name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Set.Nonempty.sigma_fst | Mathlib.Data.Set.Sigma | [
"Membership.mem",
"Sigma.fst",
"Set.Nonempty",
"_private.Mathlib.Data.Set.Sigma.0.Set.Nonempty.sigma_fst.match_1_1",
"And.left",
"Set.sigma",
"Exists.intro",
"Sigma.snd",
"Set.instMembership",
"Sigma",
"Set"
] | true |
HasLineDerivAt.le_of_lip' | Mathlib.Analysis.Calculus.LineDeriv.Basic | [
"NormedCommRing.toNormedRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real.instIsOrderedRing",
"Norm.norm",
"Eq.mpr",
"mul_nonneg",
"NormedCommRing.toSeminormedCommRing",
"Real.partialOrder",
"Real.instLE",
"Semigroup.toMul",
"Real",
"instHSMul",
"Continuous",
"NonUn... | true |
AlgebraicGeometry.Scheme.IdealSheafData.instCompleteLattice._proof_3 | Mathlib.AlgebraicGeometry.IdealSheaf.Basic | [
"GaloisCoinsertion.liftCompleteLattice",
"AlgebraicGeometry.Scheme",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Opposite",
"CommRingCat.carrier",
"CommRing.toNonUnitalCommRing",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CompleteLattice.to... | false |
Int.Linear.Poly.insert._unsafe_rec | Init.Data.Int.Linear | [
"Nat.blt",
"cond",
"Int.instDecidableEq",
"Nat.beq",
"instDecidableEqBool",
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.num",
"instBEqOfDecidableEq",
"Int.Linear.Poly.add",
"Bool.true",
"BEq.beq",
"instOfNat",
"Bool",
"Int.Linear.Poly.denote.match_1",
"Int.Linear.Poly.insert._unsafe_rec"... | false |
Matrix.nnnorm_conjTranspose | Mathlib.Analysis.Matrix.Normed | [
"SeminormedAddCommGroup",
"Matrix",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"nnnorm_star",
"AddCommGroup.toAddGroup",
"NNReal",
"StarAddMonoid.toInvolutiveStar",
"NormedStarGroup",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"Matrix.nnnorm_transpose",
"Fintype",
"AddGroup.toSubNeg... | true |
NumberField.mixedEmbedding.euclidean.toMixed | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | [
"instInnerProductSpaceRealComplex",
"WithLp",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"NumberField.mixedEmbedding.euclidean.toMixed._proof_8",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
... | true |
_private.Batteries.Data.List.Lemmas.0.List.isSome_isPrefixOf?_eq_isPrefixOf.match_1_1 | Batteries.Data.List.Lemmas | [
"List.cons",
"List",
"List.casesOn",
"List.nil"
] | false |
Aesop.PhaseSpec.phase | Aesop.Builder.Basic | [
"Aesop.SafeRuleInfo",
"Aesop.UnsafeRuleInfo",
"Aesop.PhaseName.safe",
"Aesop.PhaseName",
"Aesop.PhaseName.unsafe",
"Aesop.PhaseName.norm",
"_private.Aesop.Builder.Basic.0.Aesop.PhaseSpec.phase.match_1",
"Aesop.PhaseSpec",
"Aesop.NormRuleInfo"
] | true |
_private.Mathlib.Algebra.Group.Pointwise.Finset.Basic.0.Finset.isUnit_coe._simp_1_2 | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Finset.coe_eq_singleton",
"Finset",
"Set.instSingletonSet",
"SetLike.coe",
"Finset.instSetLike",
"propext",
"Finset.instSingleton",
"Singleton.singleton",
"Eq",
"Set"
] | false |
Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.casesOn | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.rec",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.ci",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicBound",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.co",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntI... | false |
Orientation.norm_div_cos_oangle_add_right_of_oangle_eq_pi_div_two | Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle | [
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Orientation",
"Real.partialOrder",
"Real",
"instHDiv",
"Orientation.oangle",
"Real.pi",
"Real.Angle",
"Real.Angle.coe",
"Real.cos",
"Real.instRCLike",
"SignType.instOne",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Orientati... | true |
TemperedDistribution.delta_apply | Mathlib.Analysis.Distribution.TemperedDistribution | [
