name string | module string | deps list |
|---|---|---|
_private.Mathlib.Algebra.Lie.Weights.IsSimple.0.LieAlgebra.IsKilling.chi_not_in_q_aux.match_1_3 | Mathlib.Algebra.Lie.Weights.IsSimple | [
"LieAlgebra.toModule",
"LieSubalgebra.lieAlgebra",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"LieRing.toAddCommGroup",
"LieSubalgebra.instSetLike",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Finset",
"LinearMap.addCommGroup",
"HSub.hSub",
"lieAlgebraSelfModule",
"AddC... |
AdjoinRoot.mapAlgEquiv._proof_6 | Mathlib.RingTheory.AdjoinRoot | [
"AlgEquiv.instEquivLike",
"CommRing",
"Dvd.dvd",
"Associated.dvd",
"CommSemiring.toSemiring",
"semigroupDvd",
"Algebra",
"AlgEquivClass.toAlgHomClass",
"AdjoinRoot.mapAlgEquiv._proof_2",
"Polynomial",
"Associated.symm",
"CommRing.toCommSemiring",
"AlgEquiv.instAlgEquivClass",
"Associated",... |
Associates.isUnit_iff_eq_one | Mathlib.Algebra.GroupWithZero.Associated | [
"Units.val",
"Associates.instCommMonoid",
"IsUnit",
"Units",
"Eq.rec",
"Iff",
"Associates.coe_unit_eq_one",
"isUnit_one",
"Associates",
"CommMonoid.toMonoid",
"_private.Mathlib.Algebra.GroupWithZero.Associated.0.Associates.isUnit_iff_eq_one.match_1_1",
"Iff.intro",
"One.toOfNat1",
"OfNat.o... |
mul_lt_mul_of_neg_left | Mathlib.Algebra.Order.Ring.Unbundled.Basic | [
"add_mul",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Trans.trans",
"Preorder.toLT",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"MulZeroClass.toMul",
"add_left_comm",
"congrArg",
"add_assoc",
"MulZeroClass.zero_mul",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddRig... |
MonCat.Colimits.descFunLift.eq_3 | Mathlib.Algebra.Category.MonCat.Colimits | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"HMul.hMul",
"Monoid.toMulOneClass",
"MonCat.Colimits.Prequotient",
"MulOne.toMul",
"MonCat",
"MonCat.instCategory",
"MonCat.carrier",
"MulOneClass.toMulOne",
"Eq.refl",
"MonCat.Colimits.Prequotient.mul",
"Eq",
"MonCat.str",
"MonC... |
_private.Mathlib.Algebra.Group.Finsupp.0.Finsupp.addCommute_of_disjoint._simp_1_2 | Mathlib.Algebra.Group.Finsupp | [
"Finset",
"Disjoint",
"Finset.partialOrder",
"Finset.instEmptyCollection",
"Inter.inter",
"Finset.instInter",
"Finset.disjoint_iff_inter_eq_empty",
"propext",
"EmptyCollection.emptyCollection",
"Finset.instOrderBot",
"Eq",
"DecidableEq"
] |
_private.Mathlib.Algebra.Category.CommAlgCat.Basic.0.CommAlgCat.mk._flat_ctor | Mathlib.Algebra.Category.CommAlgCat.Basic | [
"CommRing",
"CommSemiring.toSemiring",
"Algebra",
"CommRing.toCommSemiring",
"_private.Mathlib.Algebra.Category.CommAlgCat.Basic.0.CommAlgCat.mk",
"CommAlgCat"
] |
CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.Functor",
"PartialOrder.toPreorder",
"GaloisConnection.toGaloisInsertion",
"CategoryTheory.Sieve",
"CategoryTheory.Sieve.essSurjFullFunctorGaloisInsertion._proof_1",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"CategoryTheory.Sieve.functorPushfo... |
extChartAt_target_eventuallyEq_of_mem | Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | [
"extChartAt",
"NormedSpace",
"PartialEquiv.target",
"nhdsWithin",
"PseudoMetricSpace.toUniformSpace",
"nhdsWithin_eq_iff_eventuallyEq",
"Membership.mem",
"nhds",
"Filter.EventuallyEq",
"ModelWithCorners.toFun'",
"TopologicalSpace",
"ModelWithCorners",
"SeminormedAddCommGroup.toPseudoMetricSp... |
_private.Mathlib.Algebra.Polynomial.RuleOfSigns.0.List.filter.match_1.eq_1 | Mathlib.Algebra.Polynomial.RuleOfSigns | [
"Unit.unit",
"List.filter.match_1",
"Bool.true",
"Unit",
"Bool",
"Eq.refl",
"Bool.false",
"Eq"
] |
_private.Std.Data.DHashMap.Internal.WF.0.Std.DHashMap.Internal.AssocList.foldrM.eq_2 | Std.Data.DHashMap.Internal.WF | [
"Std.DHashMap.Internal.AssocList.foldrM",
"Monad.toBind",
"Eq.refl",
"Std.DHashMap.Internal.AssocList",
"Bind.bind",
"Std.DHashMap.Internal.AssocList.cons",
"Monad",
"Eq"
] |
Mathlib.Notation3.mkFoldlMatcher | Mathlib.Util.Notation3 | [
"Pure.pure",
