name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.applyReplacementFun.visitLambda.match_4 | Mathlib.Tactic.Translate.Core | [
"Lean.Expr",
"Nat.hasNotBit",
"_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.applyReplacementFun.visitLambda._sparseCasesOn_4",
"Lean.Expr.lam",
"Lean.Name",
"Lean.BinderInfo",
"Lean.Expr.ctorIdx"
] | false |
Set.mulIndicator_one | Mathlib.Algebra.Notation.Indicator | [
"Iff.mpr",
"One",
"congrArg",
"Set.mulIndicator",
"Disjoint",
"_private.Mathlib.Algebra.Notation.Indicator.0.Set.mulIndicator_one._simp_1_1",
"SemilatticeInf.toPartialOrder",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
"Set.ins... | true |
CategoryTheory.Limits.pushout.map._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.pushout.condition",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"congr",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Limits.pushou... | false |
Lean.Meta.Grind.checkMaxEmatchExceeded | Lean.Meta.Tactic.Grind.Types | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.getConfig",
"Lean.Grind.Config",
"Lean.Meta.Grind.Goal",
"StateRefT'.instAlternativeOfMonad",
"Lean.Core.instMonadLiftIOCoreM",
"Lean.Meta.Grind.State",
"IO.instMonadLiftSTRealWorldBaseIO",
"ReaderT",
"Lean.Meta.State",
"instMonadLiftT",
... | true |
Batteries.AssocList.isEmpty.eq_1 | Batteries.Data.AssocList | [
"Bool.true",
"Batteries.AssocList.isEmpty",
"Bool",
"Eq.refl",
"Eq",
"Batteries.AssocList.nil"
] | true |
Aesop.RuleTacDescr.constructors | Aesop.RuleTac.Descr | [
"Aesop.RuleTacDescr.constructors",
"Aesop.RuleTacDescr",
"Lean.Meta.TransparencyMode",
"Array",
"Lean.Name"
] | true |
div_lt_div_iff' | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"id",
"MulOne.toMul",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"CommGroup",
"MulLeftStrictMono",
"div_eq_mul_inv",
"mul_inv_lt_mul_inv_iff'",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Iff... | true |
Module.Basis.empty.congr_simp | Mathlib.RingTheory.Smooth.StandardSmoothOfFree | [
"IsEmpty",
"AddCommMonoid",
"Module.Basis",
"Module.Basis.empty",
"Semiring",
"Subsingleton",
"Eq.refl",
"Module",
"Eq"
] | true |
SNum.lt | Mathlib.Data.Num.Lemmas | [
"LT.mk",
"Int",
"SNum",
"Int.instLTInt",
"LT.lt",
"Int.ofSnum",
"LT"
] | true |
Std.DTreeMap.Internal.Impl.mem_of_mem_erase! | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.erase_eq_erase!",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Std.DTreeMap.Internal.Impl.erase!",
"Ord",
"congrArg",
"Std.TransOrd",
"HSub.hSub",
"Std.DTreeMap.Internal.Impl.erase",
"Membership.mem",
"Eq.mp",
"Std.DTreeMap.Internal.Impl.size",
"instSubNat"... | true |
String.Slice.Pos.prevAux.go.eq_def | Init.Data.String.Basic | [
"Eq.mpr",
"Decidable.casesOn",
"String.Slice.Pos.prevAux._proof_4",
"congrArg",
"HEq.refl",
"False.elim",
"Decidable",
"String.Slice",
"String.Slice.Pos.prevAux._proof_6",
"Nat.brecOn.go",
"Nat.rec",
"dif_pos",
"Nat.brecOn",
"Nat.brecOn.eq",
"id",
"String.Slice.Pos.prevAux.go.match_1",... | true |
_private.Mathlib.Tactic.Algebra.Basic.0.Mathlib.Tactic.Algebra.RingCompute.isOne.match_3 | Mathlib.Tactic.Algebra.Basic | [
"Unit.unit",
"_private.Mathlib.Tactic.Algebra.Basic.0.Mathlib.Tactic.Algebra.RingCompute.isOne._sparseCasesOn_4",
"HEq.refl",
"String",
"Mathlib.Tactic.Ring.RatCoeff",
"Lean.Expr.const",
"_private.Mathlib.Tactic.Algebra.Basic.0.Mathlib.Tactic.Algebra.RingCompute.isOne._sparseCasesOn_8",
"Mathlib.Tacti... | false |
CategoryTheory.WithTerminal.starIsoTerminal_inv | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.WithTerminal.starTerminal",
"CategoryTheory.WithTerminal",
"CategoryTheory.Limits.terminal",
"CategoryTheory.WithTerminal.instHasTerminal",
"CategoryTheory.WithTerminal.star",
"Eq.refl",
... | true |
Homeomorph.setCongr._proof_2 | Mathlib.Topology.Homeomorph.Lemmas | [
"Continuous",
"continuous_subtype_val",
"Equiv.setCongr",
"Membership.mem",
"Set.Elem",