"instInnerProductSpaceRealComplex",
"InnerProductSpace.toNormedSpace",
"Real",
"Complex.instNormedAddCommGroup",
"NormedSpace",
"SchwartzMap.instModule",
"TemperedDistribution._proof_1",
"Real.instRCLike",
"Finite",
"NormedSpace.toModule",
"Complex.instNormedField",
"setOf",
"PseudoMetricSpa... | true |
_private.Mathlib.Analysis.Normed.Group.Pointwise.0.IsCompact.mul_closedBall_one._simp_1_1 | Mathlib.Analysis.Normed.Group.Pointwise | [
"HMul.hMul",
"Mul",
"Membership.mem",
"Exists",
"And",
"propext",
"Set.mul",
"Eq",
"Set.instMembership",
"Set.mem_mul",
"instHMul",
"Set"
] | false |
EquivLike.mk | Mathlib.Data.FunLike.Equiv | [
"Function.LeftInverse",
"outParam",
"EquivLike",
"Function.RightInverse",
"EquivLike.mk",
"Eq"
] | true |
List.offDiag_singleton | Mathlib.Data.List.OffDiag | [
"List.offDiag",
"List.cons",
"List",
"Prod",
"Eq",
"rfl",
"List.nil"
] | true |
Std.DTreeMap.Internal.Impl.entryAtIdx?._sunfold | Std.Data.DTreeMap.Internal.Queries | [
"HSub.hSub",
"Option.some",
"Ordering",
"Std.DTreeMap.Internal.Impl.size",
"instSubNat",
"instOfNatNat",
"Ord.compare",
"Option.none",
"Unit",
"instHSub",
"Nat",
"Std.DTreeMap.Internal.Impl.entryAtIdx?.match_1",
"Std.DTreeMap.Internal.Impl.entryAtIdx?",
"Sigma.mk",
"Std.DTreeMap.Internal... | false |
UpperSet.sdiff_singleton | Mathlib.Order.UpperLower.Closure | [
"UpperSet",
"lowerClosure_singleton",
"congrArg",
"UpperSet.instSetLike",
"IsUpperSet",
"Preorder.toLE",
"Set.instSingletonSet",
"UpperSet.mk.congr_simp",
"id",
"UpperSet.erase",
"UpperSet.mk",
"UpperSet.erase._proof_1",
"SDiff.sdiff",
"UpperSet.sdiff._proof_1",
"SetLike.coe",
"True",
... | true |
instStarMulWithConvMatrix | Mathlib.LinearAlgebra.Matrix.WithConv | [
"instInvolutiveStarWithConvMatrix",
"Matrix",
"StarMul",
"Mul",
"instStarMulWithConvMatrix._proof_1",
"StarMul.mk",
"instMulWithConvMatrix",
"StarMul.toInvolutiveStar",
"WithConv"
] | true |
Nat.coprime_ordCompl | Mathlib.Data.Nat.Factorization.Basic | [
"Finsupp.instFunLike",
"Nat.Coprime",
"Nat.instMulZeroClass",
"Nat.Prime",
"Dvd.dvd",
"instHDiv",
"Nat.instMonoid",
"HDiv.hDiv",
"Ne",
"instOfNatNat",
"Nat.not_dvd_ordCompl",
"Monoid.toPow",
"HPow.hPow",
"Nat.instDvd",
"Nat",
"Nat.instDiv",
"Iff.mp",
"Or",
"instHPow",
"or_iff_l... | true |
CategoryTheory.Localization.instCategoryLocalizedMonoidal._aux_5 | Mathlib.CategoryTheory.Localization.Monoidal.Basic | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.MorphismProperty.IsMonoidal",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Iso",
"CategoryTheory.Functor.IsLocalization",
"CategoryTheory.MonoidalCategoryStruct.tensorUnit",
"CategoryTheory.MonoidalCategory.toMonoidalCa... | false |
UniformSpace.Completion.instNormedFieldOfCompletableTopField._proof_2 | Mathlib.Analysis.Normed.Module.Completion | [
"Continuous.comp'",
"NormedCommRing.toNormedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Continuous",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"NormedCommRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"IsTopologicalSemiring.toContinuousMul",
"Co... | false |
Pi.vaddCommClass' | Mathlib.Algebra.Group.Action.Pi | [
"Pi.instVAdd",
"VAddCommClass.vadd_comm",
"VAddCommClass.mk",
"VAdd",
"HVAdd.hVAdd",
"funext",
"instHVAdd",
"VAddCommClass",
"Pi.vadd'"
] | true |
Set.image2_iUnion₂_right | Mathlib.Data.Set.Lattice.Image | [
"congrArg",
"Set.image2_iUnion_right",
"funext",
"Set.image2",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Set.iUnion",
"Eq.trans",
"Set"
] | true |
Dynamic.mk | Init.Dynamic | [
"TypeName",
"Classical.ofNonempty",
"instNonemptyDynamic",
"Dynamic"
] | true |
CategoryTheory.InjectiveResolution.Hom.noConfusionType | Mathlib.CategoryTheory.Preadditive.Injective.Resolution | [
"CategoryTheory.InjectiveResolution.Hom",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.single₀",
"CategoryTheory.InjectiveResolution.ι",
