name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Mathlib.Tactic.BicategoryLike.MonadWhiskerLeft.mk | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | [
"Mathlib.Tactic.BicategoryLike.MonadWhiskerLeft.mk",
"Mathlib.Tactic.BicategoryLike.Atom₁",
"Mathlib.Tactic.BicategoryLike.MonadWhiskerLeft",
"Mathlib.Tactic.BicategoryLike.WhiskerLeft",
"Mathlib.Tactic.BicategoryLike.MonadHorizontalComp"
] | true |
GradedAlgHom.coe_one | Mathlib.RingTheory.GradedAlgebra.AlgHom | [
"Submodule",
"MulOne.toOne",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"GradedAlgHom",
"Algebra",
"Algebra.toModule",
"id",
"GradedAlgHom.instMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"MulOneClass.toMulOne",
"GradedAlgebra",
"NonAssocSemiring.toNonUnita... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Nat.0.Lean.Meta.Grind.Arith.Cutsat.isNonneg.match_1 | Lean.Meta.Tactic.Grind.Arith.Cutsat.Nat | [
"Option.ctorIdx",
"Option.some",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Nat.0.Lean.Meta.Grind.Arith.Cutsat.mkNatVar._sparseCasesOn_1",
"Nat.hasNotBit",
"Int",
"Option"
] | false |
AddSubgroup.mem_closure_pair | Mathlib.Algebra.Group.Subgroup.Lattice | [
"Eq.mpr",
"AddSubgroup.instCompleteLattice",
"instHSMul",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Set.singleton_union",
"Exists",
"Set.instUnion",
"AddZeroClass.toAddZero",
"SemilatticeSu... | true |
CategoryTheory.PreZeroHypercover.saturate_p₁ | Mathlib.CategoryTheory.Sites.Hypercover.Saturate | [
"CategoryTheory.PreZeroHypercover.Relation.fst",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.PreZeroHypercover.Relation.obj",
"CategoryTheory.PreZeroHypercover.saturate",
"CategoryTheory.PreZeroHyp... | true |
_private.Init.Data.String.Basic.0.String.Pos.Raw.isValid_push._proof_1_4 | Init.Data.String.Basic | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.and_not_not_of_not_or",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"String",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_di... | false |
_private.Aesop.BuiltinRules.Subst.0.Aesop.BuiltinRules.matchSubstitutableIff?._sparseCasesOn_1 | Aesop.BuiltinRules.Subst | [
"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 |
CategoryTheory.RingObjCat.Hom.recOn | Mathlib.CategoryTheory.Monoidal.Ring | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.RingObjCat.Hom.mk",
"CategoryTheory.RingObjCat.ringObj",
"CategoryTheory.RingObjCat.X",
"CategoryTheory.RingObjCat.Hom.rec",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.RingObjCat",
"Catego... | false |
ContinuousMulEquiv.recOn | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"Continuous",
"Mul",
"ContinuousMulEquiv.mk",
"MulEquiv.toEquiv",
"Equiv.toFun",
"TopologicalSpace",
"ContinuousMulEquiv.rec",
"MulEquiv",
"ContinuousMulEquiv",
"Equiv.invFun"
] | false |
MeasureTheory.L1.SimpleFunc.setToL1SCLM'._proof_2 | Mathlib.MeasureTheory.Integral.SetToL1 | [
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedAddCommGroup",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"HMul.hMul",
"MeasurableSet",
"NormedSpace",
"Real.denselyNormedField",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"... | false |
MonCat.instCategory._proof_1 | Mathlib.Algebra.Category.MonCat.Basic | [
"Monoid.toMulOneClass",
"_private.Mathlib.Algebra.Category.MonCat.Basic.0.MonCat.Hom.mk",
"id",
"MonCat",
"MonoidHom.comp",
"MonCat.carrier",
"MulOneClass.toMulOne",
"MonCat.Hom",
"MonoidHom.id",
"Eq.refl",
"Eq",
"MonCat.str",
"MonCat.Hom.hom'"
] | false |
Valuation.IsNontrivial_iff_exists_one_lt | Mathlib.RingTheory.Valuation.Basic | [
"not_lt_zero._simp_1",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"MulOne.toOne",
"False",
"Preorder.toLT",
"InvOneClass.toOne",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"DivisionCommMonoid.toDivisionMonoid",