"Equiv.subtypeEquivProp._proof_1",
"id",
"Continuous.subtype_mk",
"TopologicalSpace",
"instTopologicalSpaceSubtype",
"Equiv.subtypeEquiv._proof_4",
"Equiv.setCongr._proof_1",
"Subtype.val",
"Equiv.refl"... | false |
uniformity_pseudoedist | Mathlib.Topology.EMetricSpace.Defs | [
"Preorder.toLT",
"iInf",
"Filter.instInfSet",
"uniformity",
"PartialOrder.toPreorder",
"setOf",
"PseudoEMetricSpace",
"Prod.fst",
"GT.gt",
"PseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniformSpace",
"LT.lt",
"ENNReal",
"ENNReal.instPartialOrder",
"Filter.principal",
"Zero.toOfNa... | true |
RootPairing.PolarizationEquiv._proof_5 | Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate | [
"CommSemiring.toSemiring",
"Field.toCommRing",
"RingHomInvPair",
"CommRing.toCommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Field"
] | false |
_private.Lean.Meta.Tactic.Grind.Split.0.Lean.Meta.Grind.instBEqSplitStatus.beq._sparseCasesOn_3 | Lean.Meta.Tactic.Grind.Split | [
"Nat.ne_of_beq_eq_false",
"Lean.Meta.Grind.SplitStatus.notReady",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Nat.land",
"Lean.Meta.Grind.SplitStatus",
"Nat",
"Lean.Meta.Grind.SplitStatus.ready",
"Bool",
"Lean.Meta.Grind.SplitStatus.rec",
"Eq.refl",
"Lean.Meta.Grind.SplitStatus.ctorI... | false |
Orientation.eq_rotation_self_iff | Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | [
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Orientation",
"Orientation.rotation_eq_self_iff",
"Real.partialOrder",
"Real",
"Real.Angle",
"Real.instRCLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Iff.rfl",
"Fact",
"Real.... | true |
Applicative.mk.noConfusion | Init.Prelude | [
"Functor",
"Applicative.noConfusion",
"id",
"Pure",
"Applicative",
"Applicative.mk",
"SeqLeft",
"SeqRight",
"heq_of_eq",
"Seq",
"Eq.refl",
"HEq",
"Eq"
] | false |
AlgebraicGeometry.Scheme.ProEt.instFullOverForget | Mathlib.AlgebraicGeometry.Sites.Proetale | [
"CategoryTheory.Over",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.Scheme.instCategoryProEt",
"AlgebraicGeometry.Scheme.ProEt",
"CategoryTheory.instCategoryOver",
"AlgebraicGeometry.Scheme.ProEt.forget",
"_private.Mathlib.AlgebraicGeometry.Sites.Proetale.0.AlgebraicGeometry.Scheme.ProEt.instFullOverF... | true |
Std.Stream.noConfusion | Init.Data.Stream | [
"HEq.refl",
"Std.Stream.noConfusionType",
"Std.Stream.casesOn",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Prod",
"Eq",
"Std.Stream",
"Option"
] | false |
Complex.differentiable_sinh | Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | [
"Differentiable",
"NormedCommRing.toSeminormedCommRing",
"Complex.sinh",
"Semiring.toModule",
"Complex.instNormedAddCommGroup",
"HasDerivAt.differentiableAt",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Complex.hasDerivAt_sinh",
"Complex.instDenselyNorm... | true |
ONote.fundamentalSequenceProp_inl_some | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.NF",
"Order.succ",
"Ordinal.partialOrder",
"Iff.rfl",
"PartialOrder.toPreorder",
"Option.some",
"Sum.inl",
"Ordinal.instSuccOrder",
"And",
"Iff",
"ONote.repr",
"Nat",
"ONote.FundamentalSequenceProp",
"Eq",
"ONote",
"Ordinal",
"Option"
] | true |
AddMonoidAlgebra.symm_mapAddEquiv | Mathlib.Algebra.MonoidAlgebra.MapDomain | [
"AddMonoidAlgebra.nonUnitalNonAssocSemiring",
"Distrib.toAdd",
"AddMonoidAlgebra.mapAddEquiv",
"instDistribOfSemiring",
"Semiring",
"NonUnitalNonAssocSemiring.toDistrib",
"AddEquiv",
"AddMonoidAlgebra",
"Eq",
"Add",
"rfl",
"AddEquiv.symm"
] | true |
LocallyConstant.instMul.eq_1 | Mathlib.Topology.LocallyConstant.Algebra | [
"LocallyConstant.mk",
"Mul.mk",
"HMul.hMul",
"Mul",
"LocallyConstant",
"LocallyConstant.instMul",
"TopologicalSpace",
"LocallyConstant.instMul._proof_1",
"Pi.instMul",
"Eq.refl",
"LocallyConstant.instFunLike",
"Eq",
"DFunLike.coe",
"instHMul"
] | true |
Lean.Parser.withOpenDeclFn | Lean.Parser.Extension | [
"Lean.Parser.ParserState.stxStack",
