name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
WithTop.instOrderedSub | Mathlib.Algebra.Order.Sub.WithTop | [
"WithTop.add_eq_top._simp_1",
"Eq.mpr",
"False",
"WithTop.coe_le_coe._simp_1",
"congrArg",
"le_top._simp_2",
"WithTop.coe_ne_top._simp_1",
"OrderBot.toBot",
"WithTop.top_le_iff._simp_1",
"HSub.hSub",
"OrderBot",
"id",
"WithTop.instOrderBot",
"OrderedSub",
"Bot.bot",
"LE.le",
"WithTop... | true |
CoalgCat.Hom.casesOn | Mathlib.Algebra.Category.CoalgCat.Basic | [
"CoalgCat.toModuleCat",
"CommRing",
"Coalgebra.toCoalgebraStruct",
"CoalgCat",
"CoalgHom",
"AddCommGroup.toAddCommMonoid",
"CoalgCat.instCoalgebra",
"CoalgCat.Hom.rec",
"CommRing.toCommSemiring",
"ModuleCat.isAddCommGroup",
"CoalgCat.Hom.mk",
"ModuleCat.carrier",
"CoalgCat.Hom",
"CommRing.... | false |
AddSemigroupIdeal.coe_closure' | Mathlib.Algebra.Group.Ideal | [
"Eq.mpr",
"AddSemigroupIdeal.closure",
"AddMonoid.toAddSemigroup",
"instVAddOfAdd",
"congrArg",
"Set.univ",
"AddMonoid.toAddZeroClass",
"AddSemigroupIdeal.coe_closure",
"Membership.mem",
"Exists",
"Set.instUnion",
"AddZeroClass.toAddZero",
"id",
"HasSubset.Subset",
"zero_add",
"AddZero... | true |
zpow_natCast | Mathlib.Algebra.Group.Defs | [
"DivInvMonoid.toZPow",
"Nat.brecOn",
"DivInvMonoid.toMonoid",
"Int",
"Nat.cast",
"DivInvMonoid",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"instNatCastInt",
"instHPow",
"Eq",
"zpow_natCast._f"
] | true |
intervalIntegral.integral_mono_on_of_le_Ioo | Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic | [
"Eq.mpr",
"Set.Ioc",
"InnerProductSpace.toNormedSpace",
"Real.partialOrder",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"le_rfl",
"Real.lattice",
"NormedSpace",
"MeasureTheory.NoAtoms",
"Real.instZero",
"IsStrictOrderedModule.toIsOrderedModule",
"Real.instRCLike",
"congrArg",
"ins... | true |
Lean.Meta.TransparencyMode.reducible | Init.MetaTypes | [
"Lean.Meta.TransparencyMode",
"Lean.Meta.TransparencyMode.reducible"
] | true |
CategoryTheory.locallyDiscreteBicategory._proof_17 | Mathlib.CategoryTheory.Bicategory.LocallyDiscrete | [
"CategoryTheory.LocallyDiscrete.categoryStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.LocallyDiscrete.eq_of_hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.locallyDiscreteBicategory._proof_1",
"CategoryTheory.eqToIso",
"inferInstance",
"CategoryTheory... | false |
Aesop.instInhabitedRulePattern | Aesop.RulePattern | [
"Aesop.instInhabitedRulePattern.default",
"Aesop.RulePattern",
"Inhabited",
"Inhabited.mk"
] | true |
Lean.Meta.getCoeFnInfo? | Lean.Meta.CoeAttr | [
"Pure.pure",
"Lean.ScopedEnvExtension.StateStack",
"Lean.NameMap",
"Lean.PersistentEnvExtensionState",
"Lean.Meta.CoeFnInfo",
"Lean.Core.instMonadEnvCoreM",
"Lean.ScopedEnvExtension.Entry",
"Lean.NameMap.find?",
"IO.RealWorld",
"EIO",
"instMonadEIO",
"Applicative.toPure",
"Lean.Core.State",
... | true |
AddEquiv.symm_map_add | Mathlib.Algebra.Group.Equiv.Defs | [
"Equiv.instEquivLike",
"Equiv.right_inv",
"AddHom",
"AddHom.addHomClass",
"map_add",
"Equiv",
"AddHom.funLike",
"instHAdd",
"AddHom.inverse",
"HAdd.hAdd",
"AddEquiv",
"AddEquiv.toEquiv",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"Add",
"EquivLike.toFunLike",
"Equiv.left_inv",
"AddEquiv... | true |
MvPolynomial.instIsPushout | Mathlib.RingTheory.TensorProduct.MvPolynomial | [
"AlgHom.toLinearMap",
"Finsupp.instAddZeroClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Algebra.to_smulCommClass",
"instHSMul",
"Semiring.toModule",
"HMul.hMul",
"IsScalarTower.right",
"MvPolynomial.instIsScalarTower",
"MvPolynomial.al... | true |
Aesop.UnsafeRuleInfo.mk.injEq | Aesop.Rule | [
"Eq.propIntro",
"Aesop.UnsafeRuleInfo",
"Aesop.UnsafeRuleInfo.mk",
"Eq.ndrec",
"Eq.refl",
"Aesop.UnsafeRuleInfo.mk.inj",
"Aesop.Percent",
"Eq"
] | true |
QuadraticAlgebra.mk_eq_add_smul_omega | Mathlib.Algebra.QuadraticAlgebra.Basic | [
