name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.MonoidalClosed.pre | Mathlib.CategoryTheory.Monoidal.Closed.Basic | [
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.MonoidalCategory.tensoringLeft",
"Equiv",
"CategoryTheory.Functor.map",
"CategoryTheory.MonoidalCategory.te... | true |
SemidirectProduct.map | Mathlib.GroupTheory.SemidirectProduct | [
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"SemidirectProduct",
"OneHom.mk",
"MulAut.instGroup",
"SemidirectProduct.right",
"Group",
"SemidirectProduct.map._proof_1",
"MulAut",
"MulOne.toMul",
"MonoidHom.comp",
"DivInvMonoid.toMonoid",
"MonoidHom.mk",
... | true |
Std.IsLinearOrder.mk._flat_ctor | Init.Data.Order.Classes | [
"Std.IsPartialOrder.mk",
"LE.le",
"Std.IsLinearOrder",
"LE",
"Std.IsLinearOrder.mk",
"Or",
"Std.IsPreorder.mk",
"Eq"
] | false |
MultipliableLocallyUniformlyOn.multipliable | Mathlib.Topology.Algebra.InfiniteSum.UniformOn | [
"UniformSpace",
"Membership.mem",
"_private.Mathlib.Topology.Algebra.InfiniteSum.UniformOn.0.MultipliableLocallyUniformlyOn.multipliable.match_1_1",
"Multipliable",
"TopologicalSpace",
"HasProdLocallyUniformlyOn.hasProd",
"HasProdLocallyUniformlyOn",
"HasProd.multipliable",
"MultipliableLocallyUnifo... | true |
_private.Mathlib.Analysis.Convex.Combination.0.convexHull_sub._simp_1_1 | Mathlib.Analysis.Convex.Combination | [
"NegZeroClass.toNeg",
"ChainCompletePartialOrder.instOfCompleteLattice",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"PartialOrder",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"ClosureOperator.instFunLike",
"ClosureOperator",
"SubNegZeroMonoid.toNegZeroClass",
"Subtra... | false |
_private.Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace.0.Besicovitch.exists_goodδ._simp_1_9 | Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | [
"Finset.mem_image",
"Finset",
"Membership.mem",
"Exists",
"And",
"Finset.instSetLike",
"propext",
"Eq",
"Finset.image",
"SetLike.instMembership",
"DecidableEq"
] | false |
AdicCompletion.instAlgebra._proof_4 | Mathlib.RingTheory.AdicCompletion.Algebra | [
"Submodule",
"RingHom.instRingHomClass",
"MulOne.toOne",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"instHSMul",
"AdicCompletion.instAlgebra._proof_1",
"Semiring.toModule",
"instSMulOfMul",
"IsScalarTower.right",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMo... | false |
ModuleCat.MonModuleEquivalenceAlgebra.Algebra_of_Mon_._proof_2 | Mathlib.CategoryTheory.Monoidal.Internal.Module | [
"MulOne.toOne",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CommRing",
"RingHom.mk",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CommSemiring.toSemiring",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"AddCommGroup.toAddCommMonoid",
"OneH... | false |
Mathlib.Tactic.BicategoryLike.MkAtom₁.ctorIdx | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.MkAtom₁",
"Nat"
] | false |
Std.Tactic.BVDecide.BVExpr.decEq._proof_42 | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"False",
"congrArg",
"False.elim",
"Std.Tactic.BVDecide.BVExpr.ctorIdx",
"noConfusion_of_Nat",
"instHAdd",
"Std.Tactic.BVDecide.BVExpr.var",
"HAdd.hAdd",
"Nat",
"True",
"of_eq_true",
"instAddNat",
"Std.Tactic.BVDecide.BVExpr",
"Std.Tactic.BVDecide.BVExpr.append",
"not_false_eq_true",
"... | false |
IsMIntegralCurveOn.continuousWithinAt | Mathlib.Geometry.Manifold.IntegralCurve.Basic | [
"IsMIntegralCurveOn",
"Real",
"Semiring.toModule",
"ContinuousWithinAt",
"extChartAt",
"chartedSpaceSelf",
"NormedSpace",
"Real.denselyNormedField",
"ContinuousLinearMap.smulRight",
"IsMIntegralCurveOn._proof_1",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupTangentSpace",
"PseudoMetricSp... | true |
_private.Mathlib.Order.Filter.Map.0.Set.LeftInvOn.filter_map_Iic._simp_1_1 | Mathlib.Order.Filter.Map | [
"Filter.EventuallyEq",