"Lean.Parser.SyntaxStack.size",
"Lean.Syntax",
"instOfNatNat",
"GT.gt",
"Nat",
"Lean.Parser.withOpenDeclFnCore",
"Nat.decLt",
"Lean.Parser.ParserContext",
"Lean.Parser.ParserState",
"instLTNat",
"OfNat.ofNat",
"Lean.Parser.ParserFn",
"Lean.Parser.SyntaxS... | true |
ValuativeRel.ValueGroupWithZero.mk_one_one | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | [
"CommRing",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"Subtype",
"ValuativeRel.vle",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"instMulZeroOneClassOfSemiring",
"AddMonoidWithOne.toOne",
"ValuativeRel.vle_refl._... | true |
Module.Basis.algebraMapCoeffs_apply | Mathlib.RingTheory.AlgebraTower | [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"RingEquiv.ofBijective",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"RingHom",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"Module.Basis.algebraMapCoeffs._proof_1",
... | true |
ContinuousLinearMap.mfderiv_eq | Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | [
"mfderiv",
"chartedSpaceSelf",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupTangentSpace",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"HasMFDerivAt.mfderiv",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"instModuleTangentSpace",
"Field.toSemifield",... | true |
OrderIso.isBoundedUnder_le_comp | Mathlib.Order.Filter.IsBounded | [
"congrArg",
"Function.Surjective.exists",
"Filter.map",
"Filter.Eventually",
"Exists",
"_private.Mathlib.Order.Filter.IsBounded.0.OrderIso.isBoundedUnder_le_comp._simp_1_1",
"OrderIso",
"OrderIso.le_iff_le",
"LE.le",
"OrderIso.surjective",
"LE",
"iff_self",
"funext",
"exists_congr",
"Iff... | true |
Left.nsmul_nonpos | Mathlib.Algebra.Order.Monoid.Unbundled.Pow | [
"instHSMul",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"AddLeftMono",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"OrderDual.addLeftMono",
"LE.le",
"AddZero.toZero",
"AddSemigroup.toAdd",
"Nat",
"OrderDual.instAddMonoid",
"AddMonoid",
"AddZero.toAdd",
... | true |
Lean.Elab.Tactic.GuardMsgs.GuardMsgsSpec._sizeOf_1 | Lean.Elab.GuardMsgs | [
"Lean.Elab.Tactic.GuardMsgs.WhitespaceMode._sizeOf_inst",
"Lean.Elab.Tactic.GuardMsgs.MessageOrdering._sizeOf_inst",
"Lean.Elab.Tactic.GuardMsgs.GuardMsgsSpec.rec",
"Lean.Message",
"Lean.Elab.Tactic.GuardMsgs.FilterSpec",
"Lean.Elab.Tactic.GuardMsgs.GuardMsgsSpec",
"instOfNatNat",
"Lean.Elab.Tactic.Gu... | false |
_private.Mathlib.Order.Monotone.Basic.0.Nat.stabilises_of_antitone._proof_1_3 | Mathlib.Order.Monotone.Basic | [
"False",
"congrArg",
"Classical.byContradiction",
"False.casesOn",
"instOfNatNat",
"Nat",
"True",
"eq_self",
"Lean.Grind.not_true",
"Lean.Grind.intro_with_eq",
"OfNat.ofNat",
"Eq",
"Not",
"Eq.trans"
] | false |
_private.Mathlib.LinearAlgebra.LinearIndependent.Defs.0.not_linearIndependent_iffₛ._simp_1_2 | Mathlib.LinearAlgebra.LinearIndependent.Defs | [
"Exists",
"propext",
"Classical.not_forall",
"Eq",
"Not"
] | false |
_private.Mathlib.Topology.Instances.ENNReal.Lemmas.0.ENNReal.continuous_pow._simp_1_1 | Mathlib.Topology.Instances.ENNReal.Lemmas | [
"Continuous",
"continuous_const",
"TopologicalSpace",
"True",
"eq_true",
"Eq"
] | false |
Int.natAbs_one | Init.Data.Int.Order | [
"instOfNatNat",
"Int",
"instOfNat",
"Nat",
"Int.natAbs",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
RingAut.toAddAut._proof_1 | Mathlib.Algebra.Ring.Aut | [
"MulOne.toOne",
"Monoid.toMulOneClass",
"RingEquiv.toAddEquiv",
"Mul",
"RingAut",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"AddAut",
"One.toOfNat1",
"RingAut.instGroup",
"OfNat.ofNat",
"Eq",
"Add",
"rfl"
] | false |
Matrix.submatrixEquivInvertible._proof_1 | Mathlib.LinearAlgebra.Matrix.NonsingularInverse | [
"Eq.mpr",
"MulOne.toOne",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Matrix.submatrix",
"Equiv.instEquivLike",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Matrix.instMulOfFintypeOfAddCommMonoid",