"DivInv... | true |
RootPairing.reflection_inv | Mathlib.LinearAlgebra.RootSystem.Defs | [
"CommRing",
"DivInvOneMonoid.toInvOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"AddCommGroup",
"LinearEquiv.automorphismGroup",
"CommRing.toCommSemiring",
"Inv.inv",
"RootPairing.reflection",
"RingHomInvPair... | true |
_private.Lean.Compiler.MetaAttr.0.Lean.initFn._@.Lean.Compiler.MetaAttr.358778973._hygCtx._hyg.2 | Lean.Compiler.MetaAttr | [
"Lean.EnvExtension.AsyncMode.sync",
"Lean.Name.mkNum",
"Bool.not",
"Array.push",
"Lean.NameSet",
"Lean.SimplePersistentEnvExtensionDescr.mk",
"Lean.Name.quickLt",
"HSub.hSub",
"IO",
"Lean.OLeanEntries.mk",
"Option.some",
"Lean.registerSimplePersistentEnvExtension",
"Lean.Name.mkStr",
"Arra... | false |
MeasureTheory.Filtration.IsRightContinuous | Mathlib.Probability.Process.Filtration | [
"PartialOrder.toPreorder",
"PartialOrder",
"MeasureTheory.Filtration",
"MeasurableSpace",
"MeasureTheory.Filtration.IsRightContinuous.mk"
] | true |
Aesop.instInhabitedForwardRulePriority.default | Aesop.Rule.Forward | [
"Inhabited.default",
"Int.instInhabited",
"Int",
"Aesop.ForwardRulePriority",
"Aesop.ForwardRulePriority.normSafe"
] | true |
List.getLast_eq_getElem._f | Init.Data.List.Lemmas | [
"List.getLast",
"congrArg",
"GetElem.getElem.congr_simp",
"HSub.hSub",
"_private.Init.Data.List.Lemmas.0.List.getLast_eq_getElem.match_1_1",
"instSubNat",
"Ne",
"instOfNatNat",
"List.cons",
"GetElem.getElem",
"List",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"congr",
"LT.lt",
"Tr... | false |
MulEquiv.arrowCongr._proof_2 | Mathlib.Algebra.Group.Equiv.Basic | [
"Equiv.apply_symm_apply",
"MulEquiv.instEquivLike",
"Equiv.instEquivLike",
"congrArg",
"Mul",
"Equiv",
"funext",
"True",
"eq_self",
"of_eq_true",
"MulEquiv",
"congrFun'",
"Equiv.symm",
"MulEquiv.symm",
"Eq",
"DFunLike.coe",
"Eq.trans",
"EquivLike.toFunLike",
"MulEquiv.apply_symm_... | false |
OmegaCompletePartialOrder.Chain.pair_succ | Mathlib.Order.OmegaCompletePartialOrder | [
"OmegaCompletePartialOrder.Chain.pair",
"Preorder.toLE",
"instOfNatNat",
"LE.le",
"instHAdd",
"OmegaCompletePartialOrder.Chain",
"HAdd.hAdd",
"Nat",
"OmegaCompletePartialOrder.Chain.instFunLikeNat",
"instAddNat",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"rfl",
"Preorder"
] | true |
groupCohomology.map_one_snd_of_isCocycle₂ | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | [
"Monoid",
"MulOne.toOne",
"instHSMul",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddCancelMonoid.toAddRightCancelMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Eq.mp",
"MulOne.toMul",
"Prod.mk",
"instHAdd",
"MulOneClass.toMulOne",
"_private... | true |
Lean.RBNode.instEmptyCollection | Lean.Data.RBMap | [
"Lean.RBNode",
"EmptyCollection.mk",
"Lean.RBNode.leaf",
"EmptyCollection"
] | true |
_private.Mathlib.Algebra.Order.SuccPred.0.Order.IsPredPrelimit.lt_sub_natCast.match_1_1 | Mathlib.Algebra.Order.SuccPred | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
Filter.EventuallyEq.eventuallyEq_nhds | Mathlib.Topology.Neighborhoods | [
"Filter.Eventually",
"Filter.Eventually.eventually_nhds",
"nhds",
"Filter.EventuallyEq",
"TopologicalSpace",
"Eq"
] | true |
AlgebraicGeometry.IsImmersion.instDiagonalScheme | Mathlib.AlgebraicGeometry.Morphisms.Immersion | [
"AlgebraicGeometry.IsImmersion.instOfIsClosedImmersion",
"CategoryTheory.Limits.pullback",
"CategoryTheory.MorphismProperty.IsLocalAtTarget.toRespects",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Lattice.toSemilatticeSup",
"CategoryTheory.PreZeroHyp... | true |
CategoryTheory.Limits.hasZeroMorphismsOpposite._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms | [
"CategoryTheory.Limits.HasZeroMorphisms",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"Quiver.Hom.unop",