"Filter.eventuallyEq_principal",
"Set.EqOn",
"propext",
"Filter.principal",
"Eq",
"Set"
] | false |
Representation.LinearizeMonoidal.μ_apply_apply | Mathlib.RepresentationTheory.Action | [
"Finsupp.instFunLike",
"Monoid",
"Semiring.toModule",
"Finsupp.module",
"HMul.hMul",
"CategoryTheory.typesCartesianMonoidalCategory",
"congrArg",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"finsuppTensorFinsupp'_apply_apply",
"Representation.IntertwiningMap.instFunLike",
"Repres... | true |
LowerHemicontinuous.lowerHemicontinuousWithinAt | Mathlib.Topology.Semicontinuity.Defs | [
"LowerHemicontinuousWithinAt",
"Set.instInter",
"Inter.inter",
"SemicontinuousAt.semicontinuousWithinAt",
"TopologicalSpace",
"And",
"Set.Nonempty",
"IsOpen",
"LowerHemicontinuous",
"Set"
] | true |
_private.Mathlib.MeasureTheory.Covering.Besicovitch.0.Besicovitch.exist_disjoint_covering_families._simp_1_17 | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Exists",
"exists_eq_left",
"And",
"propext",
"Eq"
] | false |
ultrafilter_isOpen_basic | Mathlib.Topology.Compactification.StoneCech | [
"TopologicalSpace.IsTopologicalBasis.isOpen",
"setOf",
"Membership.mem",
"ultrafilterBasis_is_basis",
"ultrafilterBasis",
"Ultrafilter.topologicalSpace",
"Exists.intro",
"IsOpen",
"Ultrafilter.instMembershipSet",
"Ultrafilter",
"Eq",
"rfl",
"Set"
] | true |
Std.ExtDHashMap.contains_insert | Std.Data.ExtDHashMap.Lemmas | [
"Std.DHashMap.contains_insert",
"Std.ExtDHashMap.contains",
"Std.ExtDHashMap.inductionOn",
"LawfulHashable",
"Std.ExtDHashMap.insert",
"BEq.beq",
"EquivBEq",
"Std.ExtDHashMap",
"Bool",
"Bool.or",
"Hashable",
"BEq",
"Eq",
"Std.DHashMap"
] | true |
HasDerivAt.cexp | Mathlib.Analysis.SpecialFunctions.ExpDeriv | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"Complex.instNormedField",
"HasDerivAt",
"PseudoMetricSpace.toUniformSpace",
"Complex.instZero"... | true |
CategoryTheory.SimplicialObject.Homotopy.precomp._proof_3 | Mathlib.AlgebraicTopology.SimplicialObject.Homotopy | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.SimplicialObject.Homotopy.h_succ_comp_δ_castSucc_of_lt",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Fin.succ",
"congrArg",
"CategoryTheory.Functor.category",
"id",
"CategoryTheory.SimplicialObject.Homotopy.h",
... | false |
CategoryTheory.CostructuredArrow.w_prod_snd_assoc | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Comma.left",
"CategoryTheory.CostructuredArrow.hom",
"Eq.mp",
"id",
"CategoryTheory.CostructuredArrow",
"CategoryTheory.CostructuredArrow.w_prod_snd",
... | true |
Aesop.Frontend.DBuilderName.instToString.match_1 | Aesop.Frontend.RuleExpr | [
"Unit.unit",
"Aesop.Frontend.DBuilderName.default",
"Aesop.BuilderName",
"Aesop.Frontend.DBuilderName",
"Aesop.Frontend.DBuilderName.regular",
"Unit",
"Aesop.Frontend.DBuilderName.casesOn"
] | false |
Set.restrict_dite | Mathlib.Data.Set.Restrict | [
"Decidable",
"Membership.mem",
"Set.Elem",
"dif_pos",
"dite",
"funext",
"Set.restrict",
"Subtype.val",
"Eq",
"Set.instMembership",
"Not",
"Subtype.property",
"Set"
] | true |
instModuleTensorProductMop | Mathlib.Algebra.Azumaya.Defs | [
"Semiring.toModule",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"TensorProduct.Algebra.module",
"MulOpposite.instAlgebra",
"MulOpposite",
"MulOpposite.instModule",
"Algebra",
"Algebra.toModule",
"instModuleTensorProductMop._proof_1",
"MulOpposite.instAddCommMonoid",
"CommSemiring",
"N... | true |
IsPrimitiveRoot.toInteger_cube_eq_one | Mathlib.NumberTheory.NumberField.Cyclotomic.Three | [
"IsPrimitiveRoot.toInteger_isPrimitiveRoot",
"NumberField.instCommRingRingOfIntegers",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"instOfNatNat",
"Field.toCommRing",
"Monoid.toPow",
"AddMonoidWithOne.toOne",
"CommRing.toCommSemiring",
"HPow.hPow",
"Nat.instNeZeroSucc",