"QuadraticAlgebra.re",
"NonAssocSemiring.toAddCommMonoidWithOne",
"QuadraticAlgebra.instSMul",
"QuadraticAlgebra.ext",
"instHSMul",
"instSMulOfMul",
"QuadraticAlgebra",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"RingHom",
"QuadraticAlgebra.instC... | true |
UniformFun.uniformCore.match_7 | Mathlib.Topology.UniformSpace.UniformConvergenceTopology | [
"Filter.instMembership",
"UniformSpace",
"SetRel",
"uniformity",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"SetRel.comp",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"Prod",
"Filter",
"Set.instHasSubset",
"Set"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.getKey!_alter._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
tsum_geometric_two' | Mathlib.Analysis.SpecificLimits.Basic | [
"Real",
"instHDiv",
"Real.instDivInvMonoid",
"EMetricSpace.metrizableSpace",
"Nat.instAtLeastTwoHAddOfNat",
"PseudoMetricSpace.toUniformSpace",
"HDiv.hDiv",
"instOfNatNat",
"SummationFilter.instNeBotUnconditional",
"Monoid.toPow",
"Real.instMonoid",
"hasSum_geometric_two'",
"HasSum.tsum_eq",... | true |
_private.Std.Data.DHashMap.Internal.Defs.0.Std.DHashMap.Internal.Raw₀.insert._proof_3 | Std.Data.DHashMap.Internal.Defs | [
"Eq.mpr",
"congrArg",
"Array.instGetElemUSizeLtNatToNatSize",
"Array.set",
"id",
"instOfNatNat",
"Array.size_set",
"Array",
"GetElem.getElem",
"instHAdd",
"Array.uset_eq_set",
"HAdd.hAdd",
"USize.toNat",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"instAddNat",
"Std.DHashMap.Intern... | false |
Lean.instReprDefinitionSafety | Lean.Declaration | [
"Repr.mk",
"Lean.instReprDefinitionSafety.repr",
"Repr",
"Lean.DefinitionSafety"
] | true |
Aesop.Script.StaticStructureM.Context._sizeOf_1 | Aesop.Script.StructureStatic | [
"Aesop.Script.Step._sizeOf_inst",
"Std.HashMap._sizeOf_inst",
"Lean.instBEqMVarId",
"Aesop.Script.StaticStructureM.Context",
"Lean.MVarId",
"instOfNatNat",
"Std.HashMap",
"Aesop.Script.StaticStructureM.Context.rec",
"Lean.MVarId._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Lean.instHashableMVarId"... | false |
Lean.VersoModuleDocs.isEmpty | Lean.DocString.Extension | [
"Lean.VersoModuleDocs",
"Bool",
"Lean.VersoModuleDocs.snippets",
"Lean.PersistentArray.isEmpty",
"Lean.VersoModuleDocs.Snippet"
] | true |
Set.Finite.encard_biUnion_le | Mathlib.Data.Set.Card.Arithmetic | [
"Set.encard",
"Finset.set_encard_biUnion_le",
"_private.Mathlib.Data.Set.Card.Arithmetic.0.Set.Finite.encard_biUnion_le._simp_1_1",
"Iff.of_eq",
"congrArg",
"Finset",
"finsum",
"Set.Finite",
"Membership.mem",
"Eq.mp",
"LE.le",
"instLEENat",
"funext",
"Finset.instSetLike",
"Set.Finite.toF... | true |
Pi.counit_single | Mathlib.RingTheory.Coalgebra.Basic | [
"CoalgebraStruct",
"Semiring.toModule",
"Pi.addCommMonoid",
"CommSemiring.toSemiring",
"Pi.module",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"DFinsupp.instCoalgebraStruct._proof_3",
"CoalgebraStruct.counit",
"AddZeroClass.toAddZero",
"Pi.single",
"LinearMap",
"Pi.instCoalgebraStr... | true |
Set.prod_add_prod_comm | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"Prod.instAdd",
"Membership.mem",
"Exists",
"id",
"Prod.mk",
"Prod.fst",
"And.casesOn",
"funext",
"instHAdd",
"Set.mem_prod",
"And",
"Set.add",
"Iff",
"Exists.casesOn",
"HAdd.hAdd",
"Prod.mk.injEq",
"And.intro... | true |
SpectrumRestricts.compactSpace | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | [
"Eq.mpr",
"isCompact_iff_compactSpace",
"spectrum",
"congrArg",
"IsScalarTower",
"ContinuousMap",
"Algebra",
"Algebra.toSMul",
"Membership.mem",
"Eq.rec",
"ContinuousMap.instContinuousMapClass",
"Eq.mp",
"Set.Elem",
"Semifield",
"id",
"CompactSpace",
"TopologicalSpace",
"Semifield.... | true |
Lean.Parser.Term.num.parenthesizer | Lean.Parser.Term | [
"Lean.PrettyPrinter.Parenthesizer",
"Lean.Parser.numLit.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.andthen.parenthesizer",