"CategoryTheory.Limits.HasZeroMorphisms.zero_comp",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"congr_arg",
"Opposite.op",
"C... | false |
String.Slice.Pattern.ToForwardSearcher.defaultImplementation | Init.Data.String.Pattern.Basic | [
"String.Slice.Pattern.ToForwardSearcher",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher",
"String.Slice.Pattern.ForwardPattern",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher.iter",
"String.Slice.Pattern.ToForwardSearcher.mk"
] | true |
Monotone.monotone_iterate_of_le_map | Mathlib.Order.Iterate | [
"Eq.mpr",
"congrArg",
"Monotone",
"Preorder.toLE",
"Monotone.iterate",
"id",
"instOfNatNat",
"LE.le",
"Nat.iterate",
"instHAdd",
"HAdd.hAdd",
"Nat.instPreorder",
"Nat",
"Function.iterate_succ_apply",
"instAddNat",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"Preorder",
"monotone_nat_of_le... | true |
Derivation.compAEval_apply | Mathlib.Algebra.Polynomial.Derivation | [
"Derivation",
"Module.AEval.of",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"Polynomial.mkDerivationEquiv._proof_1",
"Polynomial.algebraOfAlgebra",
"Module.AEval",
"Algebra",
"Algebra.toSMul",
"AddZe... | true |
singleton_mul_ball | Mathlib.Analysis.Normed.Group.Pointwise | [
"Real",
"instHDiv",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"SeminormedCommGroup.toPseudoMetricSpace",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Set.instSingletonSet",
"MulOne.toMul",
"HDiv.hDiv",
... | true |
Std.HashMap.getKey?_filterMap | Std.Data.HashMap.Lemmas | [
"Option.pfilter",
"GetElem?.toGetElem",
"Std.HashMap.mem_of_getKey?_eq_some",
"Option.some",
"Membership.mem",
"Std.DHashMap.Const.getKey?_filterMap",
"Std.HashMap",
"LawfulHashable",
"GetElem.getElem",
"EquivBEq",
"Std.HashMap.filterMap",
"Std.HashMap.getKey?",
"Hashable",
"Std.HashMap.in... | true |
T5Space.toT1Space | Mathlib.Topology.Separation.Regular | [
"TopologicalSpace",
"T5Space",
"T1Space"
] | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.assoc_induction.match_1_1 | Std.Data.Internal.List.Associative | [
"Unit.unit",
"List.cons",
"List",
"Unit",
"List.casesOn",
"Sigma.mk",
"Sigma.casesOn",
"Sigma",
"List.nil"
] | false |
Lean.Parser.Tactic.MRefinePat.brecOn.eq | Std.Tactic.Do.Syntax | [
"Lean.TSyntax",
"Lean.Parser.Tactic.MRefinePat.hole",
"Lean.Parser.Tactic.MRefinePat.below_1",
"Lean.Parser.Tactic.MRefinePat.casesOn",
"Lean.Parser.Tactic.MRefinePat.brecOn.go",
"List.cons",
"Lean.Parser.Tactic.MRefinePat.tuple",
"List",
"Lean.Parser.Tactic.MRefinePat",
"Lean.Parser.Tactic.MRefin... | true |
CategoryTheory.CartesianMonoidalCategory.prodComparisonIso_comp | Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CartesianMonoidalCategory.comp_lift",
"CategoryTheory.Functor.comp",
"CategoryTheory.SemiCartesianMonoidalCategory.snd",
"CategoryTheory.Iso",
"Cate... | true |
Filter.inv_pure | Mathlib.Order.Filter.Pointwise | [
"Pure.pure",
"Inv",
"Filter.instPure",
"Inv.inv",
"Filter.instInv",
"Eq",
"Filter",
"rfl"
] | true |
Std.DHashMap.Internal.Raw₀.Const.foldM_eq_foldlM_toArray | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.Const.toList",
"List.foldlM",
"congrArg",
"Std.DHashMap.Internal.Raw₀.Const.foldM_eq_foldlM_toList",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.Const.toArray",
"LawfulMonad",
"instOfNatNat",
"Prod.fst",
"List.toArray",
"_private.Std.Data.DHashMap.Internal.RawLemmas.0.Std.DHashMap.In... | true |
Function.HasFiniteSupport.sumMk | Mathlib.Algebra.FiniteSupport.Basic | [
"Set.Finite.union",
"Eq.mpr",
"congrArg",
"Function.HasFiniteSupport",
"Set.Finite",
"Set.instUnion",
"id",
"Prod.mk",
"Function.support_prodMk",
"Prod.instZero",
"Function.support",
"Union.union",
"Prod",
"Eq",
"Zero",
"Set"
] | true |
IsDedekindDomain.HeightOneSpectrum.count_normalizedFactors_eq_multiplicity | Mathlib.RingTheory.DedekindDomain.Factorization | [