"I... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Coloring.VertexColoring.0.SimpleGraph.instNontrivialColoringOfNonempty._proof_10 | Mathlib.Combinatorics.SimpleGraph.Coloring.VertexColoring | [
"False",
"Equiv.instEquivLike",
"eq_false",
"RelHom.instFunLike",
"congrArg",
"SimpleGraph.Adj",
"RelHom",
"Classical.byContradiction",
"Equiv.swap",
"Classical.propDecidable",
"Eq.mp",
"SimpleGraph.completeGraph",
"id",
"Equiv",
"Equiv.swap_apply_def",
"Ne",
"ite_cond_eq_true",
"S... | false |
Metric.eball_ofReal | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"Set.ext",
"Eq.mpr",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Real",
"Preorder.toLT",
"ENNReal.ofReal",
"congrArg",
"ENNReal.ofReal_lt_ofReal_iff_of_nonneg",
"PartialOrder.toPreorder",
"dist_nonneg",
"Real.instLT",
"Membership.mem",
"id",
"Metric.ball",
"Metric.eball",
"_private... | true |
AddUnits.ofNSMul.eq_1 | Mathlib.Algebra.Group.Commute.Units | [
"AddUnits.leftOfAdd",
"AddUnits.val",
"instHSMul",
"HSub.hSub",
"AddMonoid.toNSMul",
"AddUnits.ofNSMul",
"AddUnits.ofNSMul._proof_2",
"instSubNat",
"Ne",
"instOfNatNat",
"AddUnits.ofNSMul._proof_1",
"instHSub",
"Nat",
"AddMonoid",
"Eq.refl",
"HSMul.hSMul",
"OfNat.ofNat",
"Eq",
"A... | true |
Asymptotics.IsEquivalent.congr_right | Mathlib.Analysis.Asymptotics.AsymptoticEquivalent | [
"Asymptotics.IsEquivalent.congr_left",
"Filter.EventuallyEq",
"Asymptotics.IsEquivalent",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Filter",
"NormedAddCommGroup",
"Asymptotics.IsEquivalent.symm"
] | true |
_private.Lean.Environment.0.Lean.AsyncConst._sizeOf_inst | Lean.Environment | [
"_private.Lean.Environment.0.Lean.AsyncConst",
"_private.Lean.Environment.0.Lean.AsyncConst._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
_private.Mathlib.LinearAlgebra.FreeModule.ModN.0.ModN.basis._simp_3 | Mathlib.LinearAlgebra.FreeModule.ModN | [
"False",
"eq_false",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"NeZero.ne",
"Zero"
] | false |
SetRel.rightDual_leftDual_le_of_le | Mathlib.Order.Rel.GaloisConnection | [
"GaloisConnection.monotone_u",
"OrderDual.toDual",
"Eq.mpr",
"Equiv.instEquivLike",
"SetRel",
"OrderDual.ofDual",
"congrArg",
"PartialOrder.toPreorder",
"Function.comp",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"id",
"Equiv",
"Prod.mk",
"BiheytingAlgebra.toCoheytingAlgebra",
... | true |
AlgebraicGeometry.Surjective.instSndScheme | Mathlib.AlgebraicGeometry.PullbackCarrier | [
"CategoryTheory.Limits.pullback",
"CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeAlongOfIsStableUnderBaseChange",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.pullback.snd",
"AlgebraicGeometry.Surjective.instIsStableUnderBaseChan... | true |
IntermediateField.Lifts.noConfusion | Mathlib.FieldTheory.Extension | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"IntermediateField",
"HEq.refl",
"AlgHom",
"IntermediateField.toField",
"Algebra",
"Membership.mem",
"Algebra.toModule",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Intermed... | false |
Int16.toInt64_div_of_ne_right | Init.Data.SInt.Lemmas | [
"Eq.mpr",
"instHDiv",
"Int16",
"Int64.toInt",
"congrArg",
"Int64.toInt_inj",
"Int16.instOfNat",
"id",
"HDiv.hDiv",
"Int64",
"Ne",
"Int",
"Int.tdiv",
"Int64.toInt_div_of_ne_right",
"instDivInt64",
"Int16.toInt_toInt64",
"Int16.instNeg",
"Iff.mp",
"Int16.toInt",
"Eq.refl",
"Int... | true |
Polynomial.X_sub_C_mul_removeFactor | Mathlib.FieldTheory.SplittingField.Construction | [
"Iff.mpr",
"Polynomial.mul_divByMonic_eq_iff_isRoot",
"Eq.mpr",
"Polynomial.C",
"Polynomial.eval",
"Semigroup.toMul",
"Dvd.dvd",
"Polynomial.eval_map",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"AdjoinRoot",
"MulZeroClass.toMul",
"congrArg",
"CommSemiring.toSemiring",
"Polynomial.IsRo... | true |
ReprTuple | Init.Data.Repr | [
"ReprTuple.mk"
