name string | module string | deps list |
|---|---|---|
have_body_congr_dep' | Init.SimpLemmas | [
"Eq"
] |
commGrpTypeEquivalenceCommGrp._proof_2 | Mathlib.CategoryTheory.Monoidal.Internal.Types.CommGrp_ | [
"CategoryTheory.Functor",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CategoryTheory.CommGrp.instCategory",
"CategoryTheory.Functor.category",
"CommGrpCat.instCategory",
"CategoryTheory.Functor.comp"... |
CompactlyGeneratedSpace.isClosed | Mathlib.Topology.Compactness.CompactlyGeneratedSpace | [
"Eq.mpr",
"Continuous",
"congrArg",
"CompactlyGeneratedSpace.isClosed'",
"CompactlyGeneratedSpace",
"Set.preimage_inter_range",
"id",
"Set.instInter",
"CompactSpace",
"Inter.inter",
"isCompact_range",
"IsClosed",
"TopologicalSpace",
"Set.preimage",
"T2Space",
"IsClosed.preimage",
"Se... |
Std.HashMap.mem_keys | Std.Data.HashMap.Lemmas | [
"Std.DHashMap.mem_keys",
"LawfulBEq",
"Membership.mem",
"Std.HashMap.keys",
"Std.HashMap",
"List",
"Iff",
"List.instMembership",
"Hashable",
"Std.HashMap.inner",
"BEq",
"Std.HashMap.instMembership"
] |
isInducing_stoneCechUnit | Mathlib.Topology.Separation.CompletelyRegular | [
"Filter.instMembership",
"Real.instIsOrderedRing",
"Eq.mpr",
"False",
"Real.partialOrder",
"ConditionallyCompleteLinearOrder.toCompactIccSpace",
"Real",
"Continuous",
"NeZero.one",
"continuous_stoneCechUnit",
"Set.Icc.instZero",
"Filter.HasBasis.mem_iff",
"Real.instZero",
"congrArg",
"Fi... |
Lean.Doc.PostponedImport.name | Lean.Elab.DocString.Builtin.Postponed | [
"Lean.Name",
"Lean.Doc.PostponedImport"
] |
_private.Mathlib.Probability.Process.HittingTime.0.MeasureTheory.Adapted.isStoppingTime_hittingBtwn_isStoppingTime._simp_1_13 | Mathlib.Probability.Process.HittingTime | [
"LE.le",
"WithTop.some",
"LE",
"propext",
"WithTop.coe_le_coe",
"Eq",
"WithTop.instLE",
"WithTop"
] |
Lean.Doc.State._sizeOf_inst | Lean.Elab.DocString | [
"Lean.Doc.State._sizeOf_1",
"SizeOf.mk",
"Lean.Doc.State",
"SizeOf"
] |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle.0.Real.Angle.two_nsmul_eq_iff._simp_1_2 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle | [
"instHSMul",
"Real.pi",
"Real.Angle",
"Real.Angle.coe",
"PseudoMetricSpace.toUniformSpace",
"Int",
"NormedAddGroup.toAddGroup",
"Real.Angle.two_zsmul_eq_iff",
"instHAdd",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"instOfNat",
"HAdd.hAdd",
"NormedAddCommGroup.... |
Part.Fix.approx._unsafe_rec | Mathlib.Control.Fix | [
"Part",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Part.instPartialOrder",
"Pi.instBotForall",
"Bot.bot",
"Stream'",
"Part.instOrderBot",
"Unit",
"Nat",
"Part.Fix.approx.match_1",
"Part.Fix.approx._unsafe_rec"
] |
CategoryTheory.GradedObject.mapTrifunctorMap_obj | Mathlib.CategoryTheory.GradedObject.Trifunctor | [
"CategoryTheory.Functor",
"CategoryTheory.GradedObject.HasMap",
"CategoryTheory.Functor.category",
"CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj",
"CategoryTheory.GradedObject.mapTrifunctor",
"CategoryTheory.GradedObject.categoryOfGradedObjects",
"Eq.refl",
"CategoryTheory.GradedObject",
"... |
FiniteDimensional.of_locallyCompactSpace | Mathlib.Analysis.Normed.Module.FiniteDimension | [
"instWeaklyLocallyCompactSpaceOfLocallyCompactSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"CompleteSpace",
"NormedSpace",