"UniqueFactorizationMonoid.normalizedFactors",
"Eq.mpr",
"NormalizationMonoid.ofUniqueUnits",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"CommRing.toNonUnitalCommRing",
"ENat.instNatCast",
"congrArg",
"CommS... | true |
AddSubmonoid.mul_subset_mul | Mathlib.Algebra.Ring.Submonoid.Pointwise | [
"HMul.hMul",
"instDistribSMul",
"AddSubmonoid.mul",
"AddMonoid.toAddZeroClass",
"AddSubmonoid",
"HasSubset.Subset",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"SetLike.coe",
"Distrib.toMul",
"AddSubmonoid.smul_subset_smul",
"NonUnitalNonAssocSemiring.toDistrib",
"AddCommMonoid.toAddMonoid",
... | true |
List.getElem_cons_drop | Init.GetElem | [
"List.brecOn",
"List.getElem_cons_drop._f",
"instOfNatNat",
"List.cons",
"GetElem.getElem",
"List",
"instHAdd",
"List.drop",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"List.instGetElemNatLtLength",
"OfNat.ofNat",
"Eq",
"List.length"
] | true |
List.findSomeRev?_eq_findSome?_reverse | Init.Data.List.Impl | [
"congrArg",
"List.findSomeRev?TR",
"List",
"List.findSome?",
"congrFun",
"True",
"eq_self",
"List.reverse",
"of_eq_true",
"congrFun'",
"List.findSomeRev?",
"Eq",
"Eq.trans",
"Option",
"List.findSomeRev?_eq_findSomeRev?TR"
] | true |
TopologicalSpace.IrreducibleCloseds.map._proof_2 | Mathlib.Topology.Sets.Closeds | [
"TopologicalSpace.IrreducibleCloseds",
"IsClosed",
"TopologicalSpace",
"SetLike.coe",
"closure",
"Set.image",
"isClosed_closure",
"TopologicalSpace.IrreducibleCloseds.instSetLike"
] | false |
CategoryTheory.Functor.LeftLinear.casesOn | Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | [
"CategoryTheory.Functor.OplaxLeftLinear",
"CategoryTheory.Functor.LaxLeftLinear.μₗ",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj",
"CategoryTheory.CategoryStruct... | false |
Lean.Parser.Term.structInstField.parenthesizer | Lean.Parser.Term.Basic | [
"Lean.Parser.optional.parenthesizer",
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.Term.optTypeForStructInst.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.Parser.many.parenthesizer",
"Lean.Parser.ppDedent.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.checkColGt.parenthesizer",... | true |
Aesop.SafeRulesResult.proved.injEq | Aesop.Search.Expansion | [
"Eq.propIntro",
"Aesop.RappRef",
"Aesop.SafeRulesResult.proved",
"Aesop.SafeRulesResult.proved.inj",
"Array",
"Eq.ndrec",
"Eq.refl",
"Aesop.SafeRulesResult",
"Eq"
] | true |
ModuleCat.MonModuleEquivalenceAlgebra.MonObj.toRing._proof_17 | Mathlib.CategoryTheory.Monoidal.Internal.Module | [
"CommRing",
"SubNegMonoid.sub_eq_add_neg",
"AddMonoid.toAddSemigroup",
"ModuleCat",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"inferInstance",
"AddCommGroup",
"SubNegMonoid.toSub",
"instHAdd",
"AddSemigroup.toAdd",
"ModuleCat.isAddCommGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"HAdd.hA... | false |
CategoryTheory.ProjectiveResolution.Hom.noConfusion | Mathlib.CategoryTheory.Preadditive.Projective.Resolution | [
"CategoryTheory.ProjectiveResolution.π",
"CategoryTheory.Limits.HasZeroMorphisms",
"ChainComplex",
"HomologicalComplex.instCategory",
"CategoryTheory.ProjectiveResolution.Hom",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"AddRigh... | false |
CompleteDistribLattice.MinimalAxioms | Mathlib.Order.CompleteBooleanAlgebra | [
"CompleteDistribLattice.MinimalAxioms.mk"
] | true |
Aesop.RuleTacDescr.cases.injEq | Aesop.RuleTac.Descr | [
"Eq.propIntro",
"Lean.injEq_helper",
"Aesop.RuleTacDescr",
"Lean.Meta.TransparencyMode",
"Array",
"And",
"Bool",
"Eq.ndrec",
"Aesop.RuleTacDescr.cases",
"Eq.refl",
"Aesop.CasesTarget",
"Eq",
"Aesop.CtorNames",
"Aesop.RuleTacDescr.cases.inj"
] | true |
Real.sinh_artanh | Mathlib.Analysis.SpecialFunctions.Artanh | [
"one_pow",
"Eq.mpr",
"MulOne.toOne",
"Real.partialOrder",
"Real",
"instHDiv",
"HMul.hMul",
"MulZeroClass.toMul",