"Lean.Parser.maxPrec",
"Lean.PrettyPrinter.Parenthesizer.checkPrec.parenthesizer"
] | true |
AddSubgroup.addCommutator_eq_bot_iff_le_centralizer | Mathlib.GroupTheory.Commutator.Basic | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"AddSubgroup.instBot",
"AddSubgroup.instCompleteLattice",
"addCommutatorElement",
"AddSubgroup.addCommutator_le",
"congrArg",
"OrderBot.toBot",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"AddSubg... | true |
Subsemigroup.centerToMulOpposite._proof_2 | Mathlib.GroupTheory.Submonoid.Center | [
"Iff.mpr",
"MulOpposite.op_mem_center_iff",
"MulOpposite",
"Mul",
"Membership.mem",
"Subtype",
"Set.center",
"Subtype.mk",
"Subsemigroup",
"MulOpposite.unop_mem_center_iff",
"Function.RightInverse",
"Eq.refl",
"MulOpposite.unop",
"Subsemigroup.instSetLike",
"Subtype.val",
"Set.instMemb... | false |
_private.Lean.Elab.DeclModifiers.0.Lean.Elab.Visibility.isPublic._sparseCasesOn_1 | Lean.Elab.DeclModifiers | [
"Lean.Elab.Visibility.rec",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Lean.Elab.Visibility.regular",
"Nat.hasNotBit",
"instOfNatNat",
"Nat.land",
"Lean.Elab.Visibility.ctorIdx",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Lean.Elab.Visibility.public",
"Bool.false",
"Lean.Elab.Visibility... | false |
CategoryTheory.LocalizerMorphism.homMap_comp | Mathlib.CategoryTheory.Localization.HomEquiv | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Category.assoc",
"CategoryTheory.LocalizerMorphism.catCommSq",
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.LocalizerMorphism.homMap",
"CategoryTheory.Functor.... | true |
CochainComplex.HomComplex.Cochain.ofHom_v | Mathlib.Algebra.Homology.HomotopyCategory.HomComplex | [
"CochainComplex.HomComplex.Cochain._proof_1",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMon... | true |
_private.Mathlib.Data.Nat.Log.0.Nat.log.go_spec._simp_1_4 | Mathlib.Data.Nat.Log | [
"Ne",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat",
"propext",
"Nat.one_le_iff_ne_zero",
"OfNat.ofNat",
"Eq"
] | false |
RootPairing.EmbeddedG2.mem_span_of_mem_allRoots | Mathlib.LinearAlgebra.RootSystem.Finite.G2 | [
"Matrix.range_cons",
"Eq.mpr",
"Pi.Function.module",
"Submodule",
"IsDomain",
"False",
"CommRing",
"instHSMul",
"Semiring.toModule",
"Pi.addCommMonoid",
"Finset.univ",
"Set.union_empty",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMon... | true |
Batteries.RBNode.Balanced.below.casesOn | Batteries.Data.RBMap.Basic | [
"Batteries.RBNode",
"Batteries.RBNode.Balanced.below.nil",
"Batteries.RBNode.nil",
"instOfNatNat",
"Batteries.RBNode.Balanced.nil",
"Batteries.RBNode.Balanced.black",
"instHAdd",
"Batteries.RBNode.Balanced.red",
"Batteries.RBColor.red",
"HAdd.hAdd",
"Batteries.RBColor",
"Nat",
"Batteries.RBN... | false |
CategoryTheory.ProjectiveResolution.ofComplex._proof_3 | Mathlib.CategoryTheory.Abelian.Projective.Resolution | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian",
"CategoryTheory.Limits.HasKernel",
"CategoryTheory.Preadditive.preadditiveHasZeroMorphisms",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.HasKernels.has_limit... | false |
Algebra.Etale.comp | Mathlib.RingTheory.Etale.Basic | [
"CommRing",
"Algebra.Etale.mk",
"Algebra.FormallyEtale.comp",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra.Etale.formallyEtale",
"Algebra",
"Algebra.toSMul",
"Algebra.Etale",
"CommRing.toCommSemiring",
"Algebra.Etale.finitePresentation",
"Algebra.FinitePresentation.trans"
] | true |
EuclideanGeometry.eq_of_dist_eq_of_dist_eq_of_finrank_eq_two | Mathlib.Geometry.Euclidean.Basic | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Submodule",
"Real",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"Real.instRCLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membersh... | true |
Lean.Doc.Parser.InList.mk._flat_ctor | Lean.DocString.Parser | [