] | true |
_private.Lean.Meta.CollectFVars.0.Lean.CollectFVars.State.addDependencies.go._sparseCasesOn_1 | Lean.Meta.CollectFVars | [
"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 |
InnerProductSpace.Core.normSq_eq_zero_of_eq_zero | Mathlib.Analysis.InnerProductSpace.Defs | [
"Real",
"AddMonoidHom.instAddMonoidHomClass",
"AddMonoid.toAddSemigroup",
"Inner.inner",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"NormedField.toField",
"AddZeroClass.toAddZero",
"map_zero",
"AddCommG... | true |
FGModuleCat.hom_comp | Mathlib.Algebra.Category.FGModuleCat.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"ModuleCat.isFG",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"LinearMap",
"LinearMap.comp",
"FGModuleCat.hom_hom_comp",
"ModuleCat.isAddCommGroup",
"ModuleCat.moduleCategory",
"Module... | true |
Order.Ideal.isPrime_iff_mem_or_compl_mem | Mathlib.Order.PrimeIdeal | [
"BooleanAlgebra",
"Compl.compl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"BooleanAlgebra.toCompl",
"SemilatticeInf.toPartialOrder",
"Order.Ideal.isPrime_of_mem_or_compl_mem",
"Order.Ideal.IsPrime",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
... | true |
_private.Init.Data.String.Decode.0.ByteArray.utf8DecodeChar?.assemble₂_eq_some_iff_utf8EncodeChar_eq.match_1_1 | Init.Data.String.Decode | [
"ByteArray.utf8DecodeChar?.parseFirstByte",
"Option.some",
"And.casesOn",
"And",
"And.intro",
"ByteArray.utf8DecodeChar?.assemble₂",
"ByteArray.utf8DecodeChar?.FirstByte",
"Char",
"ByteArray.utf8DecodeChar?.FirstByte.oneMore",
"UInt8",
"Eq",
"Option"
] | false |
Std.toList_roc_eq_toList_rcc_of_isSome_succ? | Init.Data.Range.Polymorphic.Lemmas | [
"Std.Rxc.Iterator",
"_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Roc.Internal.toList_eq_toList_iter",
"Std.PRange.UpwardEnumerable",
"Std.Rcc.Internal.iter",
"congrArg",
"Std.Roc.toList",
"_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Internal.iter_roc_eq_iter_rcc_of_isSome_succ?",
"Std.Rxc.... | true |
InformationTheory.klFun_eq_zero_iff | Mathlib.InformationTheory.KullbackLeibler.KLFun | [
"Iff.mpr",
"IsOrderedModule.toPosSMulMono",
"Real.partialOrder",
"Real.instLE",
"Real",
"Semiring.toModule",
"instSMulOfMul",
"HMul.hMul",
"Set.Ici",
"sub_self",
"Real.instZero",
"Real.instAddMonoid",
"IsStrictOrderedModule.toIsOrderedModule",
"Real.instZeroLEOneClass",
"congrArg",
"Di... | true |
_private.Init.Data.Array.Sort.Lemmas.0.List.mergeSort.match_1.eq_3 | Init.Data.Array.Sort.Lemmas | [
"_private.Init.Data.List.Sort.Basic.0.List.mergeSort.match_1",
"List.cons",
"List",
"Bool",
"Eq.refl",
"Eq",
"List.nil"
] | true |
Finsupp.mapRange_eq_zero._simp_1 | Mathlib.Data.Finsupp.Defs | [
"Finsupp.mapRange_eq_zero",
"propext",
"Zero.toOfNat0",
"Function.Injective",
"Finsupp.mapRange",
"Finsupp.instZero",
"OfNat.ofNat",
"Eq",
"Finsupp",
"Zero"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.find?_toList_eq_some_iff_getKey?_eq_some_and_get?_eq_some._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
Con.correspondence | Mathlib.GroupTheory.Congruence.Hom | [
"MulHom",
"Con.correspondence._proof_10",
"RelIso.mk",
"Con.correspondence._proof_6",
"Con.correspondence._proof_1",
"Mul",
"Con.correspondence._proof_4",
"Equiv.mk",
"Subtype",
"OrderIso",
"Con.mkMulHom._proof_1",
"Con.instLE",
"Con.mkMulHom",
"LE.le",
"Con.Quotient",
"Con.corresponde... | true |
_private.Mathlib.Data.List.Rotate.0.List.IsRotated.dropLast_tail._simp_1_3 | Mathlib.Data.List.Rotate | [
"List.getLast",
"Ne",
"List.dropLast",
"List.IsRotated",
"List.cons",
"List",
"List.IsRotated.cons_getLast_dropLast",
"True",
"eq_true",
"Eq",
"List.nil"
] | false |
_private.Init.Data.Range.Polymorphic.PRange.0.Std.instDecidableEqRoo.decEq._proof_2 | Init.Data.Range.Polymorphic.PRange | [
"False",
"Std.Roo.mk.noConfusion",
"eq_of_heq",
"HEq",