"Real.instZero",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Real.instLT",
"_private.Mathlib.Analysis.Normed.Module.FiniteDimension.0.FiniteDimensio... |
ProjectiveSpectrum.ctorIdx | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology | [
"SetLike",
"CommRing",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Nat.instAddMonoid",
"AddSubmonoidClass",
"CommRing.toCommSemiring",
"GradedRing",
"Nat",
"instDecidableEqNat",
"AddMonoidWithOne.toAddMonoid",
"CommRing.toRing",
"Ring.toAdd... |
rTensor.inverse_apply | Mathlib.LinearAlgebra.TensorProduct.RightExactness | [
"Function.Exact",
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"CommRing",
"rTensor.inverse",
"Submodule.Quotient.addCommGroup",
"congrArg",
"CommSemiring.toSemiring",
"rTensor.inverse_of_rightInverse_apply",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.mk",
"TensorProduct.addCommM... |
TopologicalSpace.NonemptyCompacts.instPartialOrder | Mathlib.Topology.Sets.Compacts | [
"PartialOrder.ofSetLike",
"TopologicalSpace.NonemptyCompacts.instSetLike",
"TopologicalSpace.NonemptyCompacts",
"PartialOrder",
"TopologicalSpace"
] |
Lean.Expr.fvar.inj | Lean.Expr | [
"Lean.Expr.fvar.noConfusion",
"Lean.Expr",
"Lean.FVarId",
"Lean.Expr.fvar",
"Eq"
] |
OpenNormalAddSubgroup.toFiniteIndexNormalAddSubgroup._proof_1 | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Completion | [
"instSeparatelyContinuousAddOfContinuousAdd",
"AddSubgroup.FiniteIndex",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"OpenAddSubgroup.toAddSubgroup",
"OpenNormalAddSubgroup.toOpenAddSubgroup",
"CompactSpace",
"TopologicalSpace",
"AddGroup",
"AddGroup.toSubNegMonoid",
"AddSubgroup.finit... |
CategoryTheory.WithTerminal.comp.eq_2 | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.WithTerminal.comp",
"CategoryTheory.WithTerminal.Hom",
"CategoryTheory.WithTerminal",
"CategoryTheory.WithTerminal.of",
"CategoryTheory.WithTerminal.star",
"Eq.refl",
"PUnit.unit",
"Eq",
"CategoryTheory.Category"
] |
_private.Mathlib.RingTheory.Extension.Cotangent.Basis.0.Algebra.Generators.PresentationOfFreeCotangent.Aux.tensorCotangentInv._proof_2 | Mathlib.RingTheory.Extension.Cotangent.Basis | [
"Ideal.Quotient.commSemiring",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"Algebra.to_smulCommClass",
"Algebra.Extension.commRing",
"Semiring.toModule",
"Algebra.Extension.instModuleCotangent",
"Algebra.Extension.ker",
"CommSemiring.toSemiring",
"instDistribSMul",
"AddCommGroup.toAdd... |
_private.Lean.Elab.Tactic.Try.0.Lean.Elab.Tactic.Try.mkGrindEqnParams | Lean.Elab.Tactic.Try | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.SourceInfo",
"Lean.Meta.State",
"Lean.Syntax.Ident",
"Array.mkArray0",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.MonadQuotation.toMonadRef",
"Lean.TSyntax.raw",
"Lean.Meta.MetaM",
"... |
Subtype.restrict_def | Mathlib.Data.Subtype | [
"Function.comp",
"Subtype",
"Subtype.restrict",
"Subtype.val",
"Eq",
"rfl"
] |
String.Pos.ofToSlice_comp_toSlice | Init.Data.String.Basic | [
"String.toSlice",
"String.Pos.ofToSlice_toSlice",
"congrArg",
"String",
"String.Pos.toSlice",
"Function.comp",
"id",
"String.Pos.Raw",
"String.Pos.ext",
"funext",
"String.Pos.ofToSlice",
"String.Pos.Raw.ext",
"Nat",
"True",
"eq_self",
"String.Pos",
"of_eq_true",
"congrFun'",
"Str... |