"Lean.Doc.Parser.OrderedListType",
"Sum",
"Lean.Doc.Parser.InList.mk",
"Nat",
"Lean.Doc.Parser.UnorderedListType",
"Lean.Doc.Parser.InList"
] | false |
AddCircle.liftIoc_zero_continuous | Mathlib.Topology.Instances.AddCircle.Defs | [
"Eq.mpr",
"OrderTopology",
"Preorder.toLT",
"Continuous",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddCommGroup.toAddGroup",
"SemilatticeInf.toPartialOrder",
"Fact",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Distr... | true |
List.mem_attach | Init.Data.List.Attach | [
"Eq.mpr",
"congrArg",
"List.map",
"Subtype.casesOn",
"Membership.mem",
"Exists",
"id",
"Subtype",
"Subtype.mk",
"And.casesOn",
"List",
"And",
"Exists.casesOn",
"List.instMembership",
"Iff.mp",
"Eq.ndrec",
"_private.Init.Data.List.Attach.0.List.mem_attach.match_1_1",
"List.mem_map",... | true |
ODE.FunSpace.mk.congr_simp | Mathlib.Analysis.ODE.PicardLindelof | [
"Real",
"LipschitzWith",
"ODE.FunSpace",
"NormedAddCommGroup.toMetricSpace",
"instPseudoEMetricSpaceSubtype",
"Membership.mem",
"Eq.rec",
"Set.Elem",
"EMetricSpace.toPseudoEMetricSpace",
"NNReal",
"Real.metricSpace",
"Set.Icc",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Eq.ndrec",
"E... | true |
RingHom.codomain_trivial_iff_range_trivial | Mathlib.Algebra.Ring.Hom.Defs | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"MulOne.toOne",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"RingHom",
"id",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"AddCommMonoidWithOne.toAddMonoid... | true |
_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Mul.0.Std.Tactic.BVDecide.BVExpr.bitblast.blastMul._proof_1 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Mul | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.combo_s... | false |
CategoryTheory.Limits.CatCospanTransformMorphism.left_coherence_assoc | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"Eq.mp",
"CategoryTheory.Functor.whiskerLeft",
"id",
"CategoryTheory.Limits.CatCospanTransform.left",
... | true |
_private.Lean.Meta.Tactic.Grind.Action.0.Lean.Meta.Grind.Action.orElse.eq_1 | Lean.Meta.Tactic.Grind.Action | [
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Action",
"Eq.refl",
"Lean.Meta.Grind.ActionResult",
"Lean.Meta.Grind.Action.orElse",
"Eq",
"Lean.Meta.Grind.ActionCont"
] | true |
FinTopCat.of | Mathlib.Topology.Category.FinTopCat | [
"FinTopCat.mk",
"FinTopCat",
"TopologicalSpace",
"Fintype",
"TopCat.of"
] | true |
Real.le_arcsin_iff_sin_le | Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"Real.pi",
"neg_le",
"Real.arcsin",
"congrArg",
"Real.instDivInvMonoid",
"covariant_swap_add_of_covariant_add",
"Iff.rfl",
"Nat.instAtLeastTwoHAddOfNat",
... | true |
CategoryTheory.Square.Hom | Mathlib.CategoryTheory.Square | [
"CategoryTheory.Square",
"CategoryTheory.Square.Hom.mk",
"CategoryTheory.Category"
] | true |
_private.Mathlib.GroupTheory.ResiduallyFinite.0.Group.residuallyFinite_iff_forall_finiteIndexNormalSubgroup._simp_1_1 | Mathlib.GroupTheory.ResiduallyFinite | [
"iInf",
"FiniteIndexNormalSubgroup.toSubgroup",
"Group.ResiduallyFinite",
"Group",
"Subgroup",
"Bot.bot",
"Group.residuallyFinite_def",
"Subgroup.instInfSet",
"propext",
"Subgroup.instBot",
"FiniteIndexNormalSubgroup",
"Eq"
] | false |
CentroidHom.centerToCentroidCenter._proof_6 | Mathlib.Algebra.Ring.CentroidHom | [
"HMul.hMul",
"NonUnitalSubsemiring.center",
"Membership.mem",
"Subtype",
"Distrib.toMul",
"Subtype.prop",
"IsMulCentral.left_assoc",
"NonUnitalSubsemiring.instSetLike",
"NonUnitalSubsemiring",
"NonUnitalNonAssocSemiring.toDistrib",
"NonUnitalNonAssocSemiring",
"Subtype.val",
"Eq",
"SetLike... | false |
Nat.Partition.mk | Mathlib.Combinatorics.Enumerative.Partition.Basic | [
"Multiset.sum",
"Nat.Partition.mk",
"Membership.mem",
"Multiset",
"instOfNatNat",
"Multiset.instMembership",
"Nat.Partition",
"Nat",
"LT.lt",
