name string | module string | deps list | allowCompletion bool |
|---|---|---|---|
Std.TreeMap.getElem?_filterMap' | Std.Data.TreeMap.Lemmas | [
"Iff.mpr",
"congrArg",
"Std.TreeMap.getKey_eq",
"Std.TreeMap.getKey",
"Option.some",
"Membership.mem",
"Ordering",
"Eq.rec",
"Option.bind",
"Std.TreeMap.mem_iff_isSome_getElem?",
"Std.TransCmp",
"Bool.true",
"Std.TreeMap.filterMap",
"Std.LawfulEqCmp",
"Std.TreeMap.instMembership",
"Std... | true |
SSet.Truncated.HomotopyCategory.BinaryProduct.functor_comp_inverse | Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal | [
"SSet.Truncated.HomotopyCategory.BinaryProduct.inverse",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"CategoryTheory.eqToHom",
"CategoryTheory.Functor.category",
"SSet.Truncated",
"CategoryTheory.Fun... | true |
Semiquot.mem_bind | Mathlib.Data.Semiquot | [
"Eq.mpr",
"congrArg",
"_private.Mathlib.Data.Semiquot.0.Semiquot.mem_bind._simp_1_1",
"Membership.mem",
"Exists",
"id",
"Semiquot.s",
"Set.mem_iUnion₂",
"funext",
"And",
"Iff",
"Semiquot.instMembership",
"Semiquot",
"Eq",
"Set.instMembership",
"Semiquot.bind",
"Set"
] | true |
StarOrderedRing.rec | Mathlib.Algebra.Order.Star.Basic | [
"HMul.hMul",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"PartialOrder",
"Distrib.toAdd",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"AddSubmonoid",
"LE.le",
"StarAddMonoid.toInvolutiveStar",
"NonUnitalNonAssocSemiring.toAddCommMo... | false |
Function.one_le_const | Mathlib.Algebra.Order.Pi | [
"One",
"Preorder.toLE",
"LE.le",
"Pi.hasLe",
"Iff",
"Pi.instOne",
"Function.const",
"Function.const_le_const",
"One.toOfNat1",
"Nonempty",
"OfNat.ofNat",
"Preorder"
] | true |
IsSemilinearSet.biInter | Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | [
"Eq.mpr",
"AddMonoid.FG",
"congrArg",
"Set.iInter",
"Set.mem_image._simp_1",
"Set.Finite",
"Membership.mem",
"Exists",
"id",
"Set.Finite.image",
"AddCommMonoid",
"forall_exists_index._simp_1",
"And",
"forall_apply_eq_imp_iff₂._simp_1",
"implies_congr",
"IsSemilinearSet",
"IsSemilinea... | true |
Lean.Lsp.RpcConnectParams._sizeOf_1 | Lean.Data.Lsp.Extra | [
"Lean.Lsp.RpcConnectParams.rec",
"Lean.Lsp.RpcConnectParams",
"instOfNatNat",
"Lean.Lsp.DocumentUri",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"String._sizeOf_inst",
"OfNat.ofNat"
] | false |
Rep.norm_comm_apply | Mathlib.RepresentationTheory.Rep.Basic | [
"Rep.V",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"LinearMap.instFunLike",
"Rep.norm",
"Group",
"Rep.instCategory",
"Rep.hV1",
"Eq.mp",
"Representation.IntertwiningMap.instFunLike",... | true |
Frm.ofHom_apply | Mathlib.Order.Category.Frm | [
"FrameHom",
"CategoryTheory.ConcreteCategory.hom",
"Frm.str",
"Frm.ofHom",
"Order.Frame.toCompleteLattice",
"Frm.instConcreteCategoryFrameHomCarrier",
"Frm.carrier",
"FrameHom.instFunLike",
"Frm",
"Order.Frame",
"Frm.of",
"Eq",
"DFunLike.coe",
"Frm.instCategory",
"rfl"
] | true |
Lean.Lsp.Location.recOn | Lean.Data.Lsp.Basic | [
"Lean.Lsp.Location.mk",
"Lean.Lsp.Location",
"Lean.Lsp.DocumentUri",
"Lean.Lsp.Location.rec",
"Lean.Lsp.Range"
] | false |
Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gt | Mathlib.Analysis.Polynomial.Basic | [
"NormedCommRing.toNormedRing",
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.C",
"Polynomial.eval",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"RingHom.instRingHomClass",
"False",
"OrderTopology",
"Filter.tendsto_neg_atBot_atTop",
"WithBot",
"Preorder.toLT",
"instHDiv",
... | true |
CategoryTheory.Limits.Cocone.ext._auto_1 | Mathlib.CategoryTheory.Limits.Cones | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Bicategory.Opposite.op2_associator | Mathlib.CategoryTheory.Bicategory.Opposites | [
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"Opposite.op",