"CategoryTheor... | false |
BitVec.fill_true | Init.Data.BitVec.Lemmas | [
"congrArg",
"BitVec.fill",
"BitVec.allOnes",
"BitVec",
"instDecidableEqBool",
"instOfNatNat",
"ite_cond_eq_true",
"BitVec.ofNat",
"Bool.true",
"Nat",
"True",
"eq_self",
"BitVec.fill_eq",
"Bool",
"of_eq_true",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Eq.trans",
"ite"
] | true |
Std.Internal.List.keys_nil | Std.Data.Internal.List.Associative | [
"List",
"Std.Internal.List.keys",
"Eq",
"Sigma",
"rfl",
"List.nil"
] | true |
USize.zero_and | Init.Data.UInt.Bitwise | [
"instAndOpUSize",
"BitVec",
"BitVec.zero_and",
"USize.toBitVec_inj",
"System.Platform.numBits",
"USize.toBitVec",
"Iff.mp",
"HAnd.hAnd",
"OfNat.ofNat",
"Eq",
"instHAndOfAndOp",
"USize",
"USize.instOfNat"
] | true |
DoubleCentralizer.instCoeTC | Mathlib.Analysis.CStarAlgebra.Multiplier | [
"instSMulOfMul",
"CoeTC",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"NonUnitalRing.toNonUnitalNonAssocRing",
"AddZeroClass.toAdd... | true |
CategoryTheory.Limits.Fork.isLimitForkPushoutEquivIsColimitForkOpPullback._proof_3 | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers | [
"CategoryTheory.Limits.pullback",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Iso.op",
"CategoryTheory.Limits.pushoutIsoUnopPullback_inv_snd",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.eqToIso",
"CategoryTheory.Iso.... | false |
Finset.sum_set_coe | Mathlib.Algebra.BigOperators.Group.Finset.Basic | [
"Finset.univ",
"Finset.sum_subtype",
"Membership.mem",
"Set.Elem",
"Subtype",
"Set.toFinset",
"AddCommMonoid",
"Fintype",
"Set.mem_toFinset",
"Eq.symm",
"Subtype.val",
"Eq",
"Set.instMembership",
"Finset.sum",
"Set"
] | true |
Lean.Grind.CommRing.Poly.mulConstC.go._unsafe_rec | Init.Grind.Ring.CommSolver | [
"cond",
"Lean.Grind.CommRing.Poly",
"HMul.hMul",
"Lean.Grind.CommRing.Poly.add",
"Int.instDecidableEq",
"instHMod",
"Lean.Grind.CommRing.Poly.denote.match_1",
"Int",
"instBEqOfDecidableEq",
"Nat.cast",
"Int.instMul",
"HMod.hMod",
"BEq.beq",
"instOfNat",
"Nat",
"Int.instMod",
"instNat... | false |
NumberField.instCommRingRingOfIntegers._aux_1 | Mathlib.NumberTheory.NumberField.Basic | [
"Subring.instSetLike",
"AddMonoid.toAddSemigroup",
"AddSubmonoidClass.toAddMonoid._proof_5",
"Membership.mem",
"Field.toDivisionRing",
"Subring.toCommRing._proof_1",
"Subtype",
"SubringClass.toRing._proof_8",
"DivisionRing.toRing",
"Int",
"AddMemClass.add._proof_1",
"CommRing.toNonAssocCommRin... | false |
Sublattice.instLatticeCoe._proof_4 | Mathlib.Order.Sublattice | [
"Sublattice",
"Lattice",
"Membership.mem",
"Subtype",
"Sublattice.instSupCoe",
"Max.max",
"Sublattice.instSetLike",
"Subtype.val",
"Eq",
"SetLike.instMembership",
"rfl"
] | false |
Lean.Meta.CaseArraySizesSubgoal.ctorIdx | Lean.Meta.Match.CaseArraySizes | [
"Nat",
"Lean.Meta.CaseArraySizesSubgoal"
] | false |
Int.Linear.dvd_solve_elim_cert.eq_1 | Init.Data.Int.Linear | [
"Int.gcd",
"HMul.hMul",
"Int.Linear.Poly.beq'",
"Bool.and",
"Nat.beq",
"Int.instNegInt",
"Int",
"Int.Linear.Var",
"Nat.cast",
"Int.instMul",
"Int.Linear.Poly.add",
"Int.Linear.dvd_solve_elim_cert",
"Int.beq'",
"Bool",
"Int.Linear.Poly.combine_mul_k",
"Eq.refl",
"instNatCastInt",
"E... | true |
continuous_sInf_dom₂ | Mathlib.Topology.Constructions.SumProd | [
"Continuous",
"Continuous.prodMap",
"Continuous.comp",
"instTopologicalSpaceProd",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"id",
"Prod.map",
"SemilatticeInf.toMin",
"continuous_sInf_dom",
"Prod.fst",
"TopologicalSpace",
"c... | true |
Aesop.Goal.safeRapps | Aesop.Tree.Data | [
"Pure.pure",
"IO.instMonadLiftSTRealWorldBaseIO",
"Monad.toApplicative",
"Aesop.Goal",
"instMonadLiftT",
"Aesop.RappRef",
"ST.Ref.get",
"IO.RealWorld",
"instOfNatNat",
"Applicative.toPure",
"Aesop.Rapp",
"Array",
"Array.filterM",
"instMonadBaseIO",
"ST",
"Nat",
"Bool",
"Monad.toBin... | true |