"Nat.instAddCommMonoid",
"instLTNat",
"OfNat.ofNat",
"Eq"
] | true |
Lean.Meta.Grind.AC.ACM.Context.mk.inj | Lean.Meta.Tactic.Grind.AC.Util | [
"Lean.Meta.Grind.AC.ACM.Context.mk.noConfusion",
"Lean.Meta.Grind.AC.ACM.Context.mk",
"Nat",
"Lean.Meta.Grind.AC.ACM.Context",
"Eq"
] | true |
AlgebraicGeometry.Spec.fiberToSpecResidueFieldIso._proof_3 | Mathlib.AlgebraicGeometry.Fiber | [
"CommRing",
"PrimeSpectrum.isPrime",
"CommSemiring.toSemiring",
"CommRing.toCommSemiring",
"Ideal.IsPrime",
"PrimeSpectrum",
"PrimeSpectrum.asIdeal"
] | false |
spectrum.inv₀_mem | Mathlib.Algebra.Algebra.Spectrum.Basic | [
"Iff.mpr",
"Units.val",
"spectrum.inv₀_mem_iff",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"spectrum",
"Algebra",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Units",
"Semifield",
"Inv.inv",
"Semifield.toCommGroupWithZero",
"Semiring.toMonoid",
"Co... | true |
DirectLimit.instDivisionRing._proof_5 | Mathlib.Algebra.Colimit.DirectLimit | [
"DirectLimit.instRingOfRingHomClass",
"AddMonoid.toZero",
"Preorder.toLE",
"DivisionRing.toDivisionSemiring",
"inferInstance",
"DivisionRing.toRing",
"Int",
"LE.le",
"DirectLimit",
"instOfNat",
"IsDirectedOrder",
"DivisionSemiring.toSemiring",
"Nonempty",
"Ring.zsmul_zero'",
"Zero.toOfNa... | false |
SemidirectProduct.inl._proof_1 | Mathlib.GroupTheory.SemidirectProduct | [
"MonoidHom.instMonoidHomClass",
"MulEquiv.instEquivLike",
"MonoidHom.instFunLike",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"SemidirectProduct",
"MulAut.instGroup",
"SemidirectProduct.right",
"Group",
"Group.toDivis... | false |
Std.Iterators.Types.ULiftIterator.ctorIdx | Init.Data.Iterators.Combinators.Monadic.ULift | [
"Std.Iterators.ULiftT",
"Std.Iterators.Types.ULiftIterator",
"Nat"
] | false |
intervalIntegral.integral_mono_on | Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic | [
"Eq.mpr",
"Set.Ioc",
"InnerProductSpace.toNormedSpace",
"instClosedIicTopology",
"Real.partialOrder",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"Real.lattice",
"NormedSpace",
"Real.instZero",
"IsStrictOrderedModule.toIsOrderedModule",
"Real.instRCLike",
"congrArg",
"instHasSolidNor... | true |
Filter.comap_cofinite_le | Mathlib.Order.Filter.Cofinite | [
"Filter.instMembership",
"Iff.mpr",
"Compl.compl",
"Filter.Eventually",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Filter.le_cofinite_iff_eventually_ne",
"Set.instSingletonSet",
"HasSubset.Subset",
"Ne",
"LE.le",
"Set.instCompl",
"ne_of_apply_ne",... | true |
Lean.Parser.Command.eoi._regBuiltin.Lean.Parser.Command.eoi.parenthesizer_7 | Lean.Parser.Command | [
"Lean.Name.mkStr5",
"IO",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.PrettyPrinter.parenthesizerAttribute",
"Unit",
"Lean.Parser.Command.eoi.parenthesizer",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
List.isEqv.match_1 | Init.Data.List.Basic | [
"List.cons",
"List",
"List.casesOn",
"Bool",
"List.nil"
] | false |
Geometry.SimplicialComplex.faces_bot | Mathlib.Analysis.Convex.SimplicialComplex.Basic | [
"AddCommGroup.toAddCommMonoid",
"PreAbstractSimplicialComplex.faces",
"Finset",
"PartialOrder",
"AddCommGroup",
"Bot.bot",
"Geometry.SimplicialComplex.toPreAbstractSimplicialComplex",
"Geometry.SimplicialComplex.hasBot",
"Set.instEmptyCollection",
"Geometry.SimplicialComplex",
"EmptyCollection.e... | true |
Subring.instInfSet | Mathlib.Algebra.Ring.Subring.Basic | [
"Subring.toSubsemiring",
"iInf",
"Subring.instSetLike",
"AddGroupWithOne.toAddGroup",
"Set.iInter",
"AddSubgroup.instInfSet",
"Submonoid.instInfSet",
"Membership.mem",
"InfSet.mk",
"InfSet",
"Subring.instInfSet._proof_3",
"Subring.toAddSubgroup",
"NonAssocSemiring.toMulZeroOneClass",
"NonA... | true |
ComputeAsymptotics.MultiseriesExpansion.Multiseries.cons_eq_cons._simp_1 | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | [
"ComputeAsymptotics.Basis",
"Real",