"Matrix",
... | false |
NormedAddGroupHom.inhabited | Mathlib.Analysis.Normed.Group.Hom | [
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"NormedAddGroupHom.zero",
"Inhabited",
"Zero.toOfNat0",
"OfNat.ofNat",
"Inhabited.mk"
] | true |
MulArchimedeanClass.liftOrderHom.eq_1 | Mathlib.Algebra.Order.Archimedean.Class | [
"MulArchimedeanClass.liftOrderHom",
"IsOrderedMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"PartialOrder",
"DistribLattice.toLattice",
"MulArchimedeanClass.lift",
"LE.le",
"CommGroup",
"MulArchimedeanClass.mk",
"MulArchimedeanClass.lift... | true |
LieAlgebra.Orthogonal.soIndefiniteEquiv._proof_1 | Mathlib.Algebra.Lie.Classical | [
"Set.ext",
"Eq.mpr",
"NegZeroClass.toNeg",
"CommRing",
"instFintypeSum",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"LieRing.toAddCommGroup",
"LieSubalgebra.instSetLike",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"instDecidableEqSum... | false |
AbstractCompletion.extend_unique | Mathlib.Topology.UniformSpace.AbstractCompletion | [
"UniformContinuous",
"UniformSpace",
"AbstractCompletion",
"Eq.mpr",
"CompleteSpace",
"congrArg",
"AbstractCompletion.space",
"AbstractCompletion.uniformStruct",
"id",
"AbstractCompletion.extend_coe",
"instT3Space",
"AbstractCompletion.coe",
"AbstractCompletion.funext",
"UniformContinuous.... | true |
Set.mem_cIcc | Mathlib.Order.Circular | [
"Iff.rfl",
"Membership.mem",
"CircularPreorder",
"CircularPreorder.toBtw",
"Iff",
"Btw.btw",
"Set.cIcc",
"Set.instMembership",
"Set"
] | true |
Asymptotics.IsBigOTVS.add | Mathlib.Analysis.Asymptotics.TVS | [
"NormedCommRing.toSeminormedCommRing",
"Asymptotics.IsBigOTVS",
"ContinuousSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"AddCommGroup.toAddGroup",
... | true |
OrderMonoidIso.unitsCongr | Mathlib.Algebra.Order.Hom.Units | [
"Monoid",
"Monoid.toMulOneClass",
"Units",
"MulOne.toMul",
"Units.mapEquiv",
"MulOneClass.toMulOne",
"OrderMonoidIso",
"OrderMonoidIso.toMulEquiv",
"MulEquiv",
"Units.instMul",
"OrderMonoidIso.mk",
"Units.instPreorder",
"Preorder",
"OrderMonoidIso.unitsCongr._proof_2"
] | true |
thickenedIndicatorAux.eq_1 | Mathlib.Topology.MetricSpace.ThickenedIndicator | [
"Real",
"instHDiv",
"ENNReal.ofReal",
"HSub.hSub",
"HDiv.hDiv",
"Metric.infEDist",
"PseudoEMetricSpace",
"thickenedIndicatorAux",
"instHSub",
"ENNReal",
"ENNReal.instDivInvMonoid",
"ENNReal.instSub",
"DivInvMonoid.toDiv",
"One.toOfNat1",
"Eq.refl",
"ENNReal.instOne",
"OfNat.ofNat",
... | true |
ValuationSubring.primeSpectrumEquiv_apply | Mathlib.RingTheory.Valuation.ValuationSubring | [
"ValuationSubring.instPartialOrder",
"Equiv.instEquivLike",
"ValuationSubring.primeSpectrumEquiv._proof_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Equiv",
"Subtype",
"LE.le",
"CommRing.toNonAssocCommRing",
"Field.toSemifield",
"Field.toCommRing",
"Subtype.mk",
"Valu... | true |
Std.DTreeMap.Raw.ordered_keys | Std.Data.DTreeMap.Raw.Lemmas | [
"List.Pairwise",
"Ord.mk",
"Ordering",
"Std.DTreeMap.Raw.keys",
"Std.TransCmp",
"Std.DTreeMap.Internal.Impl.ordered_keys",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Ordering.lt",
"Eq",
"Std.DTreeMap.Raw.WF",
"Std.DTreeMap.Raw"
] | true |
_private.Mathlib.CategoryTheory.Subfunctor.Basic.0.CategoryTheory.instCompleteLatticeSubfunctor._simp_5 | Mathlib.CategoryTheory.Subfunctor.Basic | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
Metric.sphere_subset_closedBall | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"Real",
"HasSubset.Subset",
"PseudoMetricSpace",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Metric.closedBall",
"le_of_eq",
"Real.instPreorder",
"Set.instHasSubset",
"Metric.sphere",
"Set"
] | true |
Complex.tsum_exp_neg_quadratic | Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Complex.normSq_pos",
"Int.cast",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"NormedCom... | true |