"Eq",
"Not",
"Std.Roo",
"Std.Roo.mk"
] | false |
_private.Batteries.Data.RBMap.WF.0.Batteries.RBNode.balLeft.match_1.splitter._sparseCasesOn_4 | Batteries.Data.RBMap.WF | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Batteries.RBColor.ctorIdx",
"Batteries.RBColor.rec",
"Nat.land",
"Batteries.RBColor.red",
"Batteries.RBColor",
"Nat",
"Bool",
"Eq.refl",
"Batteries.RBColor.black",
"OfNat.ofNat",
"Bool.false"
] | false |
_private.Mathlib.Algebra.Group.Nat.Even.0.Nat.succ_mod_two_eq_zero_iff._proof_1_1 | Mathlib.Algebra.Group.Nat.Even | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"of_eq_false",
"Lean.RArray.leaf",
"Int.instDiv",
"False",
"Int.Nonneg.toPoly",
"Int.Linear.le_coeff",
"instHDiv",
"Lean.Grind.not_not",
"Int.Nonneg.add",
"HMul.hMul",
... | false |
Finset.wellFoundedOn_bUnion._simp_1 | Mathlib.Order.WellFoundedSet | [
"Finset",
"Finset.wellFoundedOn_bUnion",
"Membership.mem",
"IsStrictOrder",
"Finset.instSetLike",
"propext",
"Eq",
"Set.iUnion",
"SetLike.instMembership",
"Set.WellFoundedOn",
"Set"
] | false |
CategoryTheory.Subobject.Classifier._sizeOf_inst | Mathlib.CategoryTheory.Subobject.Classifier.Defs | [
"CategoryTheory.Subobject.Classifier._sizeOf_1",
"SizeOf.mk",
"CategoryTheory.Subobject.Classifier",
"SizeOf",
"CategoryTheory.Category"
] | false |
Vector.toArray_scanlM | Batteries.Data.Vector.Lemmas | [
"Eq.mpr",
"Vector.scanlM._proof_5",
"Nat.zero_le",
"Lean.Grind.instIsPreorderNat",
"Vector",
"Array.empty_eq._simp_1",
"congrArg",
"Monad.toApplicative",
"Std.instReflLeOfIsPreorder",
"Std.le_refl._simp_1",
"Array.scanlM.loop",
"Array.scanlM._proof_3",
"Array.scanlM",
"LawfulMonad",
"ins... | true |
_private.Mathlib.Analysis.Matrix.Spectrum.0.Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary._simp_1_1 | Mathlib.Analysis.Matrix.Spectrum | [
"HMul.hMul",
"Matrix",
"Matrix.instHMulOfFintypeOfMulOfAddCommMonoid",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Fintype",
"Distrib.toMul",
"NonUnitalSemiring",
"NonUnitalNonAssocSemiring.toDistrib",
"Eq.symm",
"Matrix.mulVec",
"Eq",
"Matr... | false |
Std.HashSet.Raw.getD_insert | Std.Data.HashSet.RawLemmas | [
"Std.HashSet.Raw.getD",
"Unit.unit",
"instDecidableNot",
"Std.HashSet.Raw.insert",
"Std.HashSet.Raw.inner",
"Membership.mem",
"Std.HashSet.Raw.WF",
"instDecidableEqBool",
"LawfulHashable",
"Bool.true",
"And",
"BEq.beq",
"Unit",
"EquivBEq",
"Std.HashSet.Raw.WF.out",
"Std.HashSet.Raw.ins... | true |
CategoryTheory.simplicialToCosimplicialAugmented_map_right | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CosimplicialObject.instCategoryAugmented",
"CategoryTheory.CosimplicialObject",
"CategoryTheory.SimplicialObject.Augmented.rightOp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SimplicialObject.const",
"CategoryTheory.... | true |
IsFractionRing.semilinearEquivOfRingEquiv._proof_4 | Mathlib.RingTheory.Localization.FractionRing | [
"CommRing",
"CommSemiring.toSemiring",
"RingEquiv.instEquivLike",
"RingEquiv.instRingEquivClass",
"Distrib.toAdd",
"instDistribOfSemiring",
"CommRing.toCommSemiring",
"Distrib.toMul",
"RingEquiv",
"RingEquivClass.toRingHomClass",
"Semiring.toNonAssocSemiring",
"EquivLike.toFunLike",
"RingHom... | false |
Real.cos_antiperiodic | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.pi",
"HMul.hMul",
"Real.sin_pi",
"Real.instZero",
"Real.cos",
"congrArg",
"sub_zero",
"Real.instSub",
"HSub.hSub",
"Real.semiring",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"SubtractionMonoid.toSubNegZeroMonoid",
... | true |
Filter.IsCountablyGenerated.rec | Mathlib.Order.Filter.CountablyGenerated | [
"Filter.IsCountablyGenerated.mk",
"Exists",
"And",
"Filter.IsCountablyGenerated",
"Filter.generate",
"Set.Countable",
"Eq",
"Filter",
"Set"
] | false |
