name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Std.TreeSet.Raw.contains_maxD | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.contains",
"Std.TreeSet.Raw.WF.out",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.TreeSet.Raw",
"Unit",
"Std.TreeMap.Raw.contains_maxKeyD",
"Bool",
"Std.TreeSet.Raw.isEmpty",
"Std.TreeSet.Raw.maxD",
"Bool.false",
"Std.TreeSet.Raw.inner",
"Eq",
"Std.TreeSet.Raw.WF"
] | true |
Nat.pow_pos_iff | Init.Data.Nat.Lemmas | [
"instPowNat",
"congrArg",
"Ne",
"instOfNatNat",
"Decidable.not_not._simp_1",
"_private.Init.Data.Nat.Lemmas.0.Nat.pow_pos_iff._simp_1_1",
"iff_self",
"instNatPowNat",
"And",
"Iff",
"HPow.hPow",
"implies_congr",
"Nat",
"congr",
"LT.lt",
"True",
"of_eq_true",
"_private.Init.Data.Nat.... | true |
_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagations.mk.sizeOf_spec | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.PendingSolverPropagations",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData._sizeOf_inst",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.Pend... | true |
SetLike.GradedMul.mul_mem | Mathlib.Algebra.GradedMonoid | [
"SetLike",
"HMul.hMul",
"Mul",
"Membership.mem",
"instHAdd",
"HAdd.hAdd",
"SetLike.GradedMul",
"SetLike.instMembership",
"Add",
"instHMul"
] | true |
_private.Mathlib.Analysis.LocallyConvex.SeparatingDual.0.ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff._simp_1_8 | Mathlib.Analysis.LocallyConvex.SeparatingDual | [
"Subalgebra.instSetLike",
"Lattice.toSemilatticeSup",
"Algebra.algebraMap",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"Algebra.mem_bot",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Algebra.instCompleteLatticeSubalgebra",
"Algebra",
"Preorder.toLE",
"RingHom",
"Membership.mem"... | false |
CategoryTheory.Arrow.leftToRight_app | Mathlib.CategoryTheory.Comma.Arrow | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.hom",
"CategoryTheory.Arrow.leftFunc",
"CategoryTheory.instCategoryArrow",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Arrow.rightFunc",
"CategoryTheory.Arrow",
"... | true |
Monoid.CoprodI.Word.chain_ne | Mathlib.GroupTheory.CoprodI | [
"Monoid",
"Monoid.CoprodI.Word.toList",
"List.IsChain",
"Monoid.CoprodI.Word",
"Ne",
"Sigma.fst",
"Sigma"
] | true |
AEMeasurable.sinc | Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc | [
"Real",
"MeasureTheory.Measure",
"AEMeasurable",
"Real.measurable_sinc",
"Real.sinc",
"MeasurableSpace",
"Real.measurableSpace",
"Measurable.comp_aemeasurable"
] | true |
CommGroup.subgroupOrderIsoSubgroupMonoidHom._proof_4 | Mathlib.GroupTheory.FiniteAbelian.Duality | [
"MonoidHom.instCommGroup",
"Subgroup.instSubgroupClass",
"MonoidHom",
"Monoid.toMulOneClass",
"Units",
"DivInvMonoid.toMonoid",
"Subgroup",
"CommGroup",
"SubgroupClass.toSubmonoidClass",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"CommGroup.toGroup",
"SubmonoidC... | false |
Std.ExtDTreeMap.size_right_le_size_union | Std.Data.ExtDTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.ExtDTreeMap.instUnionOfTransCmp",
"Std.ExtDTreeMap.inductionOn₂",
"Ordering",
"LE.le",
"Std.TransCmp",
"instLENat",
"Std.DTreeMap.size_right_le_size_union",
"Nat",
"Std.ExtDTreeMap",
"Std.ExtDTreeMap.size",
"Union.union"
] | true |
Std.DTreeMap.Internal.Impl.View.mk.inj | Std.Data.DTreeMap.Internal.Operations | [
"Std.DTreeMap.Internal.Impl.View",
"And",
"Std.DTreeMap.Internal.Impl.View.mk.noConfusion",
"Std.DTreeMap.Internal.Impl.View.mk",
"Nat",
"And.intro",
"eq_of_heq",
"HEq",
"Eq",
"Std.DTreeMap.Internal.Impl.Tree"
] | true |
Std.Sat.AIG.instDecidableEqFanin | Std.Sat.AIG.Basic | [
"Std.Sat.AIG.instDecidableEqFanin.decEq",
"Std.Sat.AIG.Fanin",
"DecidableEq"
] | true |
CompactSpace.nonempty_sInter | Mathlib.Topology.Compactness.Compact | [
"Eq.mpr",
"CompactSpace.isCompact_univ",
"congrArg",
"Set.univ",
"Set.Finite",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"HasSubset.Subset",