"ComputeAsymptotics.MultiseriesExpansion.Multiseries.cons_eq_cons",
"And",
"propext",
"Eq",
"ComputeAsymptotics.MultiseriesExpansion.Multiseries.cons",
"ComputeAsymptotics.MultiseriesExpansion",
"ComputeAsymptotics.MultiseriesExpansion.Multiseries"
] | false |
CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.i₀ | Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.OneHypercoverDenseData",
"CategoryTheory.Functor.One... | true |
Lean.Lsp.instFromJsonLocation.fromJson | Lean.Data.Lsp.Basic | [
"Pure.pure",
"Lean.Lsp.Location.mk",
"Lean.Json",
"Lean.instFromJsonString",
"Lean.Lsp.Location",
"Monad.toApplicative",
"String",
"Lean.Lsp.instFromJsonRange",
"Lean.Name.mkStr3",
"Lean.Json.getObjValAs?",
"Applicative.toPure",
"ToString.toString",
"Except.instMonad",
"Lean.Lsp.DocumentUr... | true |
Aesop.ForwardRuleMatch.foldHypsM | Aesop.Forward.Match | [
"Pure.pure",
"Aesop.ForwardRuleMatch",
"Aesop.CompleteMatch.clusterMatches",
"Monad.toApplicative",
"Lean.Expr",
"Lean.FVarId",
"Aesop.Match.subst",
"Aesop.Match",
"instOfNatNat",
"Applicative.toPure",
"Array.foldlM",
"_private.Aesop.Forward.Match.0.Aesop.ForwardRuleMatch.foldHypsM.match_4",
... | true |
Lean.Meta.LazyDiscrTree.ImportData.casesOn | Lean.Meta.LazyDiscrTree | [
"Lean.Meta.LazyDiscrTree.ImportData.mk",
"Lean.Meta.LazyDiscrTree.ImportFailure",
"Lean.Meta.LazyDiscrTree.ImportData",
"Array",
"IO.Ref",
"Lean.Meta.LazyDiscrTree.ImportData.rec"
] | false |
TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq | Mathlib.Analysis.Distribution.FourierMultiplier | [
"instInnerProductSpaceRealComplex",
"NormedCommRing.toNormedRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"instIsAd... | true |
_private.Mathlib.Data.Option.NAry.0.Option.map_map₂_distrib_right._proof_1_1 | Mathlib.Data.Option.NAry | [
"False",
"eq_false",
"Option.map₂_some_some",
"congrArg",
"Classical.byContradiction",
"Option.casesOn",
"Option.some",
"Eq.mp",
"id",
"Option.map₂_none_right",
"Option.none",
"Option.map",
"Option.map_some",
"congr",
"True",
"eq_true",
"Eq.refl",
"Option.map_none",
"Option.map₂_... | false |
Lean.Meta.Grind.Arith.Cutsat.DvdSolution.mk | Lean.Meta.Tactic.Grind.Arith.Cutsat.Search | [
"Lean.Meta.Grind.Arith.Cutsat.DvdSolution.mk",
"Int",
"Lean.Meta.Grind.Arith.Cutsat.DvdSolution"
] | true |
addCommutator_centralizer_addCommutator_le_center | Mathlib.GroupTheory.Commutator.Basic | [
"Eq.mpr",
"AddSubgroup.instBot",
"AddSubgroup.instCompleteLattice",
"AddSubgroup.coe_top",
"AddSubgroup.addCommutator_comm",
"congrArg",
"addCommutator",
"Set.univ",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"AddSubgroup.addCommutator",
"Bracket.b... | true |
AlgEquiv.ofBijective_symm_apply_apply | Mathlib.Algebra.Algebra.Equiv | [
"AlgEquiv.symm",
"AlgEquiv.ofBijective",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"CommSemiring",
"AlgEquiv.symm_apply_apply",
"AlgEquiv",
"Function.Bijective",
"Semiring",
"Eq",
"DFunLike.coe",
"AlgEquiv.instFunLike"
] | true |
Vector.emptyWithCapacity._proof_1 | Init.Data.Vector.Basic | [
"congrArg",
"instOfNatNat",
"List.size_toArray",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Array.size",
"Eq.trans",
"Array.emptyWithCapacity",
"List.nil"
] | false |
IsOneApply.rec | Mathlib.Data.FunLike.IsApply | [
"One",
"IsOneApply.mk",
"IsOneApply",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"FunLike"
] | false |
Set.Nonempty.pow | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Monoid",
"Nat.brecOn",
"Set.monoid",
"Monoid.toPow",
"Set.Nonempty",
"HPow.hPow",
"Nat",
"instHPow",
"Set.Nonempty.pow._f",
"Set"
] | true |
Finsupp.mapRange.addMonoidHom_apply | Mathlib.Algebra.Group.Finsupp | [
"Finsupp.instAddZeroClass",
"Finsupp.mapRange.addMonoidHom",
"AddMonoid.toAddZeroClass",
"Finsupp.mapRange.addMonoidHom._proof_1",
"AddZeroClass.toAddZero",
"AddCommMonoid",
"AddZero.toZero",
"Eq.refl",