"CategoryTheory.Bicategory.associator",
"CategoryTheory.Iso.symm",
"CategoryTh... | true |
Finset.max_empty | Mathlib.Data.Finset.Max | [
"WithBot",
"Finset",
"LinearOrder",
"Bot.bot",
"Finset.instEmptyCollection",
"Finset.max",
"EmptyCollection.emptyCollection",
"Eq",
"WithBot.bot",
"rfl"
] | true |
ProbabilityTheory.paretoPDFReal.eq_1 | Mathlib.Probability.Distributions.Pareto | [
"Real.instPow",
"Real.instLE",
"Real",
"HMul.hMul",
"Real.instZero",
"ProbabilityTheory.paretoPDFReal",
"LE.le",
"Real.instAdd",
"Real.instOne",
"instHAdd",
"HPow.hPow",
"HAdd.hAdd",
"Real.instMul",
"Real.instNeg",
"One.toOfNat1",
"Zero.toOfNat0",
"Eq.refl",
"Real.decidableLE",
"... | true |
Option.pelim_congr_left | Init.Data.Option.Lemmas | [
"Option.instMembership",
"HEq.refl",
"Option.some",
"Membership.mem",
"Eq.rec",
"Eq.casesOn",
"Option.pelim",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"Option"
] | true |
_private.Init.Data.Range.Polymorphic.SInt.0.Int32.instUpwardEnumerable._proof_3 | Init.Data.Range.Polymorphic.SInt | [
"Int32.maxValue",
"Eq.rec",
"Int",
"LE.le",
"Int32.toInt",
"Nat.cast",
"instHAdd",
"_private.Init.Data.Range.Polymorphic.SInt.0.Int32.maxValueSealed_def",
"HAdd.hAdd",
"Nat",
"_private.Init.Data.Range.Polymorphic.SInt.0.Int32.maxValueSealed",
"Int.instAdd",
"instNatCastInt",
"Eq",
"Int32... | false |
Monoid.CoprodI.lift._proof_3 | Mathlib.GroupTheory.CoprodI | [
"FreeMonoid.lift",
"Monoid",
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"CancelMonoid.toRightCancelMonoid",
"FreeMonoid",
"MonoidHom.instFunLike",
"Equiv.instEquivLike",
"HMul.hMul",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"HEq.refl",
"Prop.le",
"Monoid.CoprodI.... | false |
AddSubmonoid.LocalizationMap.map_add_left | Mathlib.GroupTheory.MonoidLocalization.Maps | [
"Eq.mpr",
"AddSubmonoid.LocalizationMap.map",
"AddSubmonoid.LocalizationMap.map_add_right",
"congrArg",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddSubmonoid.LocalizationMap",
"AddZeroClass.toAddZero",
"id",
"Subtype",
"AddSubmonoid.LocalizationMap.instFunLike",
"AddSubmonoid",
"add_co... | true |
Aesop.Frontend.RuleExpr.noConfusionType | Aesop.Frontend.RuleExpr | [
"Aesop.Frontend.RuleExpr.casesOn",
"Array",
"Aesop.Frontend.RuleExpr",
"Aesop.Frontend.Feature",
"Eq"
] | false |
Lean.Meta.Sym.DSimp.Result._sizeOf_1 | Lean.Meta.Sym.DSimp.DSimpM | [
"Lean.Meta.Sym.DSimp.Result.rec",
"Lean.Meta.Sym.DSimp.Result",
"Lean.Expr",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Bool",
"instAddNat",
"OfNat.ofNat",
"Bool._sizeOf_inst",
"Lean.Expr._sizeOf_inst"
] | false |
Setoid.instPartialOrder._proof_2 | Mathlib.Data.Setoid.Basic | [
"Setoid",
"LE.le",
"Setoid.instLE_mathlib",
"Setoid.r"
] | false |
sInfHom.instPartialOrder | Mathlib.Order.Hom.CompleteLattice | [
"sInfHom.instPartialOrder._proof_1",
"sInfHom.instFunLike",
"PartialOrder",
"InfSet",
"CompleteLattice.toCompleteSemilatticeInf",
"Pi.partialOrder",
"sInfHom",
"CompleteLattice.toCompleteSemilatticeSup",
"CompleteSemilatticeInf.toInfSet",
"CompleteSemilatticeSup.toPartialOrder",
"CompleteLattice... | true |
Subalgebra.mem_toNonUnitalSubalgebra | Mathlib.Algebra.Algebra.Subalgebra.Basic | [
"Subalgebra.instSetLike",
"NonUnitalSubalgebra",
"Iff.rfl",
"Algebra",
"Membership.mem",
"Algebra.toModule",
"CommSemiring",
"Iff",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalSubalgebra.instSetLike",
"Semiring",
"Subalgebra",
"Semiring.toNonAssocSemiring",
"SetLike.instMembe... | true |
MvPolynomial.instFaithfulSMul | Mathlib.Algebra.MvPolynomial.Eval | [
"Iff.mpr",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"faithfulSMul_iff_algebraMap_injective",
"MvPolynomial.algebraMvPolynomial",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Finsupp.instAddMonoid",
"AddMonoidAlgebra.commSemiring",
"Algebra",