exists_isClopen_upper_or_lower_of_ne | Mathlib.Topology.Order.Priestley | [
"PartialOrder.toPreorder",
"exists_isClopen_upper_of_not_le",
"IsUpperSet",
"Preorder.toLE",
"Membership.mem",
"Exists",
"PartialOrder",
"And.imp_left",
"Ne",
"Exists.imp",
"LE.le",
"Or.casesOn",
"And.casesOn",
"TopologicalSpace",
"Ne.not_le_or_not_ge",
"And",
"Exists.casesOn",
"Is... | true |
DFinsupp.coe_sup | Mathlib.Data.DFinsupp.Order | [
"SemilatticeSup.toMax",
"DFinsupp.instDFunLike",
"DFinsupp.instSemilatticeSup",
"Pi.instMaxForall_mathlib",
"Max.max",
"DFinsupp",
"Eq",
"SemilatticeSup",
"DFunLike.coe",
"rfl",
"Zero"
] | true |
CategoryTheory.op_add | Mathlib.CategoryTheory.Preadditive.Opposite | [
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Preadditive",
"CategoryTheory.instPreadditiveOpposite",
"instHAdd",
"HAdd.hAdd",
"Opposite.op",
"CategoryTheory.Category.opposite",
"Categor... | true |
Std.DHashMap.Internal.Raw₀.replaceₘ._proof_1 | Std.Data.DHashMap.Internal.Model | [
"Eq.mpr",
"congrArg",
"Std.DHashMap.Raw",
"id",
"instOfNatNat",
"Nat",
"Std.DHashMap.Raw.buckets",
"Std.DHashMap.Internal.size_updateBucket",
"LT.lt",
"Std.DHashMap.Internal.AssocList.replace",
"Std.DHashMap.Internal.AssocList",
"Hashable",
"Std.DHashMap.Raw.size",
"instLTNat",
"Std.DHas... | false |
RCLike.continuous_im | Mathlib.Analysis.RCLike.Basic | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"Continuous",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"RCLike.toNormedAlgebra",
"AddMonoid.toAddSemigroup",
"Real.instAddMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"PseudoMetricSp... | true |
Std.Iterators.Types.Flatten.IsPlausibleStep.outerDone_flatMap | Init.Data.Iterators.Lemmas.Combinators.Monadic.FlatMap | [
"Pure.pure",
"Std.Iterators.Types.Flatten.instIterator",
"Monad.toApplicative",
"Std.Iterators.Types.Map.instIterator",
"MonadLiftT.monadLift",
"Std.Iterators.Types.Flatten.IsPlausibleStep.outerDone",
"instMonadLiftT",
"Std.IterM.flatMapAfter",
"Option.some",
"Std.IterM.IsPlausibleStep",
"Lawful... | true |
Submodule.mem_span_image_finset_iff_exists_fun | Mathlib.LinearAlgebra.Finsupp.LinearCombination | [
"Eq.mpr",
"Submodule",
"instHSMul",
"Finset.univ",
"congrArg",
"DistribMulAction.toDistribSMul",
"Finset",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"Set.Elem",
"id",
"Subtype",
"DistribSMul.toSMulZeroClass",
"Set.image_eq_range",
... | true |
_private.Mathlib.Algebra.Homology.Augment.0.ChainComplex.augment.match_3.splitter | Mathlib.Algebra.Homology.Augment | [
"Unit.unit",
"False",
"_private.Mathlib.Algebra.Homology.Augment.0.ChainComplex.augment.match_3.splitter._sparseCasesOn_3",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"dite",
"Bool.true",
"Nat.land",
"Unit",
"absurd",
"Nat",
"Eq.ndrec_symm",
"Bool",
"Nat.succ.noConfusion",
"Eq.... | true |
MonoidAlgebra.liftMagma._proof_2 | Mathlib.Algebra.MonoidAlgebra.Basic | [
"MulHom",
"MonoidAlgebra.addCommMonoid",
"Eq.mpr",
"instHSMul",
"instSMulOfMul",
"MonoidAlgebra.mul_def",
"HMul.hMul",
"Finsupp.sum_comm",
"congrArg",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Module.toMulActionWithZero",
"Finsupp.sum",
"NonUnitalNon... | false |
_private.Lean.Elab.Tactic.NormCast.0.Lean.Elab.Tactic.NormCast.splittingProcedure.match_1 | Lean.Elab.Tactic.NormCast | [
"Option.ctorIdx",
"_private.Lean.Elab.Tactic.NormCast.0.Lean.Elab.Tactic.NormCast.isCoeOf?._sparseCasesOn_1",
"Option.some",
"Lean.Meta.Simp.Result",
"Nat.hasNotBit",
"Option"
] | false |
Functor.map_comp_map | Mathlib.Control.Functor | [
"LawfulFunctor",
"Functor",
"Function.comp",
"funext",
"Eq.symm",
"Eq",
"Functor.map",
"LawfulFunctor.comp_map"
] | true |
CategoryTheory.ComposableArrows.threeδ₁Toδ₀_app_zero | Mathlib.CategoryTheory.ComposableArrows.Three | [
"instNeZeroNatHAdd_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"Fin.instOfNat",
"Preorder.smallCategory",
"instOfNatNat",
"instHAdd",