"Real.instZero",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"Real.instDivInvMonoid",
"Real.instSub",
"HSub.hSub",
"Real.i... | true |
MeasureTheory.IsSetSemiring.isSetRing_supClosure | Mathlib.MeasureTheory.SetSemiring | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Finset.sup_insert",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"BooleanAlgebra.toGeneralizedBooleanAlgebra",
"Membership.mem",
"Exists",
"Set.sup_eq_union",
"CompleteLattice.toConditionallyCompleteL... | true |
Std.DHashMap.Raw.Const.getD_modify_self | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.Const.modify",
"Std.DHashMap.Internal.Raw₀.Const.get?",
"congrArg",
"Std.DHashMap.Raw",
"Option.getD",
"id",
"Std.DHashMap.Internal.Raw₀.Const.getD",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"LawfulHashable",
"Subtyp... | true |
CategoryTheory.MonoOver.congr | Mathlib.CategoryTheory.Subobject.MonoOver | [
"CategoryTheory.Over",
"CategoryTheory.MonoOver.congr._proof_7",
"CategoryTheory.Functor",
"CategoryTheory.Equivalence.unitIso",
"CategoryTheory.MonoOver.congr._proof_2",
"CategoryTheory.MonoOver.congr._proof_13",
"CategoryTheory.Functor.category",
"CategoryTheory.MonoOver.congr._proof_1",
"Category... | true |
PresentedGroup.closure_rels_subset_ker | Mathlib.GroupTheory.PresentedGroup | [
"Iff.mpr",
"MulOne.toOne",
"MonoidHom.instFunLike",
"InvOneClass.toOne",
"Equiv.instEquivLike",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"Subgroup.normalClosure",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Group.toDivisionMonoid",
"Membership.mem",
... | true |
_private.Lean.Data.Json.Printer.0.Lean.Json.CompressWorkItemKind.ctorElimType | Lean.Data.Json.Printer | [
"cond",
"_private.Lean.Data.Json.Printer.0.Lean.Json.CompressWorkItemKind.arrayEnd",
"Nat.ble",
"_private.Lean.Data.Json.Printer.0.Lean.Json.CompressWorkItemKind.objectEnd",
"PULift",
"_private.Lean.Data.Json.Printer.0.Lean.Json.CompressWorkItemKind.objectField",
"_private.Lean.Data.Json.Printer.0.Lean.... | false |
_private.Mathlib.LinearAlgebra.Projection.0.LinearMap.ker_id_sub_eq_of_proj._simp_1_1 | Mathlib.LinearAlgebra.Projection | [
"Submodule",
"AddMonoid.toAddZeroClass",
"LinearMap.ker",
"LinearMap.instFunLike",
"RingHom",
"Membership.mem",
"AddZeroClass.toAddZero",
"LinearMap",
"AddCommMonoid",
"LinearMap.mem_ker",
"AddZero.toZero",
"Submodule.setLike",
"propext",
"Semiring",
"Zero.toOfNat0",
"AddCommMonoid.toA... | false |
ULift.group.eq_1 | Mathlib.Algebra.Group.ULift | [
"ULift.group._proof_2",
"Function.Injective.group",
"MulOne.toOne",
"ULift.inv",
"DivInvMonoid.toInv",
"Equiv.instEquivLike",
"Monoid.toMulOneClass",
"ULift.commSemigroup._proof_1",
"ULift",
"DivInvMonoid.toZPow",
"Group",
"Equiv.ulift",
"ULift.group._proof_4",
"Equiv",
"MulOne.toMul",
... | true |
_private.Mathlib.Topology.EMetricSpace.BoundedVariation.0.eVariationOn.add_point._proof_1_5 | Mathlib.Topology.EMetricSpace.BoundedVariation | [
"instLawfulOrderLT_mathlib",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"Monotone.eq_1",
"Preorder.toLT",
"instConditionallyCompleteLinearOrder",
"of_decide_eq_true",
"Lean.Grind.nestedProof",
"Lean.Grind.CommRing.Expr.var",
"congrArg",
... | false |
OrderHom.curry | Mathlib.Order.Hom.Basic | [
"RelIso.mk",
"OrderHom.curry._proof_3",
"Preorder.toLE",
"Equiv.mk",
"OrderHom.instPreorder",
"OrderIso",
"LE.le",
"Function.curry",
"OrderHom.instFunLike",
"OrderHom.curry._proof_6",
"OrderHom.curry._proof_4",
"OrderHom.curry._proof_5",
"Prod.instPreorder",
"OrderHom.mk",
"Function.uncu... | true |
Lean.Meta.Simp.State.diag | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.Simp.State",
"Lean.Meta.Simp.Diagnostics"
] | true |
CStarModule.norm_pos | Mathlib.Analysis.CStarAlgebra.Module.Defs | [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"Eq.mpr",