"Set.instInter",
"Set.univ_inter",
"Set.nonempty_sInter._simp_1",
"CompactSpace",
"Inter.inter",
"IsClosed",
"TopologicalSpace",
"Set.Nonemp... | true |
CategoryTheory.Oplax.OplaxTrans.whiskerRight | Mathlib.CategoryTheory.Bicategory.FunctorBicategory.Oplax | [
"CategoryTheory.Oplax.OplaxTrans.Hom.as",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Oplax.OplaxTrans.homCategory",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Oplax.OplaxTrans.Modification.mk",
"CategoryTheory.B... | true |
Function.onFun.eq_1 | Mathlib.Data.Finset.Sigma | [
"Function.onFun",
"Eq.refl",
"Eq"
] | true |
Submodule.localized'._proof_5 | Mathlib.Algebra.Module.LocalizedModule.Submodule | [
"Submodule",
"instHSMul",
"Submonoid.mul",
"HMul.hMul",
"IsLocalization",
"Submodule.toAddSubmonoid",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"IsLocalizedModule",
"Algebra",
"AddSubsemigroup.carrier",
"Algebra.... | false |
SSet.Subcomplex.le_iff_contains_nonDegenerate | Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | [
"SSet.Subcomplex.toSSet",
"SimplexCategory.rec",
"Opposite",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SSet.exists_nonDegenerate",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Quiver.Hom.op",
"PartialOrder.toPreorder",
"SSet.nonDegenerate",
"Subtyp... | true |
CategoryTheory.SmallObject.FunctorObjIndex | Mathlib.CategoryTheory.SmallObject.Construction | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.SmallObject.FunctorObjIndex.mk",
"CategoryTheory.Category"
] | true |
Stream'.Seq1.coeSeq | Mathlib.Data.Seq.Basic | [
"Stream'.Seq",
"Coe.mk",
"Stream'.Seq1.toSeq",
"Stream'.Seq1",
"Coe"
] | true |
locallyLipschitzOn_univ | Mathlib.Topology.EMetricSpace.Lipschitz | [
"Filter.instMembership",
"nhdsWithin_univ",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"nhdsWithin",
"instInhabitedTrue",
"Membership.mem",
"Exists",
"nhds",
"NNReal",
"LocallyLipschitz",
"PseudoEMetricSpace",
"iff_self",
"funext",
"And",
"Iff",
"implies_congr",
"PseudoEMetr... | true |
CategoryTheory.nerve.functorOfNerveMap_map | Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | [
"CategoryTheory.Cat.category",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.catToReflQuiver",
"CategoryTheory.Functor.category",
"SSet.Truncated"... | true |
NumberField.not_dvd_discr_iff_forall_mem | Mathlib.NumberTheory.NumberField.Discriminant.Different | [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"Int.cast",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"RingHom.instRingHomClass",
"IsIntegralClosure",
"IsDomain",
"AddCommGroup.intIsScalarTower",
"False",
"IsDedekindDomain.isDedekindDomainDvr",
"CommRing",
"Dvd.dvd",
"S... | true |
Std.DTreeMap.Internal.Unit.RioSliceData.mk.noConfusion | Std.Data.DTreeMap.Internal.Zipper | [
"Ord",
"HEq.refl",
"Std.DTreeMap.Internal.Unit.RioSliceData.mk",
"id",
"heq_of_eq",
"Unit",
"Std.Rio",
"Std.DTreeMap.Internal.Unit.RioSliceData.noConfusion",
"Eq.refl",
"HEq",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Unit.RioSliceData"
] | false |
Lean.IR.EmitLLVM.State._sizeOf_inst | Lean.Compiler.IR.EmitLLVM | [
"Lean.IR.EmitLLVM.State",
"Lean.IR.EmitLLVM.State._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"LLVM.Context"
] | false |
Hyperreal.exists_st_iff_not_infinite | Mathlib.Analysis.Real.Hyperreal | [
"Hyperreal.not_infinite_of_exists_st",
"Real",
"Exists",
"Iff",
"Hyperreal.Infinite",
"Iff.intro",
"Hyperreal",
"Hyperreal.exists_st_of_not_infinite",
"Hyperreal.IsSt",
"Not"
] | true |
CategoryTheory.MorphismProperty.HasPushouts.mk | Mathlib.CategoryTheory.MorphismProperty.Limits | [
"CategoryTheory.MorphismProperty.HasPushouts.hasPushout._autoParam",
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.HasPushouts",
"autoParam",
"CategoryTheory.MorphismProperty.HasPushouts.mk",
"CategoryTheory.Category.toCateg... | true |