"CategoryTheory.ComposableArrows.mk₂",
"Fin.instPartialOrder",
"CategoryTheory.ComposableArrows.threeδ₁Toδ₀",
"HAdd.h... | true |
CategoryTheory.Oplax.StrongTrans.Modification.ext_iff | Mathlib.CategoryTheory.Bicategory.Modification.Oplax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Oplax.StrongTrans.Modification.ext",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"Eq.casesOn",
"CategoryTheory.Oplax.StrongTrans.app",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.to... | true |
Polynomial.reflect_mul_induction | Mathlib.Algebra.Polynomial.Reverse | [
"add_mul",
"Distrib.leftDistribClass",
"Eq.mpr",
"Polynomial.C",
"Nat.instCanonicallyOrderedAdd",
"Semigroup.toMul",
"Nat.recAux",
"HMul.hMul",
"Polynomial.revAt",
"Polynomial.eraseLead_add_C_mul_X_pow",
"MulZeroClass.toMul",
"Monoid.toMulOneClass",
"congrArg",
"Polynomial.instDecidableEq"... | true |
_private.Lean.Server.FileWorker.0.Lean.Server.FileWorker.handlePreRequestSpecialCases?.match_3 | Lean.Server.FileWorker | [
"Unit.unit",
"String",
"dite",
"Unit",
"Eq.ndrec_symm",
"instDecidableEqString",
"Eq",
"Not"
] | false |
CategoryTheory.Limits.Cone.functoriality_obj_pt | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.Cone.pt",
"Eq.refl",
"CategoryTheory.Limits.Cone.functoriality",
"CategoryTheory.Limits.Cone.category",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Logic.Equiv.Defs.0.Equiv.permCongr_trans._proof_1_1 | Mathlib.Logic.Equiv.Defs | [
"False",
"Equiv.instEquivLike",
"eq_false",
"Equiv.trans_apply",
"Equiv.symm_apply_apply",
"Equiv.trans",
"HEq.refl",
"Classical.byContradiction",
"DFunLike.coe.hcongr_6",
"Exists",
"Eq.mp",
"id",
"Equiv",
"Lean.Grind.forall_imp_eq_or",
"Equiv.ext",
"Equiv.permCongr_apply",
"Equiv.pe... | false |
Int.gcd_comm | Init.Data.Int.Gcd | [
"Int.gcd",
"Int",
"Nat",
"Int.natAbs",
"Eq",
"Nat.gcd_comm"
] | true |
ContRepresentation.Equiv | Mathlib.RepresentationTheory.Continuous.Basic | [
"Monoid",
"AddCommGroup.toAddCommMonoid",
"ContRepresentation",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"TopologicalSpace",
"Module",
"Ring.toSemiring",
"Ring",
"IsTopologicalAddGroup",
"ContRepresentation.Equiv.mk''"
] | true |
Algebra.Extension.tensorCotangentSpaceOfFormallyEtale._proof_7 | Mathlib.RingTheory.Etale.Kaehler | [
"CommRing",
"Algebra.Extension.commRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"SMulCommClass.of_commMonoid",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Algebra",
"AddZeroClass.toAdd... | false |
Std.Sat.AIG.Fanin.flip | Std.Sat.AIG.Basic | [
"Nat.instXorOp",
"Std.Sat.AIG.Fanin.val",
"Bool.toNat",
"Std.Sat.AIG.Fanin.ofRaw",
"Nat",
"HXor.hXor",
"Bool",
"Std.Sat.AIG.Fanin",
"instHXorOfXorOp"
] | true |
Bornology.ofDist._proof_4 | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"Iff.mpr",
"Real.instLE",
"Real",
"le_rfl",
"forall_eq",
"Membership.mem",
"Exists",
"Set.instSingletonSet",
"LE.le",
"Exists.intro",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Real.instPreorder",
"Set"
] | false |
_private.Aesop.Forward.State.0.Aesop.ForwardState.enqueuePatSubsts.match_1 | Aesop.Forward.State | [
"Aesop.ForwardRule",
"Aesop.Substitution",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
MeasurableSpace.generateMeasurable_eq_rec | Mathlib.MeasureTheory.MeasurableSpace.Card | [
"Preorder.toLT",
"Order.succ",
"Ordinal.partialOrder",
"MeasurableSpace.generateMeasurableRec",
"congrArg",
"MeasurableSpace.self_subset_generateMeasurableRec",
"Compl.compl",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Eq.mp",
"MeasurableSpace.Generat... | true |
Aesop.ScriptGenerated.Method.rec | Aesop.Stats.Basic | [
"Aesop.ScriptGenerated.Method.static",
"Aesop.ScriptGenerated.Method",
"Aesop.ScriptGenerated.Method.dynamic"
] | false |
List.infix_append'._simp_1 | Init.Data.List.Sublist | [
"List.IsInfix",
"instHAppendOfAppend",
"List",
"True",
"eq_true",
"List.infix_append'",