"NonUnitalNormedRing.toNorm",
"Real",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"Inner.inner",
"Real.instZero",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"SMul",
"NormedSpace.toModule",
"Complex.instNormedField",
"Real.instLT",
... | true |
endVecRingEquivMatrixEnd._proof_3 | Mathlib.LinearAlgebra.Matrix.ToLin | [
"Pi.addCommMonoid",
"Finset.univ",
"AddMonoid.toAddSemigroup",
"congrArg",
"Matrix",
"Finset.sum_add_distrib",
"Finset",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Membership.mem",
"AddZeroClass.toAddZero",
"map_add",
"LinearMap.semilinearMapClass",
"AddCommMonoid",
"funext",
... | false |
RingHom.prodMap | Mathlib.Algebra.Ring.Prod | [
"RingHom",
"RingHom.snd",
"RingHom.comp",
"NonAssocSemiring",
"Prod.instNonAssocSemiring",
"RingHom.fst",
"Prod",
"RingHom.prod"
] | true |
natCast_zsmul._f | Mathlib.Algebra.Group.Defs | [
"SubNegMonoid.zsmul_succ'",
"instHSMul",
"Trans.trans",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"SubNegMonoid",
"AddZeroClass.toAddZero",
"instOfNatNat",
"Int",
"Nat.cast",
"zero_zsmul",
"Nat.below",
"instTransEq",
"AddZero.toZero",
"instHAdd",
"Unit",
"zero_ns... | false |
ContinuousLinearMap.inverse_of_not_isInvertible | Mathlib.Topology.Algebra.Module.Equiv | [
"ContinuousLinearEquiv.symm",
"ContinuousLinearMap.IsInvertible",
"Classical.propDecidable",
"ContinuousLinearMap.zero",
"dif_neg",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"ContinuousLinearEquiv",
"RingHomInvPair.ids",
"Semiring",
"Classical.choose",
"Zero.toOfNat0",
"C... | true |
SummationFilter.mk.noConfusion | Mathlib.Topology.Algebra.InfiniteSum.SummationFilter | [
"SummationFilter.mk",
"Finset",
"SummationFilter",
"id",
"heq_of_eq",
"Eq.refl",
"HEq",
"SummationFilter.noConfusion",
"Eq",
"Filter"
] | false |
HomotopicalAlgebra.FibrantBrownFactorization.mk.noConfusion | Mathlib.AlgebraicTopology.ModelCategory.BrownLemma | [
"CategoryTheory.MorphismProperty.MapFactorizationData.Z",
"HomotopicalAlgebra.fibrations",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.CategoryStruct.id",
"HomotopicalAlgebra.ModelCategory.categoryWithFibrations",
"HomotopicalAlgebra.FibrantBrownFactorization.i_... | false |
groupHomology.lsingle_comp_chainsMap_f_assoc | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"CategoryTheory.Category.assoc",
"Rep.V",
"CommRing",
"MonoidHom.instFunLike",
"Finsupp.module",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Ad... | true |
MeasureTheory.measure_iInter_of_ae_antitone | Mathlib.MeasureTheory.Measure.MeasureSpace | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"iInf",
"Set.iInter",
"Filter.Eventually",
"PartialOrder.toPreorder",
"Monotone",
"setOf",
"MeasureTheory.NullMeasurableSet",
"OrderDual.instIsCountablyGeneratedAtBot",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Filter.mp_mem",
"id",
"Ne"... | true |
Int.gcd_mul_right_add_right | Init.Data.Int.Gcd | [
"Int.gcd",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"id",
"Int",
"Int.add_comm",
"Int.instMul",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Int.instAdd",
"Eq.refl",
"Int.gcd_add_mul_right_right",
"Eq",
"instHMul"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.minKey_modify._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
Lean.Meta.EqnsExtState.recOn | Lean.Meta.Eqns | [
"Lean.Meta.EqnsExtState.mk",
"Lean.PHashMap",
"Lean.Meta.EqnsExtState",
"Lean.Meta.EqnsExtState.rec",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.instHashableName"
] | false |
Irrational.intCast_sub | Mathlib.NumberTheory.Real.Irrational | [
"Int.cast",
"Irrational.ratCast_sub",
"Rat.cast_intCast",
"Real",
"congrArg",
"Real.instSub",
"Real.instRatCast",
"Rat",
"HSub.hSub",
"Eq.mp",
"Rat.instIntCast",
"Rat.cast",
"DivisionRing.toRing",
"Int",
"AddGroupWithOne.toIntCast",
"instHSub",
"Irrational",