VectorField.mpullback | Mathlib.Geometry.Manifold.VectorField.Pullback | [
"mfderiv",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupTangentSpace",
"ContinuousLinearMap.funLike",
"NormedField.toField",
"instModuleTangentSpace",
"Field.toSemifield",
"instTopologicalSpaceTangentSpace",
"ContinuousLinearMap",
"TopologicalSpace",
"ModelWithCorners",
"S... | true |
compl_symmDiff_self | Mathlib.Order.SymmDiff | [
"BooleanAlgebra",
"Lattice.toSemilatticeSup",
"hnot_symmDiff_self",
"Compl.compl",
"BooleanAlgebra.toCompl",
"SemilatticeSup.toMax",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
"BooleanAlgebra.toSDiff",
"BooleanAlgebra.toTop",
"CoheytingAlgebra.toGeneralizedCoheyt... | true |
SetLike.GradeZero.instAlgebraSubtypeMemOfNat._proof_4 | Mathlib.Algebra.DirectSum.Internal | [
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Subsemiring.instSetLike",
"instSMulOfMul",
"HMul.hMul",
"SetLike.GradeZero.instAlgebraSubtypeMemOfNat._aux_1",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"RingHom",
"SetLike.GradeZero.instCommSemiring",
"Membership... | false |
_private.Lean.Meta.DiscrTree.Types.0.Lean.Meta.DiscrTree.instBEqKey.beq._sparseCasesOn_3 | Lean.Meta.DiscrTree.Types | [
"Nat.ne_of_beq_eq_false",
"Lean.Meta.DiscrTree.Key.fvar",
"Lean.Meta.DiscrTree.Key.star",
"Nat.shiftRight",
"Lean.Meta.DiscrTree.Key.rec",
"Lean.FVarId",
"Nat.hasNotBit",
"Lean.Meta.DiscrTree.Key",
"instOfNatNat",
"Lean.Literal",
"Lean.Meta.DiscrTree.Key.arrow",
"Nat.land",
"Nat",
"Lean.Me... | false |
Std.HashMap.getD_alter_self | Std.Data.HashMap.Lemmas | [
"Std.HashMap.alter",
"Option.getD",
"Membership.mem",
"Std.HashMap",
"LawfulHashable",
"EquivBEq",
"Std.DHashMap.Const.getD_alter_self",
"Hashable",
"GetElem?.getElem?",
"Std.HashMap.instGetElem?Mem",
"Std.HashMap.inner",
"BEq",
"Eq",
"Std.HashMap.getD",
"Std.HashMap.instMembership",
"... | true |
CategoryTheory.Limits.«term⨁_» | Mathlib.CategoryTheory.Limits.Shapes.Biproducts | [
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
CategoryTheory.AddGrpObj.lift_addCommutator_eq_add_add_neg_neg_assoc | Mathlib.CategoryTheory.Monoidal.Cartesian.Grp | [
"AddGroup.toSubtractionMonoid",
"CategoryTheory.Category.assoc",
"NegZeroClass.toNeg",
"CategoryTheory.AddGrpObj.lift_addCommutator_eq_add_add_neg_neg",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Hom.addMonoid",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toA... | true |
CategoryTheory.exactPairingCongrRight._proof_3 | Mathlib.CategoryTheory.Monoidal.Rigid.Basic | [
"CategoryTheory.MonoidalCoherence.iso",
"Mathlib.Tactic.Monoidal.eval_whiskerLeft",
"Eq.mpr",
"CategoryTheory.MonoidalCategory.whisker_exchange",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Mathlib.Tactic.Monoidal.evalWhiskerLeft_of_cons",
"CategoryTheory.monoidalComp",
"CategoryTheory.Monoi... | false |
isNilpotent_pi | Mathlib.GroupTheory.Nilpotent | [
"Finite",
"Group",
"Pi.group",
"Group.isNilpotent_pi",
"Group.IsNilpotent"
] | true |
CategoryTheory.Cat.freeMapCompIso._proof_1 | Mathlib.CategoryTheory.Category.Quiv | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"Prefunctor.comp",
"CategoryTheory.Iso.refl",
"id",
"CategoryTheory.Category.comp_id",
"CategoryT... | false |
Lean.Meta.Simp.Result.mk | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.Simp.Result.mk",
"Lean.Expr",
"Lean.Meta.Simp.Result",
"Bool",
"Option"
] | true |
hasGradientWithinAt_univ._simp_1 | Mathlib.Analysis.Calculus.Gradient.Basic | [
"CompleteSpace",
"HasGradientWithinAt",
"Set.univ",
"PseudoMetricSpace.toUniformSpace",
"hasGradientWithinAt_univ",
"RCLike",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"propext",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Eq",
"InnerProductSpace",
"HasGradientAt",
"NormedAddCommGrou... | false |
RootPairing.EmbeddedG2.allCoeffs | Mathlib.LinearAlgebra.RootSystem.Finite.G2 | [
"Int.instNegInt",
"instOfNatNat",
"Int",