"OptionT.instMonad",
"Lean.TSyntax",
"OptionT",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.Quote.quote",
"Array.push",
"Lean.Elab.Term.instMonadTermElabM",
"String",
"Lean.SourceInfo",
"Lean.Syntax.node5",
"Lea... |
_private.Lean.Compiler.CSimpAttr.0.Lean.Compiler.CSimp.isConstantReplacement?._sparseCasesOn_1 | Lean.Compiler.CSimpAttr | [
"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"
] |
algebraMap_comp_natCast | Mathlib.Algebra.Algebra.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"congrArg",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Function.comp",
"algebraMap",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Nat.cast",
"CommSemiring",
"funext",
"RingHom.instFun... |
ArchimedeanClass.stdPart_eq_sSup | Mathlib.Algebra.Order.Ring.StandardPart | [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"AddGroup.toSubtractionMonoid",
"Set.ext",
"Eq.mpr",
"NegZeroClass.toNeg",
"Real.partialOrder",
"Real",
"IsDomain.to_noZeroDivisors",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"AddLeftCancelSemigroup.toIsLeftCancelAdd... |
Fintype.prod_empty | Mathlib.Algebra.BigOperators.Group.Finset.Defs | [
"MulOne.toOne",
"Finset.univ",
"Monoid.toMulOneClass",
"Finset.prod_of_isEmpty",
"IsEmpty",
"Finset.prod",
"MulOneClass.toMulOne",
"Fintype",
"CommMonoid.toMonoid",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"CommMonoid"
] |
instAddCommMonoidFormalMultilinearSeries._proof_6 | Mathlib.Analysis.Calculus.FormalMultilinearSeries | [
"instHSMul",
"instAddCommMonoidFormalMultilinearSeries._proof_5",
"AddMonoid.toAddSemigroup",
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul",
"Add.mk",
"AddMonoid.toAddZeroClass",
"ContinuousMultilinearMap.addCommMonoid",
"AddMonoid.toNSMul",
"AddMonoid.mk",
"instAddCommMonoidFormal... |
CategoryTheory.Limits.WidePushout.head | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.widePushout",
"CategoryTheory.Limits.WidePushoutShape.wideSpan",
"CategoryTheory.Limits.WidePushoutShape.category",
"Option.none",
"CategoryTheory.Limits.HasWidePushout",
"CategoryTheory.Category.toCategoryStruct",
"Categ... |
BooleanSubalgebra.mem_comap | Mathlib.Order.BooleanSubalgebra | [
"BooleanAlgebra",
"BooleanSubalgebra",
"BoundedLatticeHom.instFunLike",
"Iff.rfl",
"Membership.mem",
"BooleanAlgebra.toBoundedOrder",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
"Iff",
"BoundedLatticeHom",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra",
"Boole... |
Std.TreeSet.get!_insertMany_list_of_mem | Std.Data.TreeSet.Lemmas | [
"Std.TreeSet",
"Std.TreeSet.get!",
"instForInOfForIn'",
"Membership.mem",
"Ordering",
"inferInstance",
"Std.TreeSet.inner",
"Std.TransCmp",
"Id",
"Membership",
"List",
"List.instMembership",
"Inhabited",
"Std.TreeSet.insertMany",
"Id.instMonad",
"Eq",
"Std.TreeMap.getKey!_insertManyI... |
Int.gcd_sub_right_right_of_dvd | Init.Data.Int.Gcd | [
"Int.gcd",
"Dvd.dvd",
"HMul.hMul",
"HSub.hSub",
"Int",
"Int.gcd_sub_mul_left_right",
"Int.instDvd",
"Int.instMul",
"instHSub",
"Exists.casesOn",
"Nat",
"Eq.ndrec",
"Int.instSub",
"Eq.symm",
"Eq",
"instHMul"
] |
Representation.coinvariantsToFinsupp._proof_1 | Mathlib.RepresentationTheory.Coinvariants | [
"Finsupp.instFunLike",
"CommRing",
"Representation",
"MonoidHom.instFunLike",
"Finsupp.module",
"Finsupp.ext",
"Monoid.toMulOneClass",
"LinearMap.ext",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Module.End.instSemiring",
"LinearMap.i... |
Lean.Meta.coeDeclAttr._regBuiltin.Lean.Meta.coeDeclAttr.declRange_3 | Lean.Meta.Coe | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"IO",
"Lean.Name.mkStr3",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk"
] |
_private.Mathlib.MeasureTheory.Function.ConditionalLExpectation.0.MeasureTheory.measurable_condLExp'._simp_1_1 | Mathlib.MeasureTheory.Function.ConditionalLExpectation | [
"Measurable",
"Pi.instZero",
"MeasurableSpace",
"measurable_zero",
"True",