Option.or_of_isNone | Init.Data.Option.Lemmas | [
"Option.isNone",
"Option.or",
"Bool.true",
"Option.none",
"eq_self",
"Bool",
"of_eq_true",
"_private.Init.Data.Option.Lemmas.0.Option.or_of_isNone.match_1_1",
"Eq",
"Option"
] | true |
Lean.Elab.Tactic.GuardMsgs.MessageOrdering.exact.sizeOf_spec | Lean.Elab.GuardMsgs | [
"Lean.Elab.Tactic.GuardMsgs.MessageOrdering._sizeOf_inst",
"instOfNatNat",
"Lean.Elab.Tactic.GuardMsgs.MessageOrdering",
"Nat",
"Lean.Elab.Tactic.GuardMsgs.MessageOrdering.exact",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.CommGrpObj.mk._flat_ctor | Mathlib.CategoryTheory.Monoidal.Cartesian.CommGrp_ | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.GrpObj.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsCommMonObj.mul_comm._autoParam",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"Category... | false |
Lean.Meta.Simp.UsedSimps._sizeOf_inst | Lean.Meta.Tactic.Simp.Types | [
"SizeOf.mk",
"SizeOf",
"Lean.Meta.Simp.UsedSimps",
"Lean.Meta.Simp.UsedSimps._sizeOf_1"
] | false |
Real.sin_arccos | Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"not_le",
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"instNeZeroNa... | true |
CategoryTheory.Discrete.equivOfEquivalence._proof_1 | Mathlib.CategoryTheory.Discrete.Basic | [
"CategoryTheory.Equivalence.unitIso",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp",
"Function.comp",
"CategoryTheory.Functor.id",
"id",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.Discrete.mk",
"CategoryTheory.Discrete.as",
"CategoryTheory.discreteCategory",
"CategoryThe... | false |
ProbabilityTheory.«term_⊗ₖ_» | Mathlib.Probability.Kernel.Composition.CompProd | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
_private.Lean.Elab.DocString.Builtin.Keywords.0.Lean.Doc.isAtoms.go.match_1 | Lean.Elab.DocString.Builtin.Keywords | [
"Lean.Syntax.node",
"Unit.unit",
"Lean.Syntax.ident",
"Lean.Syntax.missing",
"String",
"Lean.SourceInfo",
"Lean.Syntax.casesOn",
"Lean.Syntax.atom",
"Lean.Syntax",
"Substring.Raw",
"List.cons",
"Array",
"List",
"Unit",
"Lean.Syntax.Preresolved",
"List.casesOn",
"Lean.Name",
"Lean.S... | false |
NumberField.IsCMField.complexConj._proof_1 | Mathlib.NumberTheory.NumberField.CMField | [
"Rat.nontrivial",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"RingHom",
"Field.toDivisionRing",
"inferInstance",
"Algebra.IsIntegral",
"NumberField.Embeddings.instNonemptyRingHomOfIsAlgebraicRatOfIsAlgClosed",
"DivisionRing.toRing",
"Field.toSemifield",
"Field.toCommRing",
"instIsDomain",
... | false |
AddSubgroup.pi_mem_of_single_mem | Mathlib.Algebra.Group.Subgroup.Finite | [
"AddGroup.toSubtractionMonoid",
"Pi.addGroup",
"Finite",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"SubtractionMonoid.toSubNegZeroMonoid",
"Pi.single",
"SubNegZeroMonoid.toNegZeroClass",
"AddSubgroupClass.toAddSubmonoidClass",
"AddSubmonoid.pi_mem_of_single_mem",
"AddSubgroup",
"AddGroup",... | true |
AbsoluteValue.uniformSpace._proof_1 | Mathlib.Topology.UniformSpace.AbsoluteValue | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"sub_self",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"SemilatticeInf.toPartialOrder",
"AddZeroClass.toAddZero",
"Di... | false |
Cardinal.toENat_eq_zero | Mathlib.SetTheory.Cardinal.ENat | [
"Cardinal",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Cardinal.commSemiring",
"PartialOrder.toPreorder",
"OrderRingHom.instFunLike",
"AddZeroClass.toAddZero",
"instPreorderENat",
"OrderRingHom",
"Nat.instAddMonoidWithOne",
"AddZero.toZero",
"Cardinal.partialOrder",
"Iff",
"Ca... | true |
NonemptyInterval.instNSMul.eq_1 | Mathlib.Algebra.Order.Interval.Basic | [
"instHSMul",
"SMul",
"AddMonoid.toAddZeroClass",
"Prod.instSMul",
"AddMonoid.toNSMul",
"AddLeftMono",
"Preorder.toLE",
"AddRightMono",
"AddZeroClass.toAddZero",
"SMul.mk",
"NonemptyInterval.mk",
"Nat",