"Nat.instAddMonoid",
"RingHom",
"... | true |
zpow_left_inj₀ | Mathlib.Algebra.Order.GroupWithZero.Basic | [
"GroupWithZero.toMonoidWithZero",
"zpow_left_injOn₀",
"GroupWithZero.toDivInvMonoid",
"MulZeroClass.toMul",
"Set.InjOn.eq_iff",
"LinearOrder",
"PartialOrder.toPreorder",
"GroupWithZero",
"setOf",
"DivInvMonoid.toZPow",
"Preorder.toLE",
"Ne",
"Int",
"LE.le",
"MulPosMono",
"Iff",
"Mono... | true |
LieIdeal.comap_incl_self | Mathlib.Algebra.Lie.Ideal | [
"LieHom",
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"CommRing",
"LieRing.toAddCommGroup",
"LieSubmodule.instTop",
"congrArg",
"LieSubmodule",
"Membership.mem",
"SetLike.coe_mem._simp_1",
"Subtype",
"LieSubmodule.mem_top._simp_1",
"LieSubmodule.ext",
"iff_self",
"LieRing",
"Lie... | true |
Std.IterM.anyM_pure | Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop | [
"Pure.pure",
"congrArg",
"Monad.toApplicative",
"ULift",
"Std.IteratorLoop",
"Std.Iterators.Finite",
"Std.IterM.any_eq_anyM",
"LawfulMonad",
"Applicative.toPure",
"Std.Iterator",
"True",
"Std.LawfulIteratorLoop",
"eq_self",
"Bool",
"of_eq_true",
"Std.IterM",
"ULift.up",
"Monad",
... | true |
hasFDerivWithinAt_univ._simp_1 | Mathlib.Analysis.Calculus.FDeriv.Basic | [
"HasFDerivAt",
"AddCommGroup.toAddCommMonoid",
"Set.univ",
"HasFDerivWithinAt",
"NormedField.toField",
"AddCommGroup",
"Field.toSemifield",
"ContinuousLinearMap",
"TopologicalSpace",
"Semifield.toDivisionSemiring",
"propext",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
"Nontr... | false |
NonUnitalAlgHom.lmul._proof_4 | Mathlib.Algebra.Algebra.Bilinear | [
"instSMulOfMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.toAddHom",
"NonUnitalAlgHom.lmul._proof_1",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"AddHom.map_... | false |
MonomialOrder.sPolynomial.eq_1 | Mathlib.RingTheory.MvPolynomial.MonomialOrder | [
"Nat.instCanonicallyOrderedAdd",
"Nat.instMulZeroClass",
"Nat.instOrderedSub",
"CommRing",
"Semiring.toModule",
"HMul.hMul",
"AddMonoidAlgebra.addAddCommMonoid",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"MonomialOrder.leadingCoeff",
"AddMonoid.toAddZeroClass",
"MvPolynomial.mon... | true |
MeasureTheory.le_measureReal_sdiff._auto_1 | Mathlib.MeasureTheory.Measure.Real | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.ShortComplex.RightHomologyMapData.id._proof_4 | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.RightHomologyData",
"congrArg",
"CategoryTheory.ShortComplex",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.Category.comp_... | false |
Finmap.replace._proof_1 | Mathlib.Data.Finmap | [
"Iff.mpr",
"AList.toFinmap_eq",
"AList.perm_replace",
"List.Perm",
"AList.replace",
"AList",
"Eq",
"AList.toFinmap",
"Sigma",
"Finmap",
"DecidableEq",
"AList.entries"
] | false |
Lean.Elab.WF.GuessLex.instInhabitedBasicMeasure.default | Lean.Elab.PreDefinition.WF.GuessLex | [
"Inhabited.default",
"Lean.Elab.WF.GuessLex.BasicMeasure",
"Lean.Expr",
"Lean.Elab.instInhabitedTerminationMeasure",
"Lean.instInhabitedExpr",
"Lean.Elab.TerminationMeasure",
"Lean.Elab.WF.GuessLex.BasicMeasure.mk"
] | true |
RingEquiv.prodCongr | Mathlib.Algebra.Ring.Equiv | [
"Prod.instMul",
"Prod.instAdd",
"RingEquiv.instEquivLike",
"RingEquiv.prodCongr._proof_1",
"RingEquiv.prodCongr._proof_2",
"Equiv",
"Distrib.toAdd",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"RingEquiv.mk",
"RingEquiv",
"Prod",
"Equiv.prodCongr",
"NonUnitalNonAssocSemiring",
... | true |
ULift.nonAssocRing._proof_3 | Mathlib.Algebra.Ring.ULift | [
"AddMonoid.toZero",
"ULift",
"ULift.nonAssocSemiring",
"instOfNatNat",
"NonAssocRing",
"NatCast.natCast",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"NonAssocSemiring.toNatCast",
"OfNat.ofN... | false |