CategoryTheory.Limits.IsColimit.uniqueUpToIso._proof_1 | Mathlib.CategoryTheory.Limits.IsLimit | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.IsColimit.uniq_cocone_morphism",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.Limits.Cocone.category",
"CategoryTheory.Ca... | false |
CategoryTheory.GrothendieckTopology.plusCompIso_inv_eq_plusLift | Mathlib.CategoryTheory.Sites.CompatiblePlus | [
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"CategoryTheory.GrothendieckTopology.plusLift",
"CategoryTheory.Limits.PreservesLimit",
"Opposite",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Category... | true |
AddHom.le_map_tsub | Mathlib.Algebra.Order.Sub.Unbundled.Hom | [
"Eq.mpr",
"congrArg",
"AddHom",
"Monotone",
"HSub.hSub",
"Preorder.toLE",
"id",
"OrderedSub",
"LE.le",
"AddHom.funLike",
"tsub_le_iff_right",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"propext",
"le_tsub_add",
"Eq.symm",
"Eq",
"DFunLike.coe",
"Add",
"Preorder",
"Sub",
"AddHom.... | true |
Int.sub_modulus_modEq_iff | Mathlib.Data.Int.ModEq | [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddZeroClass.toAddZero",
"id",
"Int",
"SubNegMonoid.toSub",
"instHAdd",
"Iff",
"instHSub",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"Int.ModEq",
"propext",
"Int.instAdd",
"Int.instAddGroup",
"AddZero.toAdd"... | true |
_private.Mathlib.Data.Set.Image.0.Set.forall_subtype_range_iff._proof_1_1 | Mathlib.Data.Set.Image | [
"Lean.Grind.of_eq_eq_true",
"Set.mem_range_self",
"Lean.Grind.eq_false_of_not_eq_true",
"False",
"Set.mem_range",
"Lean.Grind.not_not",
"Lean.Grind.nestedProof",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"HEq.refl",
"Classical.byContradiction",
"Subtype.casesOn",
"Membership.mem",
"Ex... | false |
tsum_ite_eq | Mathlib.Topology.Algebra.InfiniteSum.Basic | [
"Eq.mpr",
"eq_false",
"congrArg",
"AddMonoid.toAddZeroClass",
"SummationFilter",
"AddZeroClass.toAddZero",
"id",
"Ne",
"ite_cond_eq_true",
"AddCommMonoid",
"TopologicalSpace",
"AddZero.toZero",
"tsum",
"DecidablePred",
"True",
"tsum_eq_single",
"eq_self",
"of_eq_true",
"Summation... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.size_filterMap_eq_size_iff._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.Elab.Tactic.Do.SpecAttr.SpecTheorem.prog | Lean.Elab.Tactic.Do.Attr | [
"Lean.Elab.Tactic.Do.SpecAttr.SpecTheorem",
"Lean.Expr"
] | true |
Algebra.TensorProduct.piScalarRight_tmul_apply | Mathlib.RingTheory.TensorProduct.Pi | [
"Pi.Function.module",
"instHSMul",
"Semiring.toModule",
"Pi.addCommMonoid",
"Algebra.TensorProduct.piScalarRight",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"Algebra.toModule",
"Algebra.id",
"Algebra.TensorProduct.leftAlgebra",
"CommSemiring",
"NonUnitalNonAs... | true |
OrderIso.locallyFiniteOrderBot._proof_1 | Mathlib.Order.Interval.Finset.Defs | [
"OrderIsoClass.map_le_map_iff",
"OrderIso._proof_4",
"Equiv.instEquivLike",
"RelIso.mk",
"congrArg",
"Finset",
"Finset.mem_Iic",
"Preorder.toLE",
"Finset.map",
"Membership.mem",
"LocallyFiniteOrderBot",
"Equiv",
"OrderIso",
"OrderIso.instEquivLike",
"LE.le",
"OrderIso.instOrderIsoClass... | false |
Matrix.instLieRingToLieAlgebra._aux_4 | Mathlib.Algebra.Lie.SerreConstruction | [
"LieAlgebra.toModule",
"CommRing",
"FreeLieAlgebra.instLieRing",
"LieRing.toAddCommGroup",
"Matrix",
"LieSubmodule.toSubmodule",
"Quotient.mk''",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"CartanMatrix.Relations.toIdeal",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtrac... | false |
AlternatingMap.zero_apply | Mathlib.LinearAlgebra.Alternating.Basic | [
"AlternatingMap",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddCommMonoid",
"AddZero.toZero",
"AlternatingMap.instZero",
"Semiring",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"Module",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"rfl",
"AlternatingMap.instFunLike"
] | true |