"AddMonoid",
"NonemptyInterval.instNSMul._proof_1",
"NonemptyInterval.instNSMul",
"A... | true |
_private.Mathlib.Topology.Order.IntermediateValue.0.setOf_isPreconnected_eq_of_ordered._simp_1_5 | Mathlib.Topology.Order.IntermediateValue | [
"Membership.mem",
"Set.instSingletonSet",
"Set.mem_singleton_iff",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set"
] | false |
CategoryTheory.Functor.mapSkeleton_injective | Mathlib.CategoryTheory.Skeletal | [
"CategoryTheory.Functor",
"CategoryTheory.eqToIso",
"CategoryTheory.Iso",
"CategoryTheory.Functor.instFaithfulSkeletonMapSkeleton",
"Nonempty.intro",
"CategoryTheory.skeleton_skeletal",
"CategoryTheory.Functor.preimageIso",
"CategoryTheory.Functor.mapSkeleton",
"CategoryTheory.Functor.instFullSkelet... | true |
AlgebraicTopology.DoldKan.degeneraciesVanish_zero_iff_true._simp_1 | Mathlib.AlgebraicTopology.DoldKan.Degeneracies | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"instOfNatNat",
"CategoryTheory.Preadditive",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"AlgebraicTopology.DoldKan.DegeneraciesVanish",
"True",
"propext",
"SimplexCategory",
"CategoryTheory.Category.opposite",
"CategoryT... | false |
Lean.Lsp.SymbolTag | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SymbolTag.deprecated"
] | true |
Prod.instSemilatticeInf | Mathlib.Order.Lattice | [
"Prod.instSemilatticeInf._proof_2",
"SemilatticeInf.toPartialOrder",
"Prod.instSemilatticeInf._proof_3",
"Prod.mk",
"SemilatticeInf.toMin",
"Prod.fst",
"SemilatticeInf.mk",
"SemilatticeInf",
"Prod.instSemilatticeInf._proof_1",
"Prod.instPartialOrder",
"Prod",
"Prod.snd",
"Min.min"
] | true |
_private.Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real.0.RealRMK.exists_open_approx._simp_1_1 | Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real | [
"HasSubset.Subset",
"LE.le",
"True",
"ENNReal.instLE",
"ENNReal",
"MeasureTheory.measure_mono",
"eq_true",
"MeasureTheory.OuterMeasureClass",
"Eq",
"DFunLike.coe",
"FunLike",
"Set.instHasSubset",
"Set"
] | false |
CategoryTheory.JointlyReflectIsomorphisms.mk | Mathlib.CategoryTheory.Functor.ReflectsIso.Jointly | [
"CategoryTheory.JointlyReflectIsomorphisms",
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.map",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.obj",
"CategoryTheory.JointlyReflectIsomorphisms.mk... | true |
Lean.Grind.Fin.pow_zero | Init.GrindInstances.Ring.Fin | [
"Zero.ofOfNat0",
"Lean.Grind.Fin.instHPowFinNatOfNeZero",
"Fin.instOfNat",
"instOfNatNat",
"HPow.hPow",
"Nat",
"NeZero",
"OfNat.ofNat",
"Fin",
"Eq",
"rfl"
] | true |
Lean.Lsp.RpcOptions.mk._flat_ctor | Lean.Data.Lsp.Extra | [
"Lean.Lsp.HighlightMatchesOptions",
"Lean.Lsp.RpcWireFormat",
"Lean.Lsp.RpcOptions",
"Lean.Lsp.RpcOptions.mk",
"Option"
] | false |
CategoryTheory.sheafOver_obj | Mathlib.CategoryTheory.Sites.Sheaf | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.coyoneda",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.GrothendieckTopology",
"Opposite.op",
"CategoryTheory.types",
"CategoryTheory.Category.opposite",
... | true |
CategoryTheory.Bimon.instBimonObjXXMon._proof_12 | Mathlib.CategoryTheory.Monoidal.Bimon_ | [
"CategoryTheory.Bimon",
"CategoryTheory.Mon.instIsMonHomHom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.ComonObj.counit",
"CategoryTheory.Mon.monMonoidal",... | false |
Lean.Elab.Command.Structure.StructParentInfo.recOn | Lean.Elab.Structure | [
"Lean.Elab.Command.Structure.StructParentInfo.rec",
"Lean.Syntax",
"Lean.Elab.Command.Structure.StructParentInfo",
"Lean.Expr",
"Lean.Elab.Command.Structure.StructParentInfo.mk",
"Bool",
"Lean.Name"
] | false |
LinearPMap.IsClosable.existsUnique | Mathlib.Topology.Algebra.Module.LinearPMap | [
"Eq.mpr",
"Submodule",
"CommRing",
"AddMonoid.toAddSemigroup",