_private.Mathlib.Algebra.Homology.ExactSequence.0.CategoryTheory.ComposableArrows.exact₂_iff._proof_1_9 | Mathlib.Algebra.Homology.ExactSequence | [
"_private.Mathlib.Algebra.Homology.ExactSequence.0.CategoryTheory.ComposableArrows.exact₂_iff._proof_1_6",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ComposableArrows.IsComplex",
"CategoryTheory.ComposableArrows.map'._proof_8",
"Part... | false |
MeasureTheory.lpTrimToLpMeas | Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable | [
"NormedCommRing.toNormedRing",
"Submodule",
"MeasureTheory.Measure",
"MeasurableSpace.instLE",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"MeasureTheory.lpMeasSubgroup._proof_1",
"AddCommGroup.toAddCommMonoid",
"MeasureTheory.AEEqFun.cast",
"MeasureTheory.Lp.instModule",
"NormedSpace.toModule... | true |
Filter.inf_liminf | Mathlib.Order.LiminfLimsup | [
"Filter.liminf",
"Filter.NeBot",
"Order.Coframe.toCompleteLattice",
"CompleteDistribLattice",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeInf.toMin",
"CompleteDistribLattice.toCoframe",
"Filter.sup_limsup",
"OrderDual.instCompleteDistribLattice",
"ConditionallyCompleteLattice.toL... | true |
_private.Mathlib.Order.Filter.Extr.0.IsMinFilter.bicomp_mono.match_1_1 | Mathlib.Order.Filter.Extr | [
"setOf",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"Set.instInter",
"Inter.inter",
"And.casesOn",
"And.intro",
"Set.instMembership",
"Preorder",
"Set"
] | false |
Differentiable.sigmoid | Mathlib.Analysis.SpecialFunctions.Sigmoid | [
"Differentiable",
"InnerProductSpace.toNormedSpace",
"Real",
"Semiring.toModule",
"NormedSpace",
"Real.denselyNormedField",
"Real.instRCLike",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Function.comp",
"NormedField.toField",
"Real.normedAddCommGroup",
"Real.instAddCommGroup... | true |
AddOpposite.instRightCancelSemigroup._proof_1 | Mathlib.Algebra.Group.Opposite | [
"Semigroup.toMul",
"HMul.hMul",
"AddOpposite",
"RightCancelSemigroup.toSemigroup",
"AddOpposite.unop",
"RightCancelSemigroup",
"Eq",
"AddOpposite.instMul",
"rfl",
"instHMul"
] | false |
TopologicalSpace.Clopens.coe_disjoint | Mathlib.Topology.Sets.Closeds | [
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"TopologicalSpace.Clopens.instBooleanAlgebra",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"TopologicalSpace.Clopens.instPartialOrder",
"Preorder.toLE",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toConditionallyComp... | true |
StarModule.decomposeProdAdjoint_apply | Mathlib.Algebra.Star.Module | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"DistribMulAction.toDistribSMul",
"StarModule.decomposeProdAdjoint",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"StarMul",
"Nat.instAtLeastTwoHAddOfNat",
"LinearMap.instFunLike",
"AddCommGroup.toAddGroup",
"selfAdjointPart",
"Membership... | true |
inv_mul_le_iff_le_mul' | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"Eq.mpr",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"CommMonoid.toCommSemigroup",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"Iff.rfl",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulLeftMono",
"id",
"MulOne.toMul",
"DivInvMonoid.toMon... | true |
CategoryTheory.Limits.KernelFork.mapIsLimit | Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesLimit",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.KernelFork",
"CategoryTheory.Functor.comp",
... | true |
TensorProduct.lift._proof_1 | Mathlib.LinearAlgebra.TensorProduct.Basic | [
"TensorProduct.liftAux._proof_2",
"ZeroHom.toFun",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"TensorProduct.liftAux",
"RingHom",
"AddMonoidHom.toZeroHom",
"AddZeroClass.toAddZero",
"LinearMap.module",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"instHAdd",
... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.getKeyD_modify_self._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