Asymptotics.IsBigO.mul | Mathlib.Analysis.Asymptotics.Defs | [
"SeminormedRing.toNorm",
"Real",
"NormedRing.toRing",
"HMul.hMul",
"Asymptotics.IsBigOWith",
"Asymptotics.IsBigO",
"SeminormedRing.toRing",
"Exists",
"NormMulClass",
"instDistribOfSemiring",
"Distrib.toMul",
"Real.instMul",
"Asymptotics.IsBigOWith.isBigO",
"Asymptotics.IsBigO.isBigOWith",
... | true |
FreeRing.of | Mathlib.RingTheory.FreeRing | [
"FreeMonoid",
"FreeMonoid.of",
"FreeAbelianGroup.of",
"FreeRing"
] | true |
ListSlice.toArray_mkSlice_roo | Init.Data.Slice.List.Lemmas | [
"Std.Slice.toList",
"instSliceableListSliceNat_4",
"Std.Iterators.Types.Take.instIterator",
"Std.Slice.Internal.ListSliceData",
"ListSlice.instToIterator",
"Std.Iterators.Types.ListIterator",
"Std.Slice.toArray",
"congrArg",
"Monad.toApplicative",
"HSub.hSub",
"List.drop_take",
"Std.Iterators.... | true |
Manifold.termCMDiffAt____ | Mathlib.Geometry.Manifold.Notation | [
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.const",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
Metric.infEdist_ne_top | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"Metric.infEDist_ne_top",
"Ne",
"Metric.infEDist",
"PseudoMetricSpace",
"Set.Nonempty",
"ENNReal",
"ENNReal.instTop",
"Top.top",
"PseudoMetricSpace.toPseudoEMetricSpace",
"Set"
] | true |
CategoryTheory.Limits.colimit_obj_ext | Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | [
"Eq.mpr",
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.colimitObjIsoColimitCompEvaluation_ι_inv_assoc",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Cate... | true |
CategoryTheory.Mod.instInhabited.eq_1 | Mathlib.CategoryTheory.Monoidal.Mod | [
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mod.regular",
"CategoryTheory.Mod",
"Inhabited",
"Eq.refl",
"CategoryTheory.MonObj",
"Eq",
"CategoryTheory.Category",
"Inhabited.mk",
"CategoryTheory.Mod.instInhabited",
"CategoryTheory.MonoidalCategory.selfLeftAction"
] | true |
FreeAbelianGroup.ofMulHom._proof_2 | Mathlib.GroupTheory.FreeAbelianGroup | [
"Monoid",
"HMul.hMul",
"Monoid.toMulOneClass",
"MulOne.toMul",
"MulOneClass.toMulOne",
"FreeAbelianGroup.of",
"FreeAbelianGroup",
"Eq",
"FreeAbelianGroup.mul",
"FreeAbelianGroup.of_mul",
"instHMul"
] | false |
QuotientGroup.kerLift_injective | Mathlib.GroupTheory.QuotientGroup.Basic | [
"Quotient.sound'",
"Eq.mpr",
"MulOne.toOne",
"DivInvMonoid.toInv",
"MonoidHom.instFunLike",
"inv_mul_cancel",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMon... | true |
Neg.noConfusionType | Init.Prelude | [
"Neg.casesOn",
"Neg",
"HEq"
] | false |
Fin.consOrderIso_toEquiv | Mathlib.Order.Fin.Tuple | [
"instNeZeroNatHAdd_1",
"Prod.instLE_mathlib",
"Fin.succ",
"Fin.instOfNat",
"Equiv",
"instOfNatNat",
"LE.le",
"LE",
"Pi.hasLe",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"Fin.consEquiv",
"instAddNat",
"Fin.consOrderIso",
"Eq.refl",
"RelIso.toEquiv",
"Prod",
"OfNat.of... | true |
Lean.Meta.ArgsPacker.mk.noConfusion | Lean.Meta.ArgsPacker.Basic | [
"Lean.Meta.ArgsPacker",
"id",
"Lean.Meta.ArgsPacker.mk",
"Lean.Meta.ArgsPacker.noConfusion",
"Array",
"Lean.Name",
"Eq"
] | false |
AddMonoidAlgebra.map_neg | Mathlib.Algebra.MonoidAlgebra.MapDomain | [
"NegZeroClass.toNeg",
"AddMonoidHom.map_zero",
"Finsupp.mapRange_neg",
"AddGroupWithOne.toAddGroup",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"AddZeroClass.toAddZero",
"AddMonoidAlgebra.addAddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"AddMonoidHom.map_neg",
"Su... | true |
AddGroupSeminorm.toOne._proof_2 | Mathlib.Analysis.Normed.Group.Seminorm | [
"AddGroup.toSubtractionMonoid",
"Real",
"Real.instZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"if_pos",
"SubNegZeroMonoid.toNegZeroClass",
"Real.instOne",
"AddGroup",
"One.toOfNat1",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq",
"rfl",