"List.instAppend",
"Eq",
"HAppend.hAppend"
] | false |
IsStrictOrderedRing.toContinuousInv₀ | Mathlib.Topology.Algebra.Order.Field | [
"le_max_right",
"Iff.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Ioi_mem_nhds",
"instClosedIicTopology",
"OrderTopology",
"Set.Ioi",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"Grou... | true |
ProfiniteAddGrp.limitConePtAux._proof_3 | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"CategoryTheory.Functor",
"ContinuousAddMonoidHom.instAddMonoidHomClass",
"Pi.addGroup",
"ProfiniteAddGrp.Hom.hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"ContinuousAddMonoidHom",
"setOf",
"Membership.mem",
"... | false |
CategoryTheory.SimplicialThickening.mk.sizeOf_spec | Mathlib.AlgebraicTopology.SimplicialNerve | [
"CategoryTheory.SimplicialThickening",
"LinearOrder",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"SizeOf",
"OfNat.ofNat",
"CategoryTheory.SimplicialThickening._sizeOf_inst",
"Eq",
"CategoryTheory.SimplicialThickening.mk"
] | true |
IsClosed.upperSemicontinuousAt_indicator | Mathlib.Topology.Semicontinuity.Basic | [
"Set.indicator",
"Preorder.toLE",
"UpperSemicontinuousAt",
"IsClosed.upperSemicontinuous_indicator",
"LE.le",
"IsClosed",
"TopologicalSpace",
"Zero.toOfNat0",
"UpperSemicontinuous.upperSemicontinuousAt",
"OfNat.ofNat",
"Preorder",
"Zero",
"Set"
] | true |
_private.Init.Data.Vector.Lemmas.0.Vector.mem_of_getElem?.match_1_1 | Init.Data.Vector.Lemmas | [
"Vector",
"Vector.instGetElemNatLt",
"Exists",
"GetElem.getElem",
"Exists.casesOn",
"Nat",
"LT.lt",
"Exists.intro",
"instLTNat",
"Eq"
] | false |
Lean.Server.Test.Runner.Client.instFromJsonInfoPopup.fromJson | Lean.Server.Test.Runner | [
"Pure.pure",
"Lean.Json",
"Lean.instFromJsonString",
"Monad.toApplicative",
"String",
"Lean.instFromJsonOption",
"Lean.Server.Test.Runner.Client.SubexprInfo",
"Lean.Json.getObjValAs?",
"Applicative.toPure",
"ToString.toString",
"Except.instMonad",
"Lean.Widget.TaggedText",
"instAppendString"... | true |
ContinuousMultilinearMap.sum_apply | Mathlib.Topology.Algebra.Module.Multilinear.Basic | [
"AddMonoidHom.instAddMonoidHomClass",
"ContinuousMultilinearMap.instAddMonoid",
"Finset",
"AddMonoid.toAddZeroClass",
"ContinuousMultilinearMap.addCommMonoid",
"ContinuousMultilinearMap",
"AddZeroClass.toAddZero",
"ContinuousMultilinearMap.funLike",
"map_sum",
"AddCommMonoid",
"TopologicalSpace"... | true |
IO.FS.Metadata.numLinks | Init.System.IO | [
"UInt64",
"IO.FS.Metadata"
] | true |
FintypeCat.equivEquivIso_symm_apply_apply | Mathlib.CategoryTheory.FintypeCat | [
"Equiv.instEquivLike",
"CategoryTheory.ConcreteCategory.hom",
"Finite",
"FintypeCat",
"FintypeCat.equivEquivIso",
"TypeCat.instFunLikeFun",
"CategoryTheory.ObjectProperty.FullSubcategory.concreteCategory",
"Equiv",
"CategoryTheory.Iso",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"TypeC... | true |
CategoryTheory.Lax.LaxTrans.homCategory.ext_iff | Mathlib.CategoryTheory.Bicategory.Modification.Lax | [
"CategoryTheory.Lax.LaxTrans.Modification.app",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Lax.LaxTrans.Hom.as",
"HEq.refl",
"Eq.casesOn",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Lax.LaxTrans.homCategory.ext",
"CategoryTheory.PrelaxFunctor.toPrelaxF... | true |
Lean.SourceInfo.none.sizeOf_spec | Init.SizeOf | [
"Lean.SourceInfo",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Lean.SourceInfo.none",
"Eq",
"Lean.SourceInfo._sizeOf_inst"
] | true |
ContinuousMultilinearMap.mk.inj | Mathlib.Topology.Algebra.Module.Multilinear.Basic | [
"Continuous",
"Pi.topologicalSpace",
"ContinuousMultilinearMap.mk.noConfusion",
"ContinuousMultilinearMap",
"ContinuousMultilinearMap.mk",
"MultilinearMap",
"AddCommMonoid",
"TopologicalSpace",
"MultilinearMap.toFun",
"eq_of_heq",
"Semiring",
"HEq",
"Module",
"Eq"
] | true |
Polynomial.instMulSemiringActionGalSplittingField._proof_4 | Mathlib.FieldTheory.PolynomialGaloisGroup | [