"Real.instDivisionRing"... | true |
Complex.cos_surjective | Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"exists_quadratic_eq_zero",
"Iff.mpr",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Complex.log",
"False",
"Na... | true |
Subgroup.subgroupOf_map_subtype | Mathlib.Algebra.Group.Subgroup.Map | [
"Subgroup.subgroupOf",
"Subgroup.map",
"Monoid.toMulOneClass",
"Subgroup.subtype",
"Subtype.image_preimage_coe",
"Submonoid.toSubsemigroup",
"Group",
"Membership.mem",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"Set.instInter",
"SetLike.ext'",
"Inter.inter",
"Group.toDivInvMonoid",
... | true |
CategoryTheory.Limits.ImageMap.casesOn | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Limits.ImageMap.rec",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"CategoryTheory.Limits.image.ι",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.hom",
"CategoryTheory.Limits.ImageMap",
"CategoryTheory.Limits.image",
"CategoryTheory... | false |
_private.Mathlib.Algebra.Group.ModEq.0.AddCommGroup.modEq_nsmul_cases._simp_1_1 | Mathlib.Algebra.Group.ModEq | [
"AddCommGroup.ModEq",
"AddCommGroup.toAddCommMonoid",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"SubNegMonoid.toSub",
"instHAdd",
"instHSub",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"propext",
"AddCommSemigroup.toAddCommMagma",
"AddCommGroup.sub_modEq_iff_modEq_add",
"Eq.symm... | false |
_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation.0.Real.rpow_eq_const_mul_integral_rpowIntegrand₁₂._proof_1_1 | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
_private.Mathlib.Algebra.BigOperators.Intervals.0.Finset.prod_Icc_div._proof_1_1 | Mathlib.Algebra.BigOperators.Intervals | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Nat.instOne",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Ome... | false |
_private.Init.Data.Fin.Fold.0.Fin.foldlM.loop | Init.Data.Fin.Fold | [
"_private.Init.Data.Fin.Fold.0.Fin.foldlM.loop._unary",
"Nat",
"PSigma.mk",
"Monad",
"Fin"
] | true |
Computability.Γ'.bit.injEq | Mathlib.Computability.Encoding | [
"Computability.Γ'.bit.inj",
"Eq.propIntro",
"Computability.Γ'.bit",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Computability.Γ'"
] | true |
CategoryTheory.ShortComplex.Hom.id_τ₂ | Mathlib.Algebra.Homology.ShortComplex.Basic | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.ShortComplex.Hom.τ₂",
"CategoryTheory.ShortComplex.Hom.id",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"E... | true |
Monotone.csInf_image_le | Mathlib.Order.ConditionallyCompleteLattice.Basic | [
"PartialOrder.toPreorder",
"Monotone",
"ConditionallyCompleteLattice",
"Preorder.toLE",
"Membership.mem",
"Monotone.le_csSup_image",
"LE.le",
"OrderDual.instConditionallyCompleteLattice",
"BddBelow",
"Set.image",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"ConditionallyCompleteLatt... | true |
Lean.Macro.Context.rec | Init.Prelude | [
"Lean.Syntax",
"Lean.Macro.Context",
"Lean.Macro.MethodsRef",
"Nat",
"Lean.MacroScope",
"Lean.Name",
"Lean.Macro.Context.mk"
] | false |
Std.Slice.Internal.ByteSliceData._sizeOf_inst | Std.Data.ByteSlice | [
"SizeOf.mk",
"Std.Slice.Internal.ByteSliceData._sizeOf_1",
"Std.Slice.Internal.ByteSliceData",
"SizeOf"
] | false |
TopCat.GlueData.ofOpenSubsets_toGlueData_t | Mathlib.Topology.Gluing | [
"CategoryTheory.GlueData.t",
"TopCat.GlueData.ofOpenSubsets._proof_3",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"TopCat.instCategory",
"ContinuousMap.mk",
"TopCat.GlueData.ofOpenSubsets._proof_4",
"PartialOrder.toPreorder",
"TopologicalSpac... | true |
multilinearCurryRightEquiv._proof_1 | Mathlib.LinearAlgebra.Multilinear.Curry | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LinearMap.instSMulCommClass",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"LinearMap.instSMul",
"CommMonoid.toMonoid",