"DecidableEq",
"ite"
] | false |
Pi.addGroup.eq_1 | Mathlib.Algebra.Group.Pi.Basic | [
"Pi.addGroup",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Pi.subNegMonoid",
"Pi.addGroup._proof_1",
"Eq.refl",
"Eq",
"AddGroup.mk"
] | true |
VectorBundleCore.ctorIdx | Mathlib.Topology.VectorBundle.Basic | [
"NormedSpace",
"TopologicalSpace",
"Nat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"NormedAddCommGroup",
"VectorBundleCore"
] | false |
MonoidHom.mulSingle.eq_1 | Mathlib.Algebra.Group.Pi.Lemmas | [
"MulOne.toOne",
"MonoidHom",
"OneHom.mulSingle",
"MonoidHom.mulSingle",
"MonoidHom.mk",
"Pi.mulOneClass",
"MulOneClass.toMulOne",
"Eq.refl",
"MonoidHom.mulSingle._proof_1",
"MulOneClass",
"Eq",
"DecidableEq"
] | true |
Algebra.Extension.CotangentSpace._proof_1 | Mathlib.RingTheory.Extension.Cotangent.Basic | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra",
"Algebra.toModule",
"MulOne.toMul",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"IsScalarTower.l... | false |
_private.Mathlib.NumberTheory.ModularForms.DedekindEta.0.ModularForm.one_sub_eta_q_ne_zero._simp_1_1 | Mathlib.NumberTheory.ModularForms.DedekindEta | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Polynomial.IsSplittingField.lift._proof_6 | Mathlib.FieldTheory.SplittingField.IsSplittingField | [
"Subalgebra.instSetLike",
"Multiset.toFinset",
"Iff.mpr",
"Polynomial.eval",
"Polynomial.roots",
"Dvd.dvd",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"Polynomial.lift_of_splits",
"CommSemiring.toSemiring",
"Polynomial.eval₂AlgHom._proof_1",
"AlgHom",
"Finset",
"Polynomial.IsRoo... | false |
Int.neg_nonpos_iff._simp_1 | Init.Data.Int.LemmasAux | [
"Int.instNegInt",
"Int",
"LE.le",
"instOfNat",
"propext",
"OfNat.ofNat",
"Eq",
"Int.neg_nonpos_iff",
"Neg.neg",
"Int.instLEInt"
] | false |
cfcₙ_realPart._auto_5 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.RealImaginaryPart | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Init.Data.Array.Bootstrap.0.Array.foldlM.loop.match_1.eq_1 | Init.Data.Array.Bootstrap | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Array.foldlM.loop.match_1",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
_private.Lean.Server.References.0.Lean.Server.getModuleContainingDecl?.match_1 | Lean.Server.References | [
"Lean.ModuleIdx",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"_private.Lean.Server.References.0.Lean.Server.RefInfo.toLspRefInfo._sparseCasesOn_1",
"Option"
] | false |
ULift.isLeftRegular_up | Mathlib.Algebra.Regular.ULift | [
"Equiv.instEquivLike",
"HMul.hMul",
"ULift",
"Mul",
"Function.comp",
"Equiv.ulift",
"Equiv",
"Equiv.injective_comp",
"IsLeftRegular",
"ULift.mul",
"Iff",
"Iff.trans",
"Function.Injective",
"Equiv.comp_injective",
"Equiv.symm",
"ULift.up",
"DFunLike.coe",
"ULift.down",
"Iff.symm",... | true |
_private.Mathlib.Order.OrderIsoNat.0.exists_increasing_or_nonincreasing_subseq'._proof_1_4 | Mathlib.Order.OrderIsoNat | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Int.Linear.norm_le",
"Int.Linear.Expr.eq_of_norm_eq",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Int.Linear.le_neg",
"Int.Linear.eq_norm",
"Classical.byContradiction",
"HSub.hSub",
"Lean.Grind.Semiring.... | false |
Filter.hasBasis_pi | Mathlib.Order.Filter.Pi | [
"Eq.mpr",
"congrArg",
"Set.iInter",
"Set.Finite",
"Membership.mem",
"id",
"Function.eval",
"Prod.fst",
"Filter.HasBasis.comap",
"Filter.HasBasis.iInf'",
"funext",
"And",
"Filter.HasBasis",
"Set.preimage",
"Filter.pi",
"Set.pi",
"Set.pi_def",
"Prod",
"Eq",
"Set.instMembership",
... | true |
_private.Init.Data.Iterators.Basic.0.Std.Shrink.eq_1 | Init.Data.Iterators.Basic | [
"Std.Shrink",
"id",
"Eq.refl",
"_private.Init.Data.Iterators.Basic.0.Std.Internal.idOpaque",
"Subtype.val",
"Eq"
] | true |
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