"List.cons",
"List",
"instOfNat",
"Nat",
"Matrix.vecEmpty",
"OfNat.ofNat",
"Fin",
"Matrix.vecCons",
"Neg.neg",
"List.nil"
] | true |
Finset.sum_card | Mathlib.Algebra.Order.BigOperators.Group.Finset | [
"Eq.mpr",
"HMul.hMul",
"Finset.univ",
"congrArg",
"Finset",
"Finset.sum_card_inter",
"Membership.mem",
"Fintype.card",
"id",
"instMulNat",
"Inter.inter",
"Finset.instInter",
"Fintype",
"Finset.instSetLike",
"Nat",
"True",
"eq_self",
"Finset.card",
"of_eq_true",
"Finset.univ_int... | true |
IsOpen.exists_smooth_support_eq | Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | [
"InnerProductSpace.toNormedSpace",
"Real",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero",
"Real.instRCLike",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Exists",
"ContDiff",
"Real.normedAddCommGroup",
"HasSubset.Subset",
"WithTop.some",
"Real.instOne",
"And",... | true |
Polynomial._aux_Mathlib_Algebra_Polynomial_Basic___unexpand_Polynomial_1 | Mathlib.Algebra.Polynomial.Basic | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
_private.Mathlib.AlgebraicTopology.DoldKan.Decomposition.0.AlgebraicTopology.DoldKan.decomposition_Q._simp_1_4 | Mathlib.AlgebraicTopology.DoldKan.Decomposition | [
"Finset.univ",
"Finset",
"Finset.mem_filter_univ",
"Membership.mem",
"Fintype",
"Finset.instSetLike",
"DecidablePred",
"propext",
"Finset.filter",
"Eq",
"SetLike.instMembership"
] | false |
Option.isNone_pbind_iff | Init.Data.Option.Lemmas | [
"Option.isNone",
"Iff.mpr",
"False",
"Iff.of_eq",
"Option.ctorIdx",
"congrArg",
"true_or",
"False.elim",
"Option.casesOn",
"noConfusion_of_Nat",
"Option.some.injEq",
"Option.some",
"Exists",
"false_or",
"iff_self",
"Bool.true",
"funext",
"Option.none",
"Iff",
"exists_prop_congr... | true |
CategoryTheory.instFunctorialObj | Mathlib.CategoryTheory.Functor.Functorial | [
"CategoryTheory.Functor",
"CategoryTheory.Functorial",
"CategoryTheory.Functor.map",
"CategoryTheory.Functor.map_id",
"CategoryTheory.Functor.map_comp",
"CategoryTheory.Functor.obj",
"CategoryTheory.Functorial.mk",
"CategoryTheory.Category"
] | true |
Plausible.Arbitrary.mk._flat_ctor | Plausible.Arbitrary | [
"Plausible.Arbitrary.mk",
"Plausible.Arbitrary",
"Plausible.Gen"
] | false |
Subgroup.smul_bot | Mathlib.Algebra.Group.Subgroup.Pointwise | [
"Monoid",
"instHSMul",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.End.instMonoid",
"Monoid.toMulOneClass",
"Group",
"MulDistribMulAction.toMonoidEnd",
"DivInvMonoid.toMonoid",
"Subgroup",
"Bot.bot",
"Subgroup.map_bot",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Monoid.toSemigrou... | true |
aemeasurable_lineDeriv | Mathlib.Analysis.Calculus.LineDeriv.Measurable | [
"measurable_lineDeriv",
"NormedCommRing.toSeminormedCommRing",
"MeasureTheory.Measure",
"Continuous",
"CompleteSpace",
"NormedSpace",
"Measurable.aemeasurable",
"AEMeasurable",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"BorelSpace",
"MeasurableSpace",
"SeminormedAddCommGrou... | true |
AddSubgroup.seminormedAddGroup.eq_1 | Mathlib.Analysis.Normed.Group.Subgroup | [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"SeminormedAddGroup.toAddGroup",
"AddMonoid.toAddZeroClass",
"SeminormedAddGroup",
"AddSubgroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"AddSubgroup",
"AddSubgroup.subtype",
"AddGroup.toSubNegMonoid",
"SeminormedAddGroup.m... | true |
ENNReal.ofReal_iInf | Mathlib.Data.ENNReal.Operations | [
"ENNReal.instCanonicallyOrderedAdd",
"Iff.mpr",
"Real.iInf_nonpos'",
"Eq.mpr",
"Real.iInf_nonneg",
"False",
"Real.instLE",
"Real",
"Preorder.toLT",
"iInf",
"Real.instZero",
"ENNReal.ofReal",
"lowerBounds",
"congrArg",
"CompletelyDistribLattice.toCompleteLattice",
"OrderBot.toBot",
"A... | true |
ClosedSubmodule.mem_orthogonal._simp_1 | Mathlib.Analysis.InnerProductSpace.Orthogonal | [
"InnerProductSpace.toNormedSpace",
"Inner.inner",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"ClosedSubmodule.mem_orthogonal",