"AddCommMonoid.toAddMonoid",
"AddMonoidHom",
"Finsupp.mapRange",
"AddMonoidHom.instFunLike"... | true |
Int.map_add_toList_rcc' | Init.Data.Range.Polymorphic.IntLemmas | [
"Std.Rco",
"Std.Rco.toList.congr_simp",
"Int.map_add_toList_rco'",
"congrArg",
"List.map",
"Std.PRange.instUpwardEnumerableInt",
"Int.decLe",
"Int",
"Std.PRange.instIsAlwaysFiniteInt_1",
"Int.instLTInt",
"List",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"congr",
"Std.Rcc.toList",
"True",... | true |
NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring | Mathlib.Algebra.Ring.Defs | [
"NonUnitalNonAssocCommSemiring",
"NonUnitalNonAssocSemiring"
] | true |
Lean.Elab.DefKind.example.sizeOf_spec | Lean.Elab.DefView | [
"Lean.Elab.DefKind._sizeOf_inst",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Lean.Elab.DefKind.example",
"Eq",
"Lean.Elab.DefKind"
] | true |
_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.trList.match_1.eq_2 | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.trList.match_1",
"List.cons",
"List",
"Unit",
"Nat",
"Eq.refl",
"Eq",
"List.nil"
] | true |
Lean.Grind.OrderedRing.pos_intCast_of_pos | Init.Grind.Ordered.Ring | [
"Int.cast",
"Eq.mpr",
"Lean.Grind.OrderedRing.pos_natCast_of_pos",
"False",
"Lean.Grind.Ring.intCast_natCast",
"Nat.zero_lt_succ._simp_1",
"congrArg",
"False.elim",
"Classical.byContradiction",
"Int.casesOn",
"_private.Init.Grind.Ordered.Ring.0.Lean.Grind.OrderedRing.pos_intCast_of_pos._proof_1_... | true |
ZeroAtInftyContinuousMap.instNonUnitalNonAssocSemiring._proof_1 | Mathlib.Topology.ContinuousMap.ZeroAtInfty | [
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"IsTopologicalSemiring",
"IsTopologicalSemiring.toContinuousMul",
"Function.Injective.distrib",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Distrib.left_distrib",
"ZeroAtInftyContinuousMap.instFunLike",
"ZeroAtInftyContinuousMap... | false |
PUnit.lcm_eq | Mathlib.Algebra.GCDMonoid.PUnit | [
"PUnit.commRing",
"CommSemiring.toCommMonoidWithZero",
"PUnit.normalizedGCDMonoid",
"GCDMonoid.lcm",
"CommRing.toCommSemiring",
"NormalizedGCDMonoid.toGCDMonoid",
"PUnit",
"PUnit.unit",
"Eq",
"rfl"
] | true |
Metric.thickening_subset_cthickening_of_le | Mathlib.Topology.MetricSpace.Thickening | [
"Metric.cthickening_mono",
"Real.instLE",
"Real",
"Metric.thickening_subset_cthickening",
"HasSubset.Subset.trans",
"Set.instIsTransSubset",
"HasSubset.Subset",
"LE.le",
"PseudoEMetricSpace",
"Metric.thickening",
"Metric.cthickening",
"Set.instHasSubset",
"Set"
] | true |
Equiv.Perm.IsCycle.sameCycle | Mathlib.GroupTheory.Perm.Cycle.Basic | [
"Eq.mpr",
"zpow_add",
"Equiv.instEquivLike",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"_private.Mathlib.GroupTheory.Perm.Cycle.Basic.0.Equiv.Perm.IsCycle.sameCycle.match_1_3",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"DivInvMonoid.toZPow",
"AddZeroClass.toAddZero",
"id",
"_private.Ma... | true |
IsAdicComplete.StrictMono.liftRingHom._proof_4 | Mathlib.RingTheory.AdicCompletion.RingHom | [
"StrictMono",
"StrictMono.monotone",
"Preorder.toLE",
"Nat.le_succ",
"instOfNatNat",
"LE.le",
"instHAdd",
"HAdd.hAdd",
"Nat.instPreorder",
"Nat",
"Nat.instPartialOrder",
"instAddNat",
"OfNat.ofNat"
] | false |
NonemptyInterval.addCommMonoid._proof_7 | Mathlib.Algebra.Order.Interval.Basic | [
"covariant_swap_add_of_covariant_add",
"Function.swap",
"Preorder.toLE",
"LE.le",
"AddCommMonoid",
"instHAdd",
"HAdd.hAdd",
"AddCommSemigroup.toAddCommMagma",
"AddCommMonoid.toAddCommSemigroup",
"IsOrderedAddMonoid",
"Preorder",
"AddCommMagma.toAdd",
"IsOrderedAddMonoid.toAddLeftMono",
"Co... | false |
MeasureTheory.SimpleFunc.instRing | Mathlib.MeasureTheory.Function.SimpleFunc | [
"Ring.mk",
"NegZeroClass.toNeg",
"MeasureTheory.SimpleFunc.instIntCast",
"instHSMul",
"AddGroupWithOne.toAddGroup",
"AddCommGroup.toAddGroup",
"MeasureTheory.SimpleFunc.instRing._proof_4",