"Polynomial.instMulSemiringActionGalSplittingField._proof_3",
"MulOne.toOne",
"instHSMul",
"AlgEquiv.applyMulSemiringAction._proof_2",
"Monoid.toMulOneClass",
"Polynomial.Gal",
"Polynomial.SplittingField",
"Algebra.id",
"Polynomial.instGroupGal",
"DivInvMonoid.toMonoid",
"SMul.mk",
"SemigroupA... | false |
CategoryTheory.Limits.cokernel.condition_apply | Mathlib.CategoryTheory.ConcreteCategory.Elementwise | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Limits.cokernel",
"CategoryTheory.Limits.cokernel.condition",
"Eq.mp",
"id",
"CategoryTheory.Limits.HasCokernel",
"CategoryTheory.L... | true |
UniformContinuous.nndist | Mathlib.Topology.MetricSpace.Pseudo.Constructions | [
"UniformContinuous",
"UniformSpace",
"NNDist.nndist",
"instUniformSpaceProd",
"PseudoMetricSpace.toUniformSpace",
"PseudoMetricSpace.toNNDist",
"uniformContinuous_nndist",
"UniformContinuous.prodMk",
"Prod.mk",
"NNReal",
"instPseudoMetricSpaceNNReal",
"Prod.fst",
"UniformContinuous.comp",
... | true |
ComplexShape.σ_def | Mathlib.Algebra.Homology.ComplexShapeSigns | [
"Int.instAddCommGroup",
"ComplexShape.instTotalComplexShape",
"HMul.hMul",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"Int.instLinearOrder",
"ComplexShape.instTensorSignsIntUp",
"PartialOrder.toPreorder",
"instIsRightCancelAddOfAddRightReflectLE",
"AddGroupWithOne.toAddMonoidWithOne",
"AddCommGro... | true |
WithCStarModule.instNormedAddCommGroupProd._proof_10 | Mathlib.Analysis.CStarAlgebra.Module.Constructions | [
"NonUnitalNormedRing.toNorm",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"Equiv.instEquivLike",
"PseudoMetricSpace.toBornology",
"AddCommGroup.toAddCommMonoid",
"SMul",
"NormedSpace.toModule",
"Complex.instNormedField",
"_private.Mathlib.Analysis.CStarAlgebra.Module.Constructions.0.WithCStarModu... | false |
Submodule.adjoint._proof_3 | Mathlib.Analysis.InnerProductSpace.LinearPMap | [
"NormedField.toField",
"Field.toSemifield",
"RingHomInvPair",
"RCLike.toDenselyNormedField",
"RCLike",
"Semifield.toDivisionSemiring",
"RingHomInvPair.ids",
"DivisionSemiring.toSemiring",
"DenselyNormedField.toNormedField",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
Valued.instFaithfulSMulCompletionOfUniformContinuousConstSMul | Mathlib.Topology.Algebra.Valued.ValuedField | [
"Eq.mpr",
"faithfulSMul_iff_algebraMap_injective",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Module.Free.instFaithfulSMulOfNontrivial",
"Algebra.algebraMap",
"IsTopologicalRing.toIsTopologicalSemiring",
"congrArg",
"CommSemiring.toSemiri... | true |
Lean.Lsp.CompletionOptions.allCommitCharacters?._default | Lean.Data.Lsp.LanguageFeatures | [
"String",
"id",
"Array",
"Option.none",
"Option"
] | false |
CircleDeg1Lift.translationNumber_eq_int_iff | Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | [
"Int.cast",
"Eq.mpr",
"Real",
"Continuous",
"congrArg",
"PseudoMetricSpace.toUniformSpace",
"CircleDeg1Lift.instFunLikeReal",
"Exists",
"CircleDeg1Lift.translationNumber",
"CircleDeg1Lift.translationNumber_of_eq_add_int",
"id",
"Int",
"Real.instAdd",
"funext",
"instHAdd",
"Iff",
"Exi... | true |
Std.DTreeMap.Internal.Impl.isEmpty_inter!_left | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Ord",
"congrArg",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.isEmpty_inter_left",
"id",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Std.DTreeMap.Internal.Impl.inter!",
"Bool.true",
"Std.DTreeMap.Internal.Impl.isEmpty",
"Std.DTreeMap.Internal.Impl.int... | true |
Setoid.eqvGen_of_setoid | Mathlib.Data.Setoid.Basic | [
"Eq.mpr",
"Setoid.completeLattice",
"congrArg",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"id",
"Setoid",
"LE.le",
"CompleteLattice.toCompleteSemilatticeInf",
"le_antisymm",
"Relation.EqvGen.setoid",
"sInf_le",
"Setoid.instPartialOrder",
"Relation.EqvGen.rel",
"Setoid.eqvGen... | true |
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