"Field.toSemifield",
"ClosedSubmodule.orthogonal",
"RCLike.toDenselyNormedField... | false |
smoothSheafCommGroup.compLeft._proof_1 | Mathlib.Geometry.Manifold.Sheaf.Smooth | [
"CategoryTheory.Functor",
"MonoidHom.instFunLike",
"Opposite",
"NormedSpace",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"instTopENat",
"Monoid.toMulOneClass",
"TopologicalSpace.Opens.instPartialOrder",
"TopologicalSpace.Opens.instChartedSpace",
"ContMDiff",
"Partia... | false |
Equiv.locallyFinite_comp_iff._simp_1 | Mathlib.Topology.LocallyFinite | [
"Equiv.instEquivLike",
"Function.comp",
"Equiv",
"LocallyFinite",
"TopologicalSpace",
"Equiv.locallyFinite_comp_iff",
"propext",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike",
"Set"
] | false |
Turing.ToPartrec.stepRet_then | Mathlib.Computability.TuringMachine.Config | [
"Eq.mpr",
"congrArg",
"Turing.ToPartrec.Cont.halt",
"instInhabitedNat",
"Turing.ToPartrec.Cont.comp",
"Turing.ToPartrec.Cont.fix",
"Turing.ToPartrec.Cfg.then",
"id",
"Turing.ToPartrec.Cont",
"instOfNatNat",
"if_pos",
"Turing.ToPartrec.Cont.cons₂",
"List.tail",
"dite",
"List.cons",
"Lis... | true |
CategoryTheory.ShortComplex.SnakeInput.mk.injEq | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.ShortComplex.SnakeInput.mk",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.Epi",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Eq.propIntro",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTh... | true |
AlgHom.prod | Mathlib.Algebra.Algebra.Prod | [
"AlgHom",
"Algebra",
"RingHom",
"Prod.instSemiring",
"Prod.algebra",
"CommSemiring",
"AlgHom.toRingHom",
"AlgHom.mk",
"Prod.instNonAssocSemiring",
"Semiring",
"Prod",
"AlgHom.prod._proof_1",
"Semiring.toNonAssocSemiring",
"RingHom.prod"
] | true |
isPurelyInseparable_iff_perfectClosure_eq_top | Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | [
"Eq.mpr",
"IntermediateField.instPartialOrder",
"Eq.ge",
"Lattice.toSemilatticeSup",
"trivial",
"Subring.instSetLike",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"CompleteLattice.toLattice",
"congrArg",
"IntermediateField",
"Nat.instMonoid",
"perfectClosure",
"PartialOrder.toPreorder",
... | true |
TypeCat.Fun.mk.sizeOf_spec | Mathlib.CategoryTheory.Types.Basic | [
"TypeCat.Fun._sizeOf_inst",
"TypeCat.Fun.mk",
"instOfNatNat",
"TypeCat.Fun",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"SizeOf",
"OfNat.ofNat",
"Eq"
] | true |
AddAction.nsmul_vadd_ne_of_lt_period | Mathlib.GroupTheory.GroupAction.Period | [
"instHSMul",
"AddMonoid.toAddSemigroup",
"AddMonoid.toNSMul",
"AddAction.period",
"Ne",
"instOfNatNat",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddSemigroupAction.toVAdd",
"Nat.instPreorder",
"Nat",
"LT.lt",
"AddMonoid",
"instHVAdd",
"HSMul.hSMul",
"instLTNat",... | true |
Std.DTreeMap.Raw.WF.filterMap | Std.Data.DTreeMap.Raw.WF | [
"Std.DTreeMap.Raw.filterMap",
"Ord.mk",
"Ordering",
"Std.TransCmp",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Internal.Impl.WF.filterMap!",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Raw.WF.mk",
"Std.DTreeMap.Raw.WF",
"Option",
"Std.DTreeMap.Raw"
] | true |
Lean.Core.resetMessageLog | Lean.CoreM | [
"Array.mkEmpty",
"Lean.PersistentArrayNode.node",
"Lean.NameSet",
"Lean.Message",
"Lean.PersistentArray.mk",
"Lean.PersistentArray.initShift",
"instOfNatNat",
"Lean.PersistentArrayNode",
"Unit",
"Lean.Core.setMessageLog",
"Lean.Core.CoreM",
"USize.toNat",
"Lean.NameSet.instEmptyCollection",
... | true |
_private.Batteries.Data.String.Legacy.0.String.Legacy.anyAux.eq_def | Batteries.Data.String.Legacy | [
"String.instLTRaw",
"String.Legacy.anyAux",
"String",
"InvImage",
"Nat.sub_lt_sub_left",
"_private.Batteries.Data.String.Legacy.0.String.Legacy.anyAux._proof_1",
"HSub.hSub",
"WellFounded.Nat.fix",
"WellFounded.Nat.fix_eq",
"id",
"instDecidableEqBool",
"instSubNat",
"String.Pos.Raw",
"dite... | true |