ContinuousMap.HomotopyWith.coeFn_injective | Mathlib.Topology.Homotopy.Basic | [
"Real",
"ContinuousMap",
"Set.Elem",
"ContinuousMap.HomotopyWith.instFunLike",
"ContinuousMap.HomotopyWith",
"TopologicalSpace",
"DFunLike.coe_injective",
"Function.Injective",
"Prod",
"DFunLike.coe",
"unitInterval"
] | true |
Aesop.RuleTacDescr.cases.elim | Aesop.RuleTac.Descr | [
"PULift.up",
"Aesop.RuleTacDescr.ctorElim",
"Aesop.RuleTacDescr",
"Lean.Meta.TransparencyMode",
"Array",
"Aesop.RuleTacDescr.ctorIdx",
"Nat",
"Bool",
"Aesop.RuleTacDescr.cases",
"Aesop.CasesTarget",
"Eq.symm",
"Eq",
"Aesop.CtorNames"
] | false |
_private.Mathlib.Analysis.SpecialFunctions.Gamma.Basic.0.Mathlib.Meta.Positivity.evalGamma._proof_1 | Mathlib.Analysis.SpecialFunctions.Gamma.Basic | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"PLift",
"Lean.Expr.sort",
"Lean.Level",
"PLift.down",
"List.cons",
"Qq.Quoted",
"Lean.Level.zero",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Level.instOfNat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"List.nil"
] | false |
Set.insert_eq_self._simp_1 | Mathlib.Data.Set.Insert | [
"Membership.mem",
"Insert.insert",
"Set.instInsert",
"propext",
"Set.insert_eq_self",
"Eq",
"Set.instMembership",
"Set"
] | false |
PNat.natPred.eq_1 | Mathlib.Data.PNat.Basic | [
"PNat.val",
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"instHSub",
"Nat",
"PNat.natPred",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"PNat"
] | true |
Lean.Doc.Parser.instReprUnorderedListType.repr | Lean.DocString.Parser | [
"Std.Format.group",
"GE.ge",
"instOfNatNat",
"Int",
"instLENat",
"_private.Lean.DocString.Parser.0.Lean.Doc.Parser.instReprUnorderedListType.repr.match_1",
"Unit",
"instOfNat",
"Nat",
"Std.Format",
"Repr.addAppParen",
"Lean.Doc.Parser.UnorderedListType",
"OfNat.ofNat",
"Nat.decLe",
"Std.... | true |
Matrix.swap | Mathlib.LinearAlgebra.Matrix.Swap | [
"One",
"Matrix",
"Equiv.swap",
"Equiv.Perm.permMatrix",
"DecidableEq",
"Zero"
] | true |
_private.Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four.0.CategoryTheory.Abelian.mono_of_epi_of_epi_mono'._proof_1_1 | Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.sub_nonne... | false |
String.Pos.cast_lt_cast_iff._simp_1 | Init.Data.String.Basic | [
"String.Pos.cast_lt_cast_iff",
"String",
"String.instLTPos",
"LT.lt",
"propext",
"String.Pos.cast",
"String.Pos",
"Eq"
] | false |
lowerClosure_iUnion | Mathlib.Order.UpperLower.Closure | [
"LowerSet.completeLattice",
"iSup",
"Preorder.toLE",
"GaloisConnection.l_iSup",
"LowerSet.instSupSet",
"SetLike.coe",
"CompleteBooleanAlgebra.toCompleteLattice",
"LowerSet",
"Eq",
"gc_lowerClosure_coe",
"lowerClosure",
"Set.iUnion",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
... | true |
Lean.Elab.Term.Do.Code.brecOn_5.eq | Lean.Elab.Do.Legacy | [
"Lean.Elab.Term.Do.Code.below_2",
"Lean.Elab.Term.Do.Code.below",
"Lean.Elab.Term.Do.Code.brecOn_5",
"Lean.Elab.Term.Do.Code.below_6",
"Lean.Elab.Term.Do.Code.brecOn_5.go",
"Lean.Syntax",
"Lean.Elab.Term.Do.Var",
"Lean.Elab.Term.Do.Code.below_1",
"Lean.Elab.Term.Do.Code.below_3",
"Lean.Elab.Term.D... | true |
CategoryTheory.PreOneHypercover.inter | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"CategoryTheory.PreZeroHypercover.bind",
"CategoryTheory.PreOneHypercover.inter._proof_3",
"CategoryTheory.PreOneHypercover.inter._proof_7",
"CategoryTheory.Limits.pullback",
"CategoryTheory.PreZeroHypercover.inter",
"CategoryTheory.PreZeroHypercover.f",
"Equiv.instEquivLike",
"CategoryTheory.PreOneHy... | true |
Bool.or_eq_false_iff | Init.Data.Bool | [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.true",
"And",
"Iff",
"Bool",
"Bool.or",
"Eq.refl",
"instDecidableAnd",
"Bool.false",
"Decidable.decide",
"Eq",
"instDecidableIff"