"Nat",
"Fin.last",
"CommSemiring.toCommMonoid",
"Semiring.toMonoid",
"Module.toDistri... | false |
_private.Mathlib.Order.Filter.AtTopBot.Archimedean.0.Filter.Tendsto.atBot_mul_const_of_neg'._simp_1_1 | Mathlib.Order.Filter.AtTopBot.Archimedean | [
"NegZeroClass.toNeg",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"PartialOrder",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Filter.atTop",
"Filter.tendsto_neg_atBot_iff",
"Filter.Tendsto... | false |
Prod.fst_sSup | Mathlib.Order.CompleteLattice.Basic | [
"SupSet",
"Prod.fst",
"Set.image",
"Prod.supSet",
"Prod",
"Eq",
"SupSet.sSup",
"rfl",
"Set"
] | true |
Representation.invtSubmodule.top_mem | Mathlib.RepresentationTheory.Submodule | [
"Sublattice",
"Monoid",
"Representation.invtSubmodule",
"Submodule",
"Representation",
"iInf",
"MonoidHom.instFunLike",
"Sublattice.instInfSet",
"Module.End.invtSubmodule.top_mem._simp_1",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Sublattice.mem_iInf._simp_1",
"Submodule.completeLa... | true |
_private.Init.Data.Int.Linear.0.Int.Linear.Poly.coeff.match_1.eq_1 | Init.Data.Int.Linear | [
"Int.Linear.Poly.coeff.match_1",
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.num",
"Int.Linear.Poly.add",
"Eq.refl",
"Eq",
"Int.Linear.Poly"
] | true |
_private.Mathlib.RingTheory.Polynomial.ScaleRoots.0.Polynomial.mul_scaleRoots._simp_1_2 | Mathlib.RingTheory.Polynomial.ScaleRoots | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
max_apply_eq_max | Init.Data.Order.MinMaxOn | [
"Eq.mpr",
"congrArg",
"Max",
"maxOn",
"id",
"LE.le",
"LE",
"maxOn_eq_max",
"DecidableLE",
"Iff",
"Max.max",
"max_apply",
"Std.LawfulOrderLeftLeaningMax",
"Eq.refl",
"Eq"
] | true |
codiscrete_eq_cofinite | Mathlib.Topology.DiscreteSubset | [
"IsCompact.codiscreteWithin_eq",
"congrArg",
"inf_of_le_left",
"le_top._simp_2",
"Filter.instCompleteLatticeFilter",
"Set.univ",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Filter.principal_univ",
"CompleteLattice.toConditionallyCompleteLattice",
"CoheytingAlg... | true |
Polynomial.adjSylvester_comp_sylveserMap | Mathlib.RingTheory.Polynomial.Resultant.Basic | [
"Prod.smulCommClass",
"LinearMap.id",
"Polynomial.degreeLT",
"Matrix.smul",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Polynomial.toMatrix_sylvesterMap'",
"Prod.distribSMul",
"Matrix.toLin",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toM... | true |
Equiv.instTrans | Mathlib.Logic.Equiv.Defs | [
"Equiv.trans",
"Equiv",
"Trans",
"Trans.mk"
] | true |
_private.Mathlib.Topology.MetricSpace.GromovHausdorff.0.GromovHausdorff.IsometryRel | Mathlib.Topology.MetricSpace.GromovHausdorff | [
"NormedCommRing.toNormedRing",
"TopologicalSpace.NonemptyCompacts.instSetLike",
"NormedCommRing.toSeminormedCommRing",
"Real",
"TopologicalSpace.NonemptyCompacts",
"PseudoMetricSpace.toUniformSpace",
"instAddCommGroupPreLp",
"instPseudoEMetricSpaceSubtype",
"AddCommGroup.toAddGroup",
"lp.inftyNorm... | true |
Lean.Server.Watchdog.LogMsg.deserialized.sizeOf_spec | Lean.Server.Watchdog | [
"Lean.JsonRpc.Message._sizeOf_inst",
"Lean.Server.Watchdog.LogMsg.deserialized",
"Lean.JsonRpc.MessageDirection._sizeOf_inst",
"instOfNatNat",
"Lean.JsonRpc.Message",
"instHAdd",
"HAdd.hAdd",
"Lean.Server.Watchdog.LogMsg._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"Lean.Server.Watchdog.LogMsg",
"in... | true |
Lean.Server.Ilean.ctorIdx | Lean.Server.References | [
"Nat",
"Lean.Server.Ilean"
] | false |
CategoryTheory.Localization.strictUniversalPropertyFixedTargetId_lift | Mathlib.CategoryTheory.Localization.Predicate | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CategoryTheory.Functor.id",
"CategoryTheory.MorphismProperty.isomorphisms",
"LE.le",
"CategoryTheory.MorphismProperty.IsInvertedBy",... | true |
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