_private.Std.Data.String.ToInt.0.String.Slice.toInt?_eq_of_eq_minus_append._simp_1_5 | Std.Data.String.ToInt | [
"Bool.true",
"Bool.not_eq_true",
"Bool",
"Eq.symm",
"Bool.false",
"Eq",
"Not"
] | false |
Lean.Meta.mkGeneralizationForbiddenSet | Lean.Meta.GeneralizeVars | [
"Pure.pure",
"Lean.instantiateMVars",
"Lean.CollectFVars.State",
"Array.push",
"instForInOfForIn'",
"Lean.Expr.instBEq",
"Lean.Expr.fvarId!",
"Lean.Meta.State",
"Array.instMembership",
"inferInstance",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.FVarId",
"instDecidableEqBool",
... | true |
Homeomorph.isOpen_image | Mathlib.Topology.Homeomorph.Defs | [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"id",
"Homeomorph.preimage_symm",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Iff",
"Set.preimage",
"Homeomorph.symm",
"propext",
"Homeomorph",
"Set.image",
"IsOpen",
"Eq.symm",
"Eq",
"DFunLike.coe",
"Homeomorph.isOpen_preimage",
"EquivLike.t... | true |
Projectivization.Subspace.instInfSet | Mathlib.LinearAlgebra.Projectivization.Subspace | [
"Projectivization.mk",
"AddCommGroup.toAddCommMonoid",
"Membership.mem",
"InfSet.mk",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"InfSet",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"Projectivization.Subspace",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionM... | true |
SimplexCategoryGenRel.IsAdmissible.of_cons | Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms | [
"instOfNatNat",
"_private.Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms.0.SimplexCategoryGenRel.IsAdmissible.of_cons._proof_1_1",
"List.cons",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"List.casesOn",
"_private.Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.N... | true |
Lean.Parser.Command.infix | Lean.Parser.Syntax | [
"Lean.Parser.Parser",
"Lean.Parser.leadingNode",
"instOfNatNat",
"Lean.Parser.symbol",
"Lean.Parser.withAntiquot",
"Bool.true",
"Nat",
"Lean.Parser.withCache",
"OfNat.ofNat",
"Lean.Parser.mkAntiquot",
"Bool.false",
"Lean.Name.mkStr4"
] | true |
Real.toNNReal_le_toNNReal_iff_of_pos | Mathlib.Data.NNReal.Defs | [
"False",
"Real.instLE",
"Real",
"eq_false",
"Real.instZero",
"congrArg",
"_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_le_toNNReal_iff_of_pos._simp_1_1",
"PartialOrder.toPreorder",
"Real.instLT",
"Preorder.toLE",
"NNReal",
"LE.le",
"iff_self",
"NNReal.instPartialOrder",
"Iff",
"LT... | true |
CategoryTheory.Pi.braiding_inv_apply | Mathlib.CategoryTheory.Pi.Monoidal | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pi.monoidalCategory",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.pi",
"CategoryTheory.BraidedCategory",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct",
"Cate... | true |
univLE_iff | Mathlib.Logic.UnivLE | [
"UnivLE",
"UnivLE.casesOn",
"UnivLE.mk",
"Iff",
"Iff.intro",
"Small"
] | true |
StandardEtalePresentation.hasMap | Mathlib.RingTheory.Etale.StandardEtale | [
"CommRing",
"CommSemiring.toSemiring",
"StandardEtalePresentation.P",
"Algebra",
"StandardEtalePresentation.x",
"CommRing.toCommSemiring",
"StandardEtalePair.HasMap",
"StandardEtalePresentation"
] | true |
CategoryTheory.Join.mapPair_obj_left | Mathlib.CategoryTheory.Join.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Join.instCategory",
"CategoryTheory.Join.left",
"CategoryTheory.Join",
"Eq",
"CategoryTheory.Join.mapPair",
"CategoryTheory.Functor.obj",
"rfl",
"CategoryTheory.Category"
] | true |
_private.Init.Data.Vector.Lemmas.0.Vector.append_inj._proof_1_1 | Init.Data.Vector.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.combo_sat'",
"id",
"instDecidableEqBool",
... | false |
Matroid.contract_delete_isMinor._simp_1 | Mathlib.Combinatorics.Matroid.Minor.Order | [
"Matroid.contract_delete_isMinor",
"Matroid.IsMinor",
"True",
"eq_true",
"Eq",
"Matroid",
"Matroid.contract",
"Matroid.delete",
"Set"
] | false |