Prod.mk_dvd_mk._simp_1 | Mathlib.Algebra.Divisibility.Prod | [
"Semigroup",
"Dvd.dvd",
"Prod.mk_dvd_mk",
"semigroupDvd",
"Prod.mk",
"Prod.instSemigroup",
"And",
"propext",
"Prod",
"Eq"
] |
RelEmbedding.mul_apply | Mathlib.Algebra.Order.Group.End | [
"RelEmbedding.instMonoid",
"HMul.hMul",
"Monoid.toMulOneClass",
"MulOne.toMul",
"RelEmbedding",
"MulOneClass.toMulOne",
"Eq",
"DFunLike.coe",
"RelEmbedding.instFunLike",
"rfl",
"instHMul"
] |
_private.Mathlib.Topology.Separation.Regular.0.regularSpace_TFAE.match_1_7 | Mathlib.Topology.Separation.Regular | [
"Filter.instMembership",
"Membership.mem",
"nhds",
"TopologicalSpace",
"Filter.lift'",
"closure",
"Eq",
"Filter",
"Set"
] |
Int.natCast_le_zero._simp_1 | Init.Data.Int.LemmasAux | [
"instOfNatNat",
"Int",
"LE.le",
"Nat.cast",
"instOfNat",
"Nat",
"Int.natCast_le_zero",
"propext",
"instNatCastInt",
"OfNat.ofNat",
"Eq",
"Int.instLEInt"
] |
Finset.one_le_prod' | Mathlib.Algebra.Order.BigOperators.Group.Finset | [
"Eq.mpr",
"MulOne.toOne",
"le_refl",
"Finset.prod_le_prod'",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"Preorder.toLE",
"Membership.mem",
"MulLeftMono",
"id",
"MulOne.toMul",
"LE.le",
"Finset.prod",
"Finset.prod_const_one",
"MulOneClass.toMulOne",
"Finset.instSetLike",
"CommMon... |
Lean.Grind.OrderedRing.mul_le_mul_of_nonneg_left | Init.Grind.Ordered.Ring | [
"HMul.hMul",
"congrArg",
"Std.le_refl",
"Std.IsPartialOrder",
"Std.instReflLeOfIsPreorder",
"Std.le_refl._simp_1",
"Eq.mp",
"Lean.Grind.AddCommMonoid.toZero",
"Lean.Grind.Semiring.toMul",
"LE.le",
"Std.LawfulOrderLT",
"LE",
"Lean.Grind.PartialOrder.le_iff_lt_or_eq",
"Or.casesOn",
"Lean.G... |
CategoryTheory.ComposableArrows.Precomp.map._proof_7 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"Eq.mp",
"Fin.mk",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.add_le_add_iff_right._simp_1",
"instLEFin",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Fin",
"Eq.trans",
"Fin.mk_le_mk._simp_1"
] |
_private.Mathlib.Topology.Homotopy.Product.0.Path.Homotopic.«_aux_Mathlib_Topology_Homotopy_Product___macroRules__private_Mathlib_Topology_Homotopy_Product_0_Path_Homotopic_term_⬝__1» | Mathlib.Topology.Homotopy.Product | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
... |
contDiffOn_of_analyticOn_of_fderivWithin | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedAddCommGroup",
"AnalyticOn",
"instAddMonoidWithOneENat",
"NormedSpace",
"WithTop.instPreorder",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"contDiffOn_succ_of_fderivWithin",
"PseudoMetricSpace.toUniformSpace",
"Cont... |
RootPairing.Hom.mk.injEq | Mathlib.LinearAlgebra.RootSystem.Hom | [
"RootPairing.Hom.mk",
"CommRing",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Equiv.instEquivLike",
"Eq.propIntro",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"RootPairing.flip",
"LinearMap.instFunLike",
"RootPairing.isPerfPair_toLinearMap",
"Lean.injEq_helper",
"Functi... |
CochainComplex.HomComplex.coboundaries.eq_1 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | [
"CochainComplex.HomComplex.coboundaries",
"CochainComplex.HomComplex.instAddCommGroupCochain",
"CochainComplex.HomComplex.coboundaries._proof_7",
"AddMonoid.toAddZeroClass",
"setOf",
"AddGroupWithOne.toAddMonoidWithOne",
"CochainComplex.HomComplex.instAddCommGroupCocycle",
"