FVarId",
"instDecidableEqBool",
"_priva... | true |
Graph.IsClosedSubgraph.rfl | Mathlib.Combinatorics.Graph.Subgraph | [
"Graph.IsClosedSubgraph",
"Graph",
"Graph.IsClosedSubgraph.instIsPartialOrder",
"IsPartialOrder.toIsPreorder",
"refl",
"IsPreorder.toRefl"
] | true |
AffineIsometryEquiv.pointReflection_midpoint_right | Mathlib.Analysis.Normed.Affine.Isometry | [
"NormedCommRing.toNormedRing",
"Real.partialOrder",
"Real",
"AffineIsometryEquiv.instEquivLike",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"NormedSpace",
"invertibleTwo",
"NormedSpace.toModule",
"AffineIsometryEquiv.pointReflection",
"Real.semiring",
"Real.instRing",
"AffineIsometryEqui... | true |
_private.Lean.Meta.Tactic.Contradiction.0.Lean.Meta.processGenDiseq.match_7 | Lean.Meta.Tactic.Contradiction | [
"Lean.Expr",
"Prod.mk",
"Array",
"Prod",
"Lean.BinderInfo",
"Prod.casesOn"
] | false |
Nat.gcd_pos_of_pos_left | Init.Data.Nat.Gcd | [
"Nat.gcd",
"Nat.gcd_dvd_left",
"instOfNatNat",
"Nat",
"LT.lt",
"instLTNat",
"Nat.pos_of_dvd_of_pos",
"OfNat.ofNat"
] | true |
AddGroup.instResiduallyFiniteOfFinite | Mathlib.GroupTheory.ResiduallyFinite | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"AddSubgroup.instBot",
"AddSubgroup.FiniteIndex",
"Finite",
"Membership.mem",
"SubtractionMonoid.toSubNegZeroMonoid",
"Bot.bot",
"SubNegZeroMonoid.toNegZeroClass",
"AddSubgroup",
"AddGroup",
"AddSubgroup.instSetLike",
"Zero.toOfNat0",
"OfNat.ofNat... | true |
FinEnum.recEmptyOption.eq_def | Mathlib.Data.FinEnum.Option | [
"FinEnum.recEmptyOption._proof_4",
"FinEnum.recEmptyOption._proof_2",
"FinEnum.card",
"FinEnum.recEmptyOption",
"ULift",
"FinEnum.pempty",
"id",
"FinEnum.fin",
"PEmpty",
"instOfNatNat",
"FinEnum.recEmptyOption._proof_1",
"FinEnum.recEmptyOption._unary.eq_def",
"Fin.val",
"Nat.cast",
"ins... | true |
TopologicalSpace.indiscrete_iff_forall_inseparable | Mathlib.Topology.Order | [
"IndiscreteTopology.of_forall_inseparable",
"IndiscreteTopology",
"TopologicalSpace",
"Iff",
"Inseparable.all",
"Iff.intro",
"Inseparable"
] | true |
CategoryTheory.JointlyFaithful.jointlyReflectsIsomorphisms | Mathlib.CategoryTheory.Functor.ReflectsIso.Jointly | [
"CategoryTheory.JointlyReflectIsomorphisms",
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"CategoryTheory.Epi",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.epi_of_strongEpi",
"CategoryTheory.Functor.map",
"CategoryTheory.mono_of_strongMono",
... | true |
CliffordAlgebra.contractLeft._proof_4 | Mathlib.LinearAlgebra.CliffordAlgebra.Contraction | [
"CommRing",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"instAlgebraCliffordAlgebra",
"QuadraticForm",
"AddCommGroup",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonAssocRing.toNonUnitalNonAssocRing",
"smul... | false |
SheafOfModules.relationsOfIsCokernelFree_I | Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent | [
"CategoryTheory.Functor",
"Opposite",
"AddCommGrpCat.hasLimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"ModuleCat",
"CategoryTheory.Limits.WalkingParallelPair",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.HasSheafify",
"AddMonoid.toAddZe... | true |
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