RCLike.norm_two | Mathlib.Analysis.RCLike.Basic | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"Real",
"NormedRing.toRing",
"Nat.instAtLeastTwoHAddOfNat",
"RCLike.norm_ofNat",
"AddGroupWithOne.toAddMonoidWithOne",
"NormedField.toNorm",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"RCLike.toDenselyNormedField",
"RCLike",
"Nat.instNeZeroSucc"... | true |
Array.foldl_eq_foldl_extract | Init.Data.Array.Lemmas | [
"Pure.pure",
"Eq.mpr",
"congrArg",
"Monad.toApplicative",
"id",
"instOfNatNat",
"Id.run",
"Array.foldlM_start_stop",
"Id",
"Applicative.toPure",
"Array.extract",
"Array.foldl",
"Array",
"Array.foldlM",
"Nat",
"Eq.refl",
"Id.instMonad",
"OfNat.ofNat",
"Eq",
"Array.size"
] | true |
Aesop.NormM.Context | Aesop.Search.Expansion.Norm | [
"Aesop.NormM.Context.mk"
] | true |
Countable.instBorelSpace | Mathlib.MeasureTheory.Constructions.BorelSpace.Basic | [
"MeasurableSet",
"congrArg",
"DiscreteTopology",
"MeasurableSingletonClass",
"setOf",
"Set.Countable.measurableSet",
"MeasurableSpace.measurableSet_generateFrom",
"BorelSpace",
"inferInstance",
"borel",
"iff_self",
"MeasurableSpace",
"TopologicalSpace",
"Iff",
"congr",
"BorelSpace.mk",... | true |
Lean.Meta.Instances.mk.noConfusion | Lean.Meta.Instances | [
"Lean.PHashMap",
"id",
"Lean.Meta.Instances.noConfusion",
"Lean.PHashSet",
"Lean.Meta.InstanceTree",
"Lean.Meta.Instances",
"Lean.Name",
"Lean.Meta.InstanceEntry",
"Lean.Meta.Instances.mk",
"Eq",
"Lean.Name.instBEq",
"Lean.instHashableName"
] | false |
ContinuousLinearMap.holder_smul_left | Mathlib.MeasureTheory.Function.Holder | [
"MeasureTheory.ae",
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"MeasureTheory.Measure",
"NormedRing.toRing",
"SemilinearMapClass.toMulActionSemiHomClass",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"C... | true |
algebraMapCLM_toLinearMap | Mathlib.Topology.Algebra.Algebra | [
"Semiring.toModule",
"ContinuousSMul",
"CommSemiring.toSemiring",
"algebraMapCLM",
"Algebra",
"Algebra.toSMul",
"Algebra.toModule",
"ContinuousLinearMap.toLinearMap",
"Algebra.linearMap",
"toLinearMap_algebraMapCLM",
"LinearMap",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
... | true |
AlternatingMap.domCoprod.summand_mk'' | Mathlib.LinearAlgebra.Alternating.DomCoprod | [
"AlternatingMap",
"MonoidHom.range",
"Equiv.Perm.sumCongrHom",
"instFintypeSum",
"instHSMul",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"MultilinearMap.domCoprod",
"TensorProduct.addCommMonoid",
"instDecidableEqSu... | true |
_private.Mathlib.CategoryTheory.Limits.Shapes.IsTerminal.0.CategoryTheory.Limits.coneOfDiagramTerminal._simp_1 | Mathlib.CategoryTheory.Limits.Shapes.IsTerminal | [
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsIso.eq_inv_comp",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.inv",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | false |
CategoryTheory.Coverage.mk | Mathlib.CategoryTheory.Sites.Coverage | [
"CategoryTheory.Coverage",
"CategoryTheory.Precoverage",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"CategoryTheory.Presieve.FactorsThruAlong",
"Membership.mem",
"Exists",
"And",
"CategoryTheory.Coverage.mk",
"CategoryTheory.Precoverage.coverings",
"Cate... | true |
CFC.log.congr_simp | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic | [
"IsSelfAdjoint",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"NormedRing.toRing",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"PseudoMetricSpace.toUniformSpace",
"Eq.rec",
"instIsTopologicalRingReal",
"NonUnitalNonAssocRing.toNonUnitalNonA... | true |
ProbabilityTheory.Kernel.setIntegral_deterministic' | Mathlib.Probability.Kernel.Integral | [
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"CompleteSpace",
"MeasurableSet",
"NormedSpace",
"congrArg",
"Measurable",
"PseudoMetricSpace.toUniformSpace",
"Decidable",
"ProbabilityTheory.Kernel.deterministic_apply",
"Membership.mem",