"eq_true",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Zero"
] |
_private.Mathlib.Topology.Sets.CompactOpenCovered.0.IsCompactOpenCovered.exists_mem_of_isBasis._simp_1_8 | Mathlib.Topology.Sets.CompactOpenCovered | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] |
Subalgebra.algebraicClosure | Mathlib.RingTheory.Algebraic.Integral | [
"IsDomain",
"CommRing",
"IsAlgebraic",
"Subsemigroup.mk",
"CommSemiring.toSemiring",
"setOf",
"Algebra",
"Subalgebra.algebraicClosure._proof_4",
"MulOne.toMul",
"Subalgebra.algebraicClosure._proof_3",
"Subalgebra.algebraicClosure._proof_1",
"NonAssocSemiring.toMulZeroOneClass",
"MulZeroOneCl... |
Submodule.orthogonal_disjoint | Mathlib.Analysis.InnerProductSpace.Orthogonal | [
"InnerProductSpace.toNormedSpace",
"Submodule",
"congrArg",
"OrderBot.toBot",
"Submodule.completeLattice",
"NormedSpace.toModule",
"_private.Mathlib.Analysis.InnerProductSpace.Orthogonal.0.Submodule.orthogonal_disjoint._simp_1_1",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"Pre... |
_private.Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer.0.CategoryTheory.Limits.WalkingMultispan.functorExt.match_1.eq_1 | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.WalkingMultispan.functorExt.match_1",
"CategoryTheory.Limits.WalkingMultispan",
"CategoryTheory.Limits.MultispanShape.L",
"CategoryTheory.Limits.MultispanShape",
"CategoryTheory.Limits.WalkingMultispan.left",
"CategoryTheory.Limits.WalkingMultispan.right",
"CategoryTheory.Limits.M... |
CategoryTheory.ComposableArrows.homMk₅_app_three | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"CategoryTheory.ComposableArrows.homMk₅",
"CategoryTheory.ComposableArrows.homMk₅._proof_4",
"_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._auto_483",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ComposableArrows.map'._proof_8",
"PartialOrder.toPreorder",
"_priva... |
BitVec.reverse.eq_1 | Init.Data.BitVec.Lemmas | [
"BitVec.reverse",
"BitVec",
"instOfNatNat",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] |
WithTop.coe_sInf._simp_1 | Mathlib.Order.ConditionallyCompleteLattice.Basic | [
"WithTop.instInfSet",
"iInf",
"ConditionallyCompleteLinearOrderBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"WithTop.some",
"Set.Nonempty",
"BddBelow",
"ConditionallyCompleteLinearOrderBot.toConditionallyCo... |
SemistandardYoungTableau.casesOn | Mathlib.Combinatorics.Young.SemistandardTableau | [
"SemistandardYoungTableau.rec",
"YoungDiagram",
"SemistandardYoungTableau.mk",
"Membership.mem",
"Prod.mk",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat",
"LT.lt",
"instLTNat",
"Prod",
"OfNat.ofNat",
"Eq",
"Not",
"SetLike.instMembership",
"YoungDiagram.instSetLikeProdNat",
"Semistand... |
Lean.Compiler.LCNF.SpecEntry.mk.sizeOf_spec | Lean.Compiler.LCNF.SpecInfo | [
"Lean.Compiler.LCNF.SpecParamInfo",
"instOfNatNat",
"Lean.Compiler.LCNF.SpecEntry.mk",
"Array._sizeOf_inst",
"Array",
"instHAdd",
"Lean.Compiler.LCNF.SpecEntry._sizeOf_inst",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"Lean.Compiler.LCNF.SpecParamInfo._sizeOf_inst",
"SizeOf.sizeOf",
"Bool",
... |
Real.sinh_eq_tsum | Mathlib.Analysis.SpecialFunctions.Trigonometric.Series | [
"Real",
"instHDiv",
"HMul.hMul",
"Real.hasSum_sinh",
"Real.instDivInvMonoid",
"EMetricSpace.metrizableSpace",
"PseudoMetricSpace.toUniformSpace",
"Real.sinh",
"HDiv.hDiv",
"instMulNat",
"instOfNatNat",
"Nat.cast",
"SummationFilter.instNeBotUnconditional",
"Monoid.toPow",
"Real.instMonoid... |
CategoryTheory.MonoidalCategory.«term𝟙__» | Mathlib.CategoryTheory.Monoidal.Category | [
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] |
Turing.ListBlank.tail_cons | Mathlib.Computability.TuringMachine.Tape | [
"Quotient.mk''",
"Turing.ListBlank.tail",
"List",
"Quotient",
"Turing.ListBlank.cons",
"Turing.ListBlank",
"Quotient.ind'",
"Inhabited",
"Turing.BlankRel.setoid",
"Eq",
"rfl"
] |