"ContinuousSMul",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LinearPMap.eq_of_eq_graph",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"instTopologicalSpaceProd",
"AddCommGroup.toAddGr... | true |
_private.Mathlib.Logic.Embedding.Set.0.subtypeOrEquiv._proof_1 | Mathlib.Logic.Embedding.Set | [
"Or.inl",
"Or"
] | false |
Std.Sat.AIG.mkGate_decl_eq._proof_2 | Std.Sat.AIG.Lemmas | [
"Std.Sat.AIG.mkGate",
"Std.Sat.AIG.Entrypoint.aig",
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.BinaryInput",
"LE.le",
"instLENat",
"_private.Std.Sat.AIG.Lemmas.0.Std.Sat.AIG.mkGate_decl_eq._proof_1",
"Std.Sat.AIG",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"Nat.decLt",
"Hashable",
"instLTNat",
... | false |
Polynomial.IsEisensteinAt.mem | Mathlib.RingTheory.Polynomial.Eisenstein.Basic | [
"Semiring.toModule",
"CommSemiring.toSemiring",
"Membership.mem",
"Ideal",
"Polynomial",
"Polynomial.coeff",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"Submodule.setLike",
"LT.lt",
"Polynomial.IsEisensteinAt",
"instL... | true |
_private.Init.Data.Vector.Lemmas.0.Vector.any_iff_exists._simp_1_1 | Init.Data.Vector.Lemmas | [
"Array.any_iff_exists",
"Exists",
"Array.any",
"LE.le",
"instLENat",
"Array",
"GetElem.getElem",
"Bool.true",
"And",
"Array.instGetElemNatLtSize",
"Nat",
"LT.lt",
"propext",
"Bool",
"instLTNat",
"Eq",
"Array.size"
] | false |
_private.Mathlib.Probability.Kernel.Proper.0.ProbabilityTheory.Kernel.IsProper.lintegral_indicator_mul_indicator._simp_1_2 | Mathlib.Probability.Kernel.Proper | [
"MeasurableSet",
"Set.univ",
"MeasurableSpace",
"True",
"eq_true",
"Eq",
"MeasurableSet.univ"
] | false |
CategoryTheory.LiftRightAdjoint.otherMap | Mathlib.CategoryTheory.Adjunction.Lifting.Right | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.Functor.id",
"CategoryTheory.Functor.map",
"CategoryTheory.Adjunction.counit",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Ca... | true |
Std.DTreeMap.Internal.Impl.getKey?_union! | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Ord",
"congrArg",
"Std.TransOrd",
"id",
"Option.or",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Std.DTreeMap.Internal.Impl.union!",
"Std.DTreeMap.Internal.Impl.getKey?",
"Eq.symm",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.g... | true |
Lean.SimplePersistentEnvExtensionDescr.noConfusionType | Lean.EnvExtension | [
"autoParam",
"Array",
"Lean.EnvExtension.AsyncMode",
"Lean.SimplePersistentEnvExtensionDescr.casesOn",
"List",
"Lean.OLeanEntries",
"Lean.Name",
"HEq",
"Lean.SimplePersistentEnvExtensionDescr",
"Prod",
"Eq",
"Lean.Environment",
"Lean.SimplePersistentEnvExtensionDescr.name._autoParam",
"Opt... | false |
ContinuousLinearEquiv.automorphismGroup._proof_10 | Mathlib.Topology.Algebra.Module.Equiv | [
"Mul.mk",
"One.mk",
"HMul.hMul",
"ContinuousLinearEquiv.trans",
"ContinuousLinearEquiv.automorphismGroup._proof_7",
"AddCommMonoid",
"ContinuousLinearEquiv.refl",
"TopologicalSpace",
"ContinuousLinearEquiv",
"RingHomInvPair.ids",
"Semiring",
"One.toOfNat1",
"Module",
"OfNat.ofNat",
"Ring... | false |
RingNorm | Mathlib.Analysis.Normed.Unbundled.RingSeminorm | [
"NonUnitalNonAssocRing",
"RingNorm.mk"
] | true |
_private.Mathlib.SetTheory.Cardinal.Regular.0.Cardinal.isSingular_aleph_omega0._simp_1_1 | Mathlib.SetTheory.Cardinal.Regular | [
"Preorder.toLT",
"Cardinal.aleph",
"Cardinal.IsSingular",
"Ordinal.partialOrder",
"Cardinal",
"PartialOrder.toPreorder",
"Cardinal.isSingular_aleph_iff",
"Preorder.toLE",
"Order.IsSuccLimit",
"Cardinal.instLE",
"And",
"Cardinal.partialOrder",
"LT.lt",
"propext",
"Ordinal.cof",
"OrderEm... | false |
TwoSidedIdeal.coeAddMonoidHom._proof_2 | Mathlib.RingTheory.TwoSidedIdeal.Basic | [
"NonUnitalNonAssocRing",
"TwoSidedIdeal",
"AddMonoid.toAddZeroClass",
"TwoSidedIdeal.addCommGroup",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"instHAdd",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"TwoSidedIdeal.setLike",