"MeasureTheory.Measure.restrict",
"ProbabilityTheory.Kern... | true |
FirstOrder.Language.Relations.formula₂ | Mathlib.ModelTheory.Syntax | [
"FirstOrder.Language.Term",
"instOfNatNat",
"Nat",
"FirstOrder.Language.Relations",
"FirstOrder.Language.Formula",
"Matrix.vecEmpty",
"FirstOrder.Language",
"OfNat.ofNat",
"Matrix.vecCons",
"FirstOrder.Language.Relations.formula"
] | true |
Submodule.prod_bot | Mathlib.LinearAlgebra.Span.Basic | [
"Submodule",
"congrArg",
"AddMonoid.toAddZeroClass",
"Submodule.mem_bot._simp_1",
"Membership.mem",
"AddZeroClass.toAddZero",
"Prod.mk",
"Bot.bot",
"Submodule.prod",
"Prod.fst",
"AddCommMonoid",
"iff_self",
"AddZero.toZero",
"Submodule.instBot",
"And",
"Iff",
"Submodule.mem_prod._sim... | true |
PFunctor.M.approx_mk | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor",
"PFunctor.A",
"PFunctor.M",
"PFunctor.B",
"PFunctor.MIntl.approx",
"PFunctor.Approx.CofixA.intro",
"PFunctor.Approx.CofixA",
"Nat",
"Sigma.mk",
"Nat.succ",
"Eq",
"rfl",
"PFunctor.M.mk"
] | true |
List.map_toArray | Init.Data.Array.Lemmas | [
"congrArg",
"List.map",
"Array.ext'",
"Array.map",
"Array.toList",
"List.toArray",
"Array",
"List",
"True",
"eq_self",
"of_eq_true",
"Array.toList_map",
"congrFun'",
"Eq",
"Eq.trans"
] | true |
List.isNone_finIdxOf? | Init.Data.List.Find | [
"Option.isNone",
"Eq.mpr",
"Bool.not",
"congrArg",
"List.contains",
"List.isSome_finIdxOf?",
"id",
"List",
"List.finIdxOf?",
"PartialEquivBEq",
"Bool",
"Eq.refl",
"Option.not_isSome",
"Option.isSome",
"Eq.symm",
"Fin",
"BEq",
"Eq",
"List.length"
] | true |
Nat.digitChar_eq_f._simp_1 | Init.Data.Nat.ToString | [
"Nat.digitChar_eq_f",
"Nat.digitChar",
"instOfNatNat",
"Nat",
"propext",
"Char",
"OfNat.ofNat",
"Eq",
"Char.ofNat"
] | false |
_private.Mathlib.Combinatorics.Digraph.Basic.0.Digraph.ext.match_1 | Mathlib.Combinatorics.Digraph.Basic | [
"Digraph",
"Digraph.mk",
"Digraph.casesOn"
] | false |
ModularForm.qExpansion_of_pow | Mathlib.NumberTheory.ModularForms.QExpansion | [
"ModularForm",
"Eq.mpr",
"Int.instAddCommMonoid",
"Subgroup.HasDetPlusMinusOne",
"Real",
"instHSMul",
"HMul.hMul",
"instAddCommMonoidDirectSum",
"UpperHalfPlane.qExpansion",
"Real.instZero",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Matrix",
"DirectSum.GR... | true |
CompactExhaustion.ctorIdx | Mathlib.Topology.Compactness.SigmaCompact | [
"TopologicalSpace",
"Nat",
"CompactExhaustion"
] | false |
WeierstrassCurve.a₃_of_isCharThreeJNeZeroNF | Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms | [
"CommRing",
"CommSemiring.toSemiring",
"WeierstrassCurve",
"WeierstrassCurve.a₃",
"CommRing.toCommSemiring",
"WeierstrassCurve.IsCharThreeJNeZeroNF",
"Zero.toOfNat0",
"WeierstrassCurve.IsCharThreeJNeZeroNF.a₃",
"OfNat.ofNat",
"Eq",
"MulZeroClass.toZero",
"instMulZeroClassOfSemiring"
] | true |
HomotopicalAlgebra.ModelCategory.transport._proof_11 | Mathlib.AlgebraicTopology.ModelCategory.Transport | [
"CategoryTheory.HasLiftingProperty",
"Eq.mpr",
"HomotopicalAlgebra.ModelCategory.cm4b",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Equivalence",
"HomotopicalAlgebra.ModelCategory.categoryWithFibrations",
"inferInstance",
"id",
"HomotopicalAlgebra.Cofibrat... | false |
CategoryTheory.Sheaf.isConstant_iff_isIso_counit_app' | Mathlib.CategoryTheory.Sites.ConstantSheaf | [
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"Opposite",
"CategoryTheory.Limits.IsTerminal",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Sheaf.IsConstant",
"CategoryTheory.Functor.essImage",
"CategoryTheory.Adjunction.counit",... | true |
Lean.Server.Watchdog.WorkerEvent.crashed.elim | Lean.Server.Watchdog | [
"PULift.up",
"Lean.Server.Watchdog.WorkerEvent",
"Lean.Server.Watchdog.WorkerEvent.crashed",
"Nat",
"Lean.Server.Watchdog.WorkerEvent.ctorIdx",
"UInt32",
"Eq.symm",
"Eq",
"Lean.Server.Watchdog.WorkerEvent.ctorElim"
] | false |
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