] | true |
_private.Mathlib.Data.Nat.Factors.0.Nat.isChain_cons_primeFactorsList.match_1_1 | Mathlib.Data.Nat.Factors | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
NonemptyInterval.instLinearOrderLex | Mathlib.Order.Interval.Lex | [
"LinearOrder.toOrd",
"NonemptyInterval.toDualProd",
"Preorder.toLT",
"Max.mk",
"Equiv.instEquivLike",
"LinearOrder.toDecidableEq",
"Lex",
"compareLex",
"NonemptyInterval.instLinearOrderLex._proof_5",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ord.mk",
"Min.mk",
"Semilatt... | true |
WithVal.ctorIdx | Mathlib.Topology.Algebra.Valued.WithVal | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"LinearOrderedCommGroupWithZero",
"WithVal",
"Nat",
"Ring",
"Valuation"
] | false |
TopCat.GlueData.MkCore.mk.inj | Mathlib.Topology.Gluing | [
"Lattice.toSemilatticeSup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopCat.GlueData.MkCore.mk.noConfusion",
"CompleteLattice.toLattice",
"TopologicalSpace.Opens.instCompleteLattice",
"TopologicalSpace.Opens.instPartialOrder",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCatego... | true |
SemiNormedGrp₁.Hom.normNoninc | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"SemiNormedGrp₁",
"SemiNormedGrp₁.Hom",
"SemiNormedGrp₁.carrier",
"SemiNormedGrp₁.str",
"NormedAddGroupHom.NormNoninc",
"SemiNormedGrp₁.Hom.hom'"
] | true |
LinearEquiv.isIsotypicOfType_iff_type | Mathlib.RingTheory.SimpleModule.Isotypic | [
"LinearEquiv.symm",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"IsIsotypicOfType.of_linearEquiv_type",
"Iff",
"RingHomInvPair.ids",
"LinearEquiv",
"Iff.intro",
"IsIsotypicOfType",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Ring"
] | true |
RelIso.default_def | Mathlib.Order.RelIso.Basic | [
"Inhabited.default",
"RelIso.refl",
"RelIso",
"RelIso.instInhabited",
"Eq",
"rfl"
] | true |
_private.Mathlib.MeasureTheory.Covering.Besicovitch.0.Besicovitch.exist_disjoint_covering_families._simp_1_11 | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Membership.mem",
"SDiff.sdiff",
"And",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.mem_sdiff",
"Set.instSDiff",
"Set"
] | false |
Qq.Impl.MVarSynth.type.noConfusion | Qq.Macro | [
"Qq.Impl.MVarSynth.type",
"Lean.MVarId",
"id",
"Qq.Impl.MVarSynth.noConfusion",
"Eq",
"Qq.Impl.MVarSynth"
] | false |
CommSemigroup.noConfusion | Mathlib.Algebra.Group.Defs | [
"CommSemigroup.noConfusionType",
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"HEq.refl",
"CommSemigroup",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"CommSemigroup.casesOn",
"Eq",
"instHMul"
] | false |
_private.Mathlib.RingTheory.Etale.Field.0.Algebra.FormallyEtale.equivPiOfIsSepClosed._proof_4 | Mathlib.RingTheory.Etale.Field | [
"CommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"isArtinian_of_fg_of_artinian'",
"Algebra.FormallyEtale",
"DivisionRing.instIsArtinianRing",
"Algebra",
"Algebra.toSMul",
"Algebra.EssFiniteType",
"Field.toDivisionRing",
"inferInstance",
"Algebra.toModule",
... | false |
closure_subset_mul_self_of_mem_nhds_one | Mathlib.Topology.Algebra.Group.Pointwise | [
"Filter.instMembership",
"Iff.mpr",
"Eq.mpr",
"MulOne.toOne",
"instHDiv",
"InvOneClass.toOne",
"HMul.hMul",
"mem_closure_iff_nhds",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"ContinuousAt.preimage_mem_nhds",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
... | true |
Std.Internal.instInhabitedIndexMultiMap._proof_1 | Std.Http.Internal.IndexMultiMap | [
"False",
"False.elim",
"Array.instMembership",
"Membership.mem",
"Eq.mp",
"instOfNatNat",
"Std.HashMap",
"Std.HashMap.get",
"List.toArray",
"Array",
"Std.HashMap.not_mem_emptyWithCapacity._simp_1",
"GT.gt",
"And",
"Nat",
"LT.lt",
"Hashable",
"instLTNat",
"Std.HashMap.emptyWithCapac... | false |
SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Prod___unexpand_SimpleGraph_boxProd_1 | Mathlib.Combinatorics.SimpleGraph.Prod | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
CommMonCat.instCoeMonCat.eq_1 | Mathlib.Algebra.Category.MonCat.Basic | [
"MonoidHom.instFunLike",
"CommMonCat.instConcreteCategoryMonoidHomCarrier",
"MonoidHom",
"Monoid.toMulOneClass",
"Coe.mk",
"CommMonCat.str",
"MonCat",
"CommMonCat.instCoeMonCat",
"MonCat.instCategory",
"CommMonCat.hasForgetToMonCat",
"CommMonCat.carrier",
"MonCat.carrier",
"MulOneClass.toMul... | true |
_private.Mathlib.Algebra.BigOperators.Intervals.0.Fin.prod_Iic_div._proof_1_16 | Mathlib.Algebra.BigOperators.Intervals | [
"dite_cond_eq_true",
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"Lean.Grind.CommRing.le_norm_expr",
"instNeZeroNatHAdd_1",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"dite_congr",
"instHDiv",
"InvOneClass.toOne",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
... | false |
TensorProduct.equivOfCompatibleSMul._proof_5 | Mathlib.LinearAlgebra.TensorProduct.Basic | [
"LinearMap.toAddMonoidHom",
"TensorProduct.liftAux._proof_2",
"TensorProduct.CompatibleSMul",
"AddMonoidHom.instAddMonoidHomClass",
"Equiv.instEquivLike",
"TensorProduct.mapOfCompatibleSMul._proof_3",
"TensorProduct.mapOfCompatibleSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
... | false |
Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.coreToInt.noConfusion | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Expr",
"id",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.noConfusion",
"Int.Linear.Expr",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.coreToInt",
"Eq",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof"
] | false |
Set.iUnion_sum | Mathlib.Data.Set.Lattice | [
"Set.instUnion",
"Sum",
"Sum.inl",
"Sum.inr",
"CompleteBooleanAlgebra.toCompleteLattice",
"Union.union",
"Eq",
"Set.iUnion",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
"Set.instCompleteAtomicBooleanAlgebra",
"iSup_sum",
"Set"
] | true |
String.Pos.utf8ByteSize_byte | Init.Data.String.Basic | [
"String.toSlice",
"String.Pos.get._proof_2",
"String.Pos.byte",
"String",
"String.Pos.toSlice",
"UInt8.utf8ByteSize",
"Ne",
"String.Pos.isUTF8FirstByte_byte",
"Nat",
"String.endPos",
"String.Pos",
"String.Slice.Pos.utf8ByteSize_byte",
"Eq",
"Char.utf8Size",
"String.Pos.get"
] | true |
Set.image_mul_left_Ioo | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"GroupWithZero.toMonoidWithZero",
"Preorder.toLT",
"HMul.hMul",
"MulZeroClass.toMul",
"PartialOrder.toPreorder",
"GroupWithZero",
"PartialOrder",
"OrderIso.mulLeft₀",
"MonoidWithZero.toMulZeroOneClass",
"PosMulReflectLT",
"LT.lt",
"Zero.toOfNat0",
"Set.image",
"MulZeroOneClass.toMulZeroCla... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.maxKeyD_modify_eq_maxKeyD._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 |
_private.Mathlib.RingTheory.NoetherNormalization.0.NoetherNormalization.hom2._proof_3 | Mathlib.RingTheory.NoetherNormalization | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"instSMulOfMul",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"IsScalarTower",
"AddMonoidAlgebra.algebra",
"Polynomial.algebraOfAlgebra",
"Finsupp.instAddMonoid",
"Nat.instAddMonoid",
"Algebra.toSMul",
"Field.toDivisionRing",
"Algebra... | false |
Except.bind.eq_2 | Init.Control.Lawful.MonadLift.Instances | [
"Except.ok",
"Except.bind",
"Eq.refl",
"Except",
"Eq"
] | true |
Finset.fold_sup_bot_singleton | Mathlib.Data.Finset.Fold | [
"instCommutativeMax_mathlib",
"Finset.instGeneralizedBooleanAlgebra",
"Lattice.toSemilatticeSup",
"instAssociativeMax_mathlib",
"Finset",
"Finset.fold",
"SemilatticeSup.toMax",
"Finset.fold_union_empty_singleton",
"Bot.bot",
"GeneralizedBooleanAlgebra.toBot",
"Max.max",
"Finset.instLattice",