ContinuousLinearMap.completion._proof_4 | Mathlib.Topology.Algebra.LinearMapCompletion | [
"LinearMap.toAddMonoidHom",
"UniformSpace",
"UniformSpace.Completion.map",
"Continuous",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"RingHom",
"AddZeroClass.toAddZero",
"AddCommGroup",
"ContinuousLinearMap.toLinearMap",
"ContinuousLinearMap",
"Unif... |
LinearGrowth.le_linearGrowthSup_iff | Mathlib.Analysis.Asymptotics.LinearGrowth | [
"instAddCommMonoidWithOneEReal",
"Iff.mpr",
"Eq.mpr",
"EReal.instDivInvMonoid",
"Preorder.toLT",
"instHDiv",
"HMul.hMul",
"congrArg",
"Filter.isBounded_le_of_top",
"Filter.map",
"Nat.cast_lt._simp_1",
"Filter.Eventually",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
... |
Lean.Meta.Tactic.Backtrack.BacktrackConfig.discharge._default | Lean.Meta.Tactic.Backtrack | [
"Lean.MVarId",
"Lean.Meta.MetaM",
"id",
"List",
"Alternative.failure",
"Lean.Meta.instAlternativeMetaM",
"Option"
] |
_private.Std.Data.ExtTreeMap.Lemmas.0.Std.ExtTreeMap.alter_eq_empty_iff._simp_1_1 | Std.Data.ExtTreeMap.Lemmas | [
"_private.Std.Data.ExtTreeMap.Lemmas.0.Std.ExtTreeMap.ext_iff",
"Ordering",
"Std.ExtTreeMap",
"Std.ExtTreeMap.inner",
"propext",
"Std.ExtDTreeMap",
"Eq"
] |
_private.Mathlib.Control.Basic.0.map_seq._simp_1_1 | Mathlib.Control.Basic | [
"Pure.pure",
"Seq.seq",
"Applicative.toPure",
"Applicative",
"Unit",
"LawfulApplicative.pure_seq",
"Applicative.toFunctor",
"Applicative.toSeq",
"Eq.symm",
"Eq",
"Functor.map",
"LawfulApplicative"
] |
Numbering.prefixedEquiv._proof_14 | Mathlib.Combinatorics.KatonaCircle | [
"Eq.mpr",
"Compl.compl",
"Finset",
"Finset.mem_compl._simp_1",
"Membership.mem",
"BooleanAlgebra.toCompl",
"id",
"Fintype",
"Finset.instSetLike",
"Finset.booleanAlgebra",
"Eq",
"Not",
"SetLike.instMembership",
"DecidableEq"
] |
Order.IsSuccLimit.sSup_Iio | Mathlib.Order.SuccPred.CompleteLinearOrder | [
"ConditionallyCompleteLinearOrderBot",
"PartialOrder.toPreorder",
"Order.IsSuccLimit",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"Order.IsSuccLimit.isSuccPrelimit",
"ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder",
"ConditionallyCompletePartialOrderSup.to... |
Std.Tactic.BVDecide.LRAT.Internal.Clause.isUnit | Std.Tactic.BVDecide.LRAT.Internal.Clause | [
"outParam",
"Std.Tactic.BVDecide.LRAT.Internal.Clause",
"Std.Sat.Literal",
"Option"
] |
IsLocalizedModule.commonDenom | Mathlib.Algebra.Module.LocalizedModule.Int | [
"instHSMul",
"IsLocalizedModule.exist_integer_multiples",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Finset",
"AddMonoid.toAddZeroClass",
"IsLocalizedModule",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"DistribSMul.toSMulZeroClass",
"NonAssocSemiring.toMulZeroOne... |
TensorPower.gMul._proof_4 | Mathlib.LinearAlgebra.TensorPower.Basic | [
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra.toSMul",
"Algebra.id",
"PiTensorProduct.instSMul",
"AddCommMonoid",
"CommSemiring",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"PiTensorProduct",
"Module",
"Fin",
"PiTensorProduct.instIsScalarTower"
] |
AntivaryOn.empty | Mathlib.Order.Monotone.Monovary | [
"Preorder.toLT",
"False.elim",
"Preorder.toLE",
"Membership.mem",
"AntivaryOn",
"LE.le",
"LT.lt",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Set.instMembership",
"Preorder",
"Set"
] |
CategoryTheory.Limits.initialMonoClass_of_coproductsDisjoint | Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct | [
"CategoryTheory.Limits.IsInitial.hom_ext",
"CategoryTheory.Limits.BinaryCofan.inr",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.CoproductsOfShapeDisjoint.coproductDisjoint",
"CategoryTheory.Functor.category",
... |
DifferentiableOn.sub_iff_left._simp_2 | Mathlib.Analysis.Calculus.FDeriv.Add | [
"NormedSpace",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"NormedAddGroup.toAddGroup",
"SubNegMonoid.toSub",
"instHSub",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"NormedAddCommGroup.toNormedAddGroup",