"AddZero.toAdd",
"SubNegMonoid.... | false |
ContextFreeGrammar.Derives | Mathlib.Computability.ContextFreeGrammar | [
"ContextFreeGrammar",
"Symbol",
"ContextFreeGrammar.Produces",
"List",
"ContextFreeGrammar.NT",
"Relation.ReflTransGen"
] | true |
mkFactorOrderIsoOfFactorDvdEquiv_apply_coe | Mathlib.RingTheory.ChainOfDivisors | [
"CommMonoidWithZero.toCommMonoid",
"Associates.mk",
"MulEquiv.instEquivLike",
"Dvd.dvd",
"Equiv.instEquivLike",
"MulZeroClass.toMul",
"semigroupDvd",
"Preorder.toLE",
"Membership.mem",
"SemigroupWithZero.toSemigroup",
"Units",
"Set.Elem",
"Equiv",
"Subtype",
"CommMonoidWithZero.toMonoidW... | true |
Nat.sub_add_cancel | Init.Data.Nat.Basic | [
"Eq.mpr",
"congrArg",
"HSub.hSub",
"Nat.add_sub_of_le",
"id",
"instSubNat",
"LE.le",
"instLENat",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"Eq",
"Nat.add_comm"
] | true |
UInt64.toUSize_ofNatTruncate_of_le | Init.Data.UInt.Lemmas | [
"instPowNat",
"UInt64.size",
"UInt64.toUSize_ofNatTruncate_of_le._proof_1",
"UInt64.toUSize",
"congrArg",
"HSub.hSub",
"UInt64.size_sub_one_mod_uSizeSize",
"USize.toNat_ofNatLT",
"Nat.instMod",
"instHMod",
"UInt64.ofNatTruncate",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"UIn... | true |
SeminormedAddGroup.noConfusionType | Mathlib.Analysis.Normed.Group.Defs | [
"Norm.norm",
"Real",
"AddMonoid.toAddSemigroup",
"SeminormedAddGroup",
"Norm",
"SeminormedAddGroup.casesOn",
"instHAdd",
"AddSemigroup.toAdd",
"PseudoMetricSpace",
"AddGroup",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"SubNegMonoid.toNeg",
"HEq",
"Dist.dist",
"PseudoMetricSpace.toDist",
... | false |
KaehlerDifferential.D._proof_3 | Mathlib.RingTheory.Kaehler.Basic | [
"CommRing",
"Algebra.to_smulCommClass",
"instSMulOfMul",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.toSMul",
"instDistribOfSemiring",
"CommRing.toCommSemiring",
"Distrib.toMul",
"SMulCommClass"
] | false |
_private.Init.Data.Array.Lemmas.0.Array.back_append._simp_2 | Init.Data.Array.Lemmas | [
"instOfNatNat",
"List.toArray",
"Array",
"Nat",
"propext",
"Array.eq_empty_iff_size_eq_zero",
"OfNat.ofNat",
"Eq",
"Array.size",
"List.nil"
] | false |
Lean.Widget.WidgetSource.noConfusionType | Lean.Widget.UserWidget | [
"Lean.Widget.WidgetSource.casesOn",
"Lean.Widget.WidgetSource",
"String",
"Eq"
] | false |
_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.Internal.List.interSmallerFn.match_1.eq_1 | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"Option.some",
"Option.none",
"Unit",
"Eq.refl",
"Eq",
"Sigma",
"_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.interSmallerFn.match_1",
"Option"
] | true |
IsScalarTower.contMDiffSMul | Mathlib.Geometry.Manifold.Algebra.SMul | [
"Monoid",
"MulOne.toOne",
"instHSMul",
"Prod.normedSpace",
"Prod.normedAddCommGroup",
"NormedSpace",
"smul_assoc",
"Monoid.toMulOneClass",
"congrArg",
"ContMDiff",
"IsScalarTower",
"ContMDiff.smul",
"SMul",
"instTopologicalSpaceProd",
"ContMDiffSMul",
"Eq.mp",
"contMDiff_snd",
"ins... | true |
Lean.Meta.NativeEqTrueResult.casesOn | Lean.Meta.Native | [
"Lean.Meta.NativeEqTrueResult",
"Lean.Expr",
"Lean.Meta.NativeEqTrueResult.notTrue",
"Lean.Meta.NativeEqTrueResult.success",
"Lean.Meta.NativeEqTrueResult.rec"
] | false |
ProfiniteAddGrp.instHasForget₂FiniteAddGrpAddMonoidHomCarrierToAddGrpContinuousAddMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfinite._proof_1 | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"FiniteAddGrp.instCategory",
"id",
"ProfiniteAddGrp",
"FiniteAddGrp",
"ProfiniteAddGrp.ofFiniteAddGrpHom",
"ProfiniteAddGrp.ofFiniteAddGrp",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
... | false |
_private.Mathlib.Tactic.CongrExclamation.0.Lean.MVarId.congrImplies?'._sparseCasesOn_1 | Mathlib.Tactic.CongrExclamation | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