... | true |
CFC.nnrpow._proof_2 | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | [
"Real",
"instSMulOfMul",
"NNReal.instSMulOfReal",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"AddZeroClass.toAddZero",
"Real.semiring",
"NonUnitalNonA... | false |
_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0.CategoryTheory.ComposableArrows.homMk._proof_7 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"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",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.ev... | false |
_private.Mathlib.Algebra.Order.Ring.WithTop.0.WithBot.instNoZeroDivisors._proof_1 | Mathlib.Algebra.Order.Ring.WithTop | [
"WithBot",
"MulZeroClass.toMul",
"WithBot.instMulZeroClass",
"WithBot.zero",
"MulZeroClass",
"NoZeroDivisors",
"WithTop.instNoZeroDivisors",
"MulZeroClass.toZero",
"DecidableEq"
] | false |
Lean.Elab.Tactic.Omega.Justification.toString._f | Lean.Elab.Tactic.Omega.Core | [
"Lean.Elab.Tactic.Omega.Justification.combine",
"Lean.Elab.Tactic.Omega.Justification.below",
"Lean.Omega.Constraint.combo",
"Lean.Omega.bmod_coeffs",
"Lean.Omega.Coeffs.combo",
"Lean.Omega.tidyCoeffs",
"String",
"Lean.Omega.Constraint.exact",
"instToStringList",
"Lean.Elab.Tactic.Omega.Justificat... | false |
dec_em' | Mathlib.Logic.Basic | [
"Decidable",
"Or.symm",
"Or",
"Not",
"dec_em"
] | true |
ULift.mulOneClass.eq_1 | Mathlib.Algebra.Group.ULift | [
"MulOne.toOne",
"Equiv.instEquivLike",
"ULift.commSemigroup._proof_1",
"ULift",
"Equiv.ulift",
"Equiv",
"MulOne.toMul",
"ULift.one",
"ULift.mulOneClass._proof_1",
"ULift.mul",
"MulOneClass.toMulOne",
"Function.Injective.mulOneClass",
"Eq.refl",
"ULift.mulOneClass",
"MulOneClass",
"Eq",... | true |
_private.Init.Data.Vector.Lemmas.0.Vector.map_inj._simp_1_3 | Init.Data.Vector.Lemmas | [
"Array.replicate",
"Array.instMembership",
"Membership.mem",
"Ne",
"instOfNatNat",
"Array.mem_replicate",
"Array",
"And",
"Nat",
"propext",
"OfNat.ofNat",
"Eq"
] | false |
IsUnit.isQuotientMap_nsmul | Mathlib.Topology.Algebra.ConstMulAction | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"instHSMul",
"AddMonoidHom.instAddMonoidHomClass",
"Monoid.toMulOneClass",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"IsUnit",
"AddZeroClass.toAddZero",
"IsUnit.isQuotien... | true |
Set.Ioi.eq_1 | Mathlib.Order.Interval.Set.Defs | [
"Set.Ioi",
"Preorder.toLT",
"setOf",
"LT.lt",
"Eq.refl",
"Eq",
"Preorder",
"Set"
] | true |
LinearPMap.instSubtractionCommMonoid._proof_3 | Mathlib.LinearAlgebra.LinearPMap | [
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toZero",
"RingHom",
"AddCommGroup",
"Int",
"LinearPMap.instAddMonoid",
"zsmulRec",
"LinearPMap",
"instOfNat",
"nsmulRec",
"LinearPMap.instZero",
"Zero.toOfNat0",
"Eq.refl",
"LinearPMap.instNeg",
"LinearPMap.instAdd",
"Module",
"OfNat.ofNat",... | false |
TensorProduct.assoc._proof_5 | Mathlib.LinearAlgebra.TensorProduct.Associator | [
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"CommMonoid.toMonoid",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"TensorProduct",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMonoid.toAddMonoid",
"Mod... | false |
IsLocalRing.ResidueField.mapAlgEquiv._proof_6 | Mathlib.RingTheory.LocalRing.ResidueField.Basic | [
"MulOne.toOne",
"CommRing",
"AlgEquiv.toAlgHom",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AlgHom.commutes'",
"IsLocalRing.ResidueField.algebra",
"Algebra",
"RingHom",
"IsLocalRing.ResidueField.field",
"NonAssocSemiring.toMulZeroOneClass",
"IsLocalRing",
"Field.toSemifield",
"IsLoc... | false |
AddHomClass.toAddHom.congr_simp | Mathlib.Algebra.DirectSum.Module | [
"AddHom",
"Eq.rec",
"AddHomClass.toAddHom",
"AddHomClass",
"Eq.refl",
"Eq",
"Add",
"FunLike"
] | true |
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