"DifferentiableOn",
"propext",
... |
BitVec.noConfusionType | Init.Prelude | [
"instPowNat",
"BitVec",
"instOfNatNat",
"instNatPowNat",
"BitVec.casesOn",
"HPow.hPow",
"Nat",
"HEq",
"instHPow",
"OfNat.ofNat",
"Fin"
] |
SimpleGraph.IsCompleteBetween.disjoint | Mathlib.Combinatorics.SimpleGraph.Basic | [
"Iff.mpr",
"Std.Irrefl.irrefl",
"Set.disjoint_left",
"SimpleGraph.Adj",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"Set.inst... |
BialgCat.category | Mathlib.Algebra.Category.BialgCat.Basic | [
"Quiver.mk",
"BialgCat.instBialgebra",
"CommRing",
"Coalgebra.toCoalgebraStruct",
"CategoryTheory.CategoryStruct.mk",
"BialgCat",
"BialgCat.category._proof_1",
"Bialgebra.toCoalgebra",
"BialgHom.id",
"BialgCat.category._proof_3",
"CategoryTheory.Category.mk",
"BialgCat.Hom.toBialgHom'",
"Alg... |
_private.Mathlib.Algebra.Ring.NonZeroDivisors.0.le_nonZeroDivisorsLeft_iff_isLeftRegular._simp_1_1 | Mathlib.Algebra.Ring.NonZeroDivisors | [
"SetLike",
"SetLike.le_def",
"Membership.mem",
"LE.le",
"LE",
"IsConcreteLE",
"propext",
"Eq",
"SetLike.instMembership"
] |
Fin.castLT_sub_nezero._proof_2 | Mathlib.Data.Fin.Basic | [
"_private.Mathlib.Data.Fin.Basic.0.Fin.castLT_sub_nezero._proof_1",
"Zero.ofOfNat0",
"HSub.hSub",
"instSubNat",
"Ne",
"instOfNatNat",
"Fin.val",
"instHSub",
"Nat",
"LT.lt",
"instLTFin",
"Zero.toOfNat0",
"OfNat.ofNat",
"Fin"
] |
norm_pow | Mathlib.Analysis.Normed.Ring.Basic | [
"NormOneClass",
"Norm.norm",
"SeminormedRing.toNorm",
"Real",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddMonoidWithOne",
"SeminormedRing.toRing",
"Real.semiring",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonAssocSemiring.toMulZeroOneClass",
"NormMulClass",
"NonAssocRing.toNonUni... |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.minKey?_eq_some_iff_getKey?_eq_self_and_forall._simp_1_2 | Std.Data.Internal.List.Associative | [
"Option.some",
"Exists",
"Option.map",
"And",
"propext",
"Eq",
"Option.map_eq_some_iff",
"Option"
] |
Lean.instHashableLevelMVarId.hash | Lean.Level | [
"UInt64.instOfNat",
"mixHash",
"UInt64",
"Lean.LevelMVarId",
"Hashable.hash",
"_private.Lean.Level.0.Lean.instHashableLevelMVarId.hash.match_1",
"Lean.Name",
"OfNat.ofNat",
"Lean.instHashableName"
] |
AlgHomClass.toRingHomClass | Mathlib.Algebra.Algebra.Hom | [
"outParam",
"Algebra",
"AlgHomClass",
"CommSemiring",
"Semiring",
"Semiring.toNonAssocSemiring",
"FunLike",
"RingHomClass"
] |
suggestSteps | Mathlib.Tactic.Widget.Calc | [
"Pure.pure",
"String.replicate",
"Lean.Meta.ppExpr",
"CalcParams",
"Array.isPrefixOf",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"_private.Mathlib.Tactic.Widget.Calc.0.suggestSteps.match_1",
"Lean.MetavarKind.natural",
"String.Slice.Pattern.CharPred.instTo... |
AffineSubspace.direction_bot | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | [
"Eq.mpr",
"Submodule",
"Lattice.toSemilatticeSup",
"vectorSpan",
"Set.vsub",
"CompleteLattice.toLattice",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"AffineSubspace.bot_coe",
"CompleteLattice.toBounde... |
DerivedCategory.instPretriangulated._proof_1 | Mathlib.Algebra.Homology.DerivedCategory.Basic | [
"CategoryTheory.Abelian.toPreadditive",
"HasDerivedCategory._proof_1",
"CategoryTheory.ObjectProperty.instIsCompatibleWithTriangulationTrWOfIsTriangulatedOfIsTriangulated",
"HomotopyCategory.instAdditiveIntUpShiftFunctor",
"AddGroupWithOne.toAddMonoidWithOne",
"AddCancelMonoid.toAddRightCancelMonoid",
"... |
connectedComponentIn_mem_nhds | Mathlib.Topology.Connected.LocallyConnected | [
"Filter.instMembership",
"Iff.mpr",
"Filter.HasBasis.mem_iff",
"IsConnected",
"congrArg",
"mem_nhds_iff",
"Membership.mem",
"Exists",
"nhds",
"Eq.mp",
"id",
"HasSubset.Subset",
"And.casesOn",
"TopologicalSpace",
"And",
"Exists.casesOn",
"IsConnected.isPreconnected",
"And.intro",
... |
_private.Lean.Elab.DeclModifiers.0.Lean.Elab.Modifiers.isPartial._sparseCasesOn_1 | Lean.Elab.DeclModifiers | [