MeasureTheory.StronglyMeasurable.stronglyMeasurable_in_set | Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic | [
"Eq.mpr",
"MeasureTheory.StronglyMeasurable.approx",
"MeasurableSet",
"congrArg",
"tendsto_const_nhds",
"Set.indicator",
"Classical.propDecidable",
"MeasureTheory.SimpleFunc",
"Membership.mem",
"Exists",
"nhds",
"id",
"dite",
"MeasureTheory.SimpleFunc.instFunLike",
"Filter.atTop",
"Mea... | true |
_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.cnfSatAssignment.eq_1 | Std.Sat.AIG.CNF | [
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.Ref.mk",
"instHashableNat",
"Fin.val",
"Std.Sat.AIG",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEqNat",
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.cnfSatAssignment",
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.cnfSatAssignment._proof_1",
"Std.Sat.AIG.Entrypo... | true |
CategoryTheory.HasSplitCoequalizer.rec | Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.HasSplitCoequalizer",
"Exists",
"CategoryTheory.HasSplitCoequalizer.mk",
"CategoryTheory.IsSplitCoequalizer",
"Nonempty",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | false |
SemiNormedGrp.instConcreteCategoryNormedAddGroupHomCarrier._proof_3 | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"NormedAddGroupHom",
"CategoryTheory.CategoryStruct.id",
"id",
"NormedAddGroupHom.funLike",
"SemiNormedGrp.carrier",
"Eq.refl",
"SemiNormedGrp.instLargeCategory",
"CategoryTheory.Category.toCategoryStruct",
"SemiNormedGrp.str",
"Eq",
"DFunLike.coe",
"SemiNormedGrp.Hom.hom'",
"SemiNormedGrp"
... | false |
_private.Mathlib.Data.Finsupp.Single.0.Finsupp.erase_single_ne._proof_1_1 | Mathlib.Data.Finsupp.Single | [
"Finsupp.instFunLike",
"False",
"Finsupp.erase",
"Finsupp.ext",
"eq_false",
"Finsupp.erase_apply",
"Classical.byContradiction",
"Classical.propDecidable",
"Exists",
"Eq.mp",
"id",
"Lean.Grind.forall_imp_eq_or",
"Ne",
"ite_cond_eq_true",
"Lean.Grind.em",
"Or.casesOn",
"Exists.casesOn"... | false |
LinearMap.BilinForm.isNonneg_def | Mathlib.LinearAlgebra.BilinearForm.Properties | [
"_private.Mathlib.LinearAlgebra.BilinearForm.Properties.0.LinearMap.BilinForm.isNonneg_def.match_1_1",
"Semiring.toModule",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"LE.le",
"LinearMap.module",
"LinearMap",
"LE",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonA... | true |
MeasureTheory.ProbabilityMeasure.toWeakDualBCNN | Mathlib.MeasureTheory.Measure.ProbabilityMeasure | [
"NNReal.instTopologicalSpace",
"MeasureTheory.FiniteMeasure",
"NonAssocSemiring.toAddCommMonoidWithOne",
"NNReal.instCommSemiring",
"Semiring.toModule",
"NNReal.isBoundedSMul",
"CommSemiring.toSemiring",
"SeparatelyContinuousMul.to_continuousSMul",
"BoundedContinuousFunction.instAddCommMonoid",
"P... | true |
instLinearOrderNNRat._proof_8 | Mathlib.Data.NNRat.Defs | [
"Rat.instOfNat",
"LT.mk",
"instLinearOrderNNRat._aux_1",
"Rat",
"instLinearOrderNNRat._proof_6",
"Rat.linearOrder",
"Preorder.toLE",
"Preorder.mk",
"instLinearOrderNNRat._proof_7",
"NNRat",
"LE.le",
"Rat.instLE",
"Subtype.partialOrder._proof_1",
"instLinearOrderNNRat._aux_3",
"LE.mk",
... | false |
_private.Lean.Elab.Declaration.0.Lean.Elab.Command.expandDeclNamespace?._sparseCasesOn_5 | Lean.Elab.Declaration | [
"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 |
Submodule.quotientRel | Mathlib.LinearAlgebra.Quotient.Defs | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Setoid",
"Submodule.toAddSubgroup",
"QuotientAddGroup.leftRel",
"Module",
"Ring.toSemiring",
"Ring"
] | true |
CategoryTheory.GrothendieckTopology.sheafifyCompIso.congr_simp | Mathlib.CategoryTheory.Sites.CompatibleSheafification | [
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.GrothendieckTopology.sheafify",
"Opposite",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Functor.category",
"C... | true |
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