"MeasureTheory.SimpleFunc",
"MeasureTheory.SimpleFunc.instRing._proof_6",
"MeasureTheory.SimpleFunc.instRing.... | true |
Rep.FiniteCyclicGroup.moduleCatChainComplex._proof_1 | Mathlib.RepresentationTheory.Homological.FiniteCyclic | [
"LinearMap.id",
"Representation.IntertwiningMap.instSub",
"Rep.V",
"CommRing",
"Representation",
"MonoidHom.instFunLike",
"LinearMap.comp.congr_simp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"sub_self",
"ModuleCat",
"Monoid.toMulOneClass",
"LinearMap.ext",
"congrArg",
"Co... | false |
_private.Mathlib.NumberTheory.JacobiSum.Basic.0.jacobiSum_trivial_trivial._simp_1_1 | Mathlib.NumberTheory.JacobiSum.Basic | [
"Finset",
"Finset.instSDiff",
"Membership.mem",
"Finset.mem_sdiff",
"SDiff.sdiff",
"And",
"Finset.instSetLike",
"propext",
"Eq",
"Not",
"SetLike.instMembership",
"DecidableEq"
] | false |
_private.Mathlib.MeasureTheory.Measure.CharacteristicFunction.TaylorExpansion.0.MeasureTheory.iteratedFDeriv_charFun._simp_1_7 | Mathlib.MeasureTheory.Measure.CharacteristicFunction.TaylorExpansion | [
"False",
"eq_false",
"instOfNatNat",
"two_ne_zero",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
SymAlg.unsym_ne_zero_iff | Mathlib.Algebra.Symmetrized | [
"Equiv.instEquivLike",
"Equiv",
"Ne",
"Iff",
"SymAlg.unsym",
"Zero.toOfNat0",
"SymAlg.instZero",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"not_congr",
"EquivLike.toFunLike",
"SymAlg",
"Zero",
"SymAlg.unsym_eq_zero_iff"
] | true |
UnitAddTorus.coe_symm_measurableEquivPiIoc_apply | Mathlib.Analysis.Fourier.AddCircleMulti | [
"MeasurableEquiv.instEquivLike",
"Set.Ioc",
"Real",
"AddCommGroup.toAddGroup",
"Membership.mem",
"MeasurableEquiv.symm",
"QuotientAddGroup.mk",
"Subtype",
"Real.instAddCommGroup",
"Real.instAdd",
"Real.instOne",
"QuotientAddGroup.measurableSpace",
"instHAdd",
"Real.measurableSpace",
"HAd... | true |
IsCoveringMap.monodromy | Mathlib.Topology.Homotopy.Lifting | [
"Real.instIsOrderedRing",
"Path.continuousMapClass",
"Real.partialOrder",
"Real",
"IsCoveringMap.monodromy._proof_2",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"Real.semiring",
"Set.Elem",
"Set.instSingletonSet",
"IsCoveringMap.liftPath",
"toContinuousMap",
"Pa... | true |
Std.IterM.empty | Std.Data.Iterators.Producers.Monadic.Empty | [
"Std.Iterators.Types.Empty",
"Std.IterM.mk",
"Std.Iterators.Types.Empty.mk",
"Std.IterM"
] | true |
_private.Lean.Meta.Tactic.Simp.Main.0.Lean.Meta.Simp.mainCore.match_1 | Lean.Meta.Tactic.Simp.Main | [
"Lean.Meta.Simp.Result",
"Prod.mk",
"Lean.Meta.Simp.State",
"Prod",
"Prod.casesOn"
] | false |
_private.Lean.Server.Logging.0.Lean.Server.Logging.LogEntry.mk | Lean.Server.Logging | [
"Lean.JsonRpc.MessageKind",
"Lean.JsonRpc.Message",
"_private.Lean.Server.Logging.0.Lean.Server.Logging.LogEntry",
"Std.Time.ZonedDateTime",
"Lean.JsonRpc.MessageDirection",
"_private.Lean.Server.Logging.0.Lean.Server.Logging.LogEntry.mk"
] | true |
LieModule.maxTrivLinearMapEquivLieModuleHom._proof_7 | Mathlib.Algebra.Lie.Abelian | [
"CommRing",
"CommSemiring.toSemiring",
"RingHomInvPair",
"CommRing.toCommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
BitVec.getMsbD_srem | Init.Data.BitVec.Bitblast | [
"BitVec.getMsbD",
"congrArg",
"BitVec",
"id",
"instDecidableEqBool",
"instHMod",
"BitVec.sdiv.match_1",
"BitVec.getElem_sdiv.match_1",
"BitVec.instNeg",
"BitVec.srem",
"dite",
"Bool.true",
"HMod.hMod",
"Unit",
"Nat",
"congr",
"True",
"Bool.of_not_eq_true",
"eq_self",
"Bool",
... | true |
LinearMap.proj_surjective | Mathlib.LinearAlgebra.Pi | [
"Pi.addCommMonoid",
"Function.surjective_eval",
"Pi.module",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"Zero.instNonempty",
"LinearMap",
"AddCommMonoid",
"LinearMap.proj",
"AddZero.toZero",
"Semiring",
"AddCommMonoid.toAddMonoid",
"Module",
"RingHom.i... | true |
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