"Nat.ne_of_beq_eq_false",
"Lean.Elab.RecKind.partial",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Elab.RecKind",
"Nat.land",
"Lean.Elab.RecKind.default",
"Nat",
"Bool",
"Eq.refl",
"Lean.Elab.RecKind.rec",
"Lean.Elab.RecKind.nonrec",
"OfNat.ofNat",
"Bool.false",
"Lean.Elab... |
TensorialAt.mkHom₂ | Mathlib.Geometry.Manifold.VectorBundle.Tensoriality | [
"LinearMap.toContinuousBilinearMap",
"NormedCommRing.toSeminormedCommRing",
"Prod.normedSpace",
"CompleteSpace",
"instAddMonoidWithOneENat",
"Prod.normedAddCommGroup",
"NormedSpace",
"ContinuousSMul",
"FiberBundle",
"ContinuousLinearMap.topologicalSpace",
"VectorBundle.finiteDimensional",
"Dis... |
zpow_one_add | Mathlib.Algebra.Group.Basic | [
"Eq.mpr",
"zpow_add",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"DivInvMonoid.toZPow",
"Group",
"zpow_one",
"id",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Int",
"Group.toDivInvMonoid",
"instHAdd",
"MulOneClass.toMulOne",
"HPow.hPow",
"instOfNat",
"HAdd.hAdd",
"Int.instAdd... |
Subbimodule.mk._proof_5 | Mathlib.Algebra.Module.Bimodule | [
"AddSubmonoid.add_mem",
"Eq.mpr",
"instHSMul",
"TensorProduct.add",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.Algebra.module",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"Membership.mem",
"AddZeroClass.toAddZero",... |
Absorbs.zero | Mathlib.Topology.Bornology.Absorbs | [
"Iff.mpr",
"instHSMul",
"SMulZeroClass",
"Membership.mem",
"Filter.Eventually.of_forall",
"HasSubset.Subset",
"Set.zero",
"Set.zero_subset",
"Absorbs",
"Zero.toOfNat0",
"Bornology.cobounded",
"HSMul.hSMul",
"Set.zero_mem_smul_set",
"SMulZeroClass.toSMul",
"OfNat.ofNat",
"Set.instMember... |
InformationTheory.klDiv_of_not_ac | Mathlib.InformationTheory.KullbackLeibler.Basic | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"MeasureTheory.Measure",
"ENNReal.ofReal",
"Real.instRCLike",
"congrArg",
"Real.instSub",
"Set.univ",
"MeasureTheory.Measure.real",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"Classical.propDe... |
MeasureTheory.Measure.haarMeasure_eq_iff | Mathlib.MeasureTheory.Measure.Haar.Basic | [
"Eq.mpr",
"MulOne.toOne",
"instHSMul",
"MeasureTheory.Measure",
"Semiring.toModule",
"IsScalarTower.right",
"MeasureTheory.Measure.haarMeasure_unique",
"TopologicalSpace.PositiveCompacts.instSetLike",
"ENNReal.instAddCommMonoid",
"MeasureTheory.Measure.haarMeasure_self",
"Monoid.toMulOneClass",
... |
FreeMonoid.lift_restrict | Mathlib.Algebra.FreeMonoid.Basic | [
"FreeMonoid.lift",
"Monoid",
"CancelMonoid.toRightCancelMonoid",
"FreeMonoid",
"Equiv.apply_symm_apply",
"MonoidHom.instFunLike",
"Equiv.instEquivLike",
"MonoidHom",
"Monoid.toMulOneClass",
"FreeMonoid.instCancelMonoid",
"Function.comp",
"Equiv",
"MulOneClass.toMulOne",
"FreeMonoid.of",
... |
Filter.tendsto_atTop_atBot_of_antitone | Mathlib.Order.Filter.AtTopBot.Tendsto | [
"Preorder.toLE",
"Exists",
"LE.le",
"Filter.tendsto_atTop_atTop_of_monotone",
"Filter.atTop",
"Antitone",
"Filter.Tendsto",
"Filter.atBot",
"OrderDual",
"OrderDual.instPreorder",
"Preorder"
] |
String.append_left_inj | Init.Data.String.Defs | [
"congrArg",
"String",
"String.toByteArray",
"iff_self",
"_private.Init.Data.String.Defs.0.String.append_left_inj._simp_1_1",
"instAppendString",
"instHAppendOfAppend",
"Iff",
"congr",
"True",
"ByteArray.append_left_inj._simp_1",
"of_eq_true",
"String.toByteArray_append",
"ByteArray.instApp... |
TwoUniqueSums.of_addOpposite | Mathlib.Algebra.Group.UniqueProds.Basic | [
"Eq.mpr",
"HMul.hMul",
"SProd.sprod",
"congrArg",
"Finset",
"AddOpposite.op_injective",
"Finset.card_map",
"Mathlib.Tactic.Contrapose.contrapose₄",
"Finset.map",
"Membership.mem",
"Exists",
"Function.Embedding.mk",
"AddOpposite",
"AddOpposite.instAdd",
"Eq.mp",
"Prod.ext_iff",
"id",
... |
CategoryTheory.Cat.HasLimits.limitConeX_str | Mathlib.CategoryTheory.Category.Cat.Limit | [
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.Cat.HasLimits.limitConeX",
"CategoryTheory.Bundled.str",
"CategoryTheory.Functor.comp",
"inferInstance",
"CategoryTheory.SmallCategory",
"CategoryTheory.Cat",
"CategoryTheory.Limits.limit",
"CategoryTheory.Cat.HasLimits.instC... |
Lean.Meta.Grind.ParentSet.mk | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.ParentSet",
"Lean.Expr",
"Lean.Meta.Grind.ParentSet.mk",
"List"
] |
Monoid.CoprodI.NeWord.head.eq_2 | Mathlib.GroupTheory.CoprodI | [
"Monoid",
"Monoid.CoprodI.NeWord",
"Ne",
"Monoid.CoprodI.NeWord.append",
"Eq.refl",
"Monoid.CoprodI.NeWord.head",
"Eq"
] |
UniqueProds.casesOn | Mathlib.Algebra.Group.UniqueProds.Basic | [
"UniqueMul",
"UniqueProds.mk",
"Finset",
"Mul",
"UniqueProds",
"Membership.mem",
"Exists",
"And",
"Finset.instSetLike",
"Finset.Nonempty",
"UniqueProds.rec",
"SetLike.instMembership"
] |
Lean.Meta.Grind.EMatchTheoremPtr | Lean.Meta.Tactic.Grind.EMatchTheoremPtr | [
"Lean.Meta.Grind.EMatchTheoremPtr.mk"
] |
Set.Ici.coe_sup._simp_1 | Mathlib.Order.LatticeIntervals | [
"Set.Ici",
"PartialOrder.toPreorder",
"Membership.mem",
"SemilatticeSup.toMax",
"Set.Elem",
"Set.Ici.coe_sup",
"Set.Ici.semilatticeSup",
"Max.max",
"SemilatticeSup.toPartialOrder",
"Eq.symm",
"Subtype.val",
"Eq",
"SemilatticeSup",
"Set.instMembership",
"Set"
] |
_private.Init.Data.String.Defs.0.String.utf8ByteSize_eq_zero_iff._simp_1_1 | Init.Data.String.Defs | [
"String.toByteArray_inj",
"String",
"String.toByteArray",
"propext",
"ByteArray",
"Eq.symm",
"Eq"
] |
FirstOrder.Language.Relations.formula₂.eq_1 | Mathlib.ModelTheory.Semantics | [
"FirstOrder.Language.Term",
"instOfNatNat",
"Nat",
"FirstOrder.Language.Relations",
"FirstOrder.Language.Formula",
"Matrix.vecEmpty",
"Eq.refl",
"FirstOrder.Language",
"OfNat.ofNat",
"Eq",
"Matrix.vecCons",
"FirstOrder.Language.Relations.formula",
"FirstOrder.Language.Relations.formula₂"
] |
Lean.Compiler.LCNF.Simp.simpProj? | Lean.Compiler.LCNF.Simp.SimpValue | [
"Pure.pure",
"OptionT.instMonad",
"Lean.Compiler.LCNF.Simp.DiscrM",
"OptionT",
"Lean.Compiler.LCNF.Arg",
"Lean.ConstructorVal",
"ReaderT",
"Lean.Compiler.LCNF.Arg.toLetValue",
"_private.Lean.Compiler.LCNF.Simp.SimpValue.0.Lean.Compiler.LCNF.Simp.simpProj?.match_1",
"instMonadLiftT",
"Lean.Compil... |
MeasureTheory.Lp.zero_smul | Mathlib.MeasureTheory.Function.Holder | [
"MeasureTheory.ae",
"Eq.mpr",
"instHSMul",
"MeasureTheory.Measure",
"NormedRing.toRing",
"MeasureTheory.MemLp.zero",
"Ring.toNonAssocRing",
"congrArg",
"SMulWithZero.toSMulZeroClass",
"DistribMulAction.toDistribSMul",
"HEq.refl",
"MeasureTheory.AEEqFun.cast",
"AddMonoid.toAddZeroClass",
"s... |
_private.Init.Data.AC.0.Lean.Data.AC.removeNeutrals.loop.match_1.eq_1 | Init.Data.AC | [
"Unit.unit",
"Bool.true",
"Unit",
"Bool",
"Eq.refl",
"Lean.Data.AC.removeNeutrals.loop.match_1",
"Bool.false",
"Eq"
] |
_private.Lean.Compiler.ExportAttr.0.Lean.isValidCppName | Lean.Compiler.ExportAttr | [
"Lean.Name.below",
"_private.Lean.Compiler.ExportAttr.0.Lean.isValidCppName.match_1",
"String",
"Bool.and",
"Lean.Name.brecOn",
"_private.Lean.Compiler.ExportAttr.0.Lean.isValidCppId",
"Lean.Name.str",
"Lean.Name.anonymous",
"Bool",
"Lean.Name",
"Bool.false"
] |
AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom_assoc | Mathlib.AlgebraicGeometry.Cover.Open | [
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.Scheme.Cover.pullbackHom",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AlgebraicGeometry.Scheme.OpenCover.pullbackCoverAffineRefinementObjIso_inv_pullbackHom",... |
CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_snd_assoc | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_snd",
"CategoryTheory.Limits.pullbackRightPullbackFstIso",
"Eq.mp",
"i... |
_private.Mathlib.RingTheory.HahnSeries.Basic.0.HahnSeries.ext.match_1 | Mathlib.RingTheory.HahnSeries.Basic | [
"Set.IsPWO",
"PartialOrder.toPreorder",
"PartialOrder",
"HahnSeries.mk",
"HahnSeries.casesOn",
"Function.support",
"HahnSeries",
"Zero"
] |
MeasureTheory.Measure.IsOpenPosMeasure.mk | Mathlib.MeasureTheory.Measure.OpenPos | [
"MeasureTheory.Measure",
"Ne",
"instZeroENNReal",
"MeasurableSpace",
"MeasureTheory.Measure.IsOpenPosMeasure.mk",
"TopologicalSpace",
"MeasureTheory.Measure.IsOpenPosMeasure",
"Set.Nonempty",
"ENNReal",
"Zero.toOfNat0",
"IsOpen",
"OfNat.ofNat",
"DFunLike.coe",
"MeasureTheory.Measure.instFu... |
Denumerable.nat | Mathlib.Logic.Denumerable | [
"Nat.encodable",
"Denumerable.mk",
"Denumerable.nat._proof_1",
"Nat",
"Denumerable"
] |
groupHomology.single_isCycle₁_of_mem_fixedPoints | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"instHSMul",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"DistribMulAction.toDistribSMul",
"Finsupp.sum_single_index",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Finsupp.sum",
"Group",
"Group.toDivisionMonoid",
"AddCommGroup.toAddGroup",
"smul_zero",
"Membership.mem",
"D... |
_private.Lean.Meta.Tactic.Grind.Arith.CommRing.EqCnstr.0.Lean.Meta.Grind.Arith.CommRing.toRingExpr?.match_1 | Lean.Meta.Tactic.Grind.Arith.CommRing.EqCnstr | [
"Option.ctorIdx",
"_private.Lean.Meta.Tactic.Grind.Arith.CommRing.EqCnstr.0.Lean.Meta.Grind.Arith.CommRing.inSameRing?._sparseCasesOn_1",
"Option.some",
"Nat.hasNotBit",
"Lean.Grind.CommRing.Var",
"Option"
] |
_private.Init.Data.Option.Monadic.0.Option.instForIn'InferInstanceMembershipOfMonad.match_1.eq_1 | Init.Data.Option.Monadic | [
"ForInStep.done",
"Option.instForIn'InferInstanceMembershipOfMonad.match_1",
"ForInStep",
"Eq.refl",
"Eq",
"ForInStep.yield"
] |
_private.Init.Data.Int.LemmasAux.0.Int.ble'_eq_true._proof_1_2 | Init.Data.Int.LemmasAux | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Lean.Omega.Int.le_of_not_lt",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.... |
LightCondensed.finYoneda._proof_1 | Mathlib.Condensed.Discrete.Colimit | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"SecondCountableTopology",
"Finite",
"FintypeCat",
"Quiver.Hom.unop",
"Function.comp",
"CategoryTheory.CategoryStruct.id",
"id",
... |
submonoidOfIdempotent._proof_1 | Mathlib.GroupTheory.OrderOfElement | [
"Eq.mpr",
"Nat.recAux",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"pow_succ",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"MulOne.toMul",
"LeftCancelMonoid.toMonoid",
"instOfNatNat",
"zero_add",
"Monoid.toPow",
"AddZero.to... |
RootPairing.exist_set_root_not_disjoint_and_le_ker_coroot'_of_invtSubmodule | Mathlib.LinearAlgebra.RootSystem.Irreducible | [
"Sublattice",
"Eq.mpr",
"Submodule",
"IsDomain",
"CommRing",
"_private.Mathlib.LinearAlgebra.RootSystem.Irreducible.0.RootPairing.exist_set_root_not_disjoint_and_le_ker_coroot'_of_invtSubmodule._simp_1_1",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCom... |
_private.Mathlib.RingTheory.FiniteType.0.AddMonoidAlgebra.finiteType_iff_fg._simp_1_1 | Mathlib.RingTheory.FiniteType | [
"Submodule",
"Membership.mem",
"Submodule.instTop",
"AddCommMonoid",
"Submodule.setLike",
"True",
"eq_true",
"Semiring",
"Module",
"Top.top",
"Eq",
"Submodule.mem_top",
"SetLike.instMembership"
] |
MeasureTheory.integrableOn_indicator_iff | Mathlib.MeasureTheory.Integral.IntegrableOn | [
"Eq.mpr",
"MeasureTheory.Measure",
"MeasurableSet",
"congrArg",
"Set.indicator",
"AddMonoid.toAddZeroClass",
"ESeminormedAddMonoid",
"MeasureTheory.Integrable",
"AddZeroClass.toAddZero",
"MeasureTheory.Measure.restrict",
"MeasureTheory.IntegrableOn",
"id",
"MeasureTheory.Measure.restrict_res... |
SimpleGraph.Walk.IsPath.of_append_left | Mathlib.Combinatorics.SimpleGraph.Paths | [
"Eq.mpr",
"List.Nodup.of_append_left",
"congrArg",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"id",
"List.tail",
"SimpleGraph",
"List.Nodup",
"instHAppendOfAppend",
"List",
"implies_congr",
"SimpleGraph.Walk.support_append",
"SimpleGraph.Walk.IsPath",
"List.instAppend",
"Eq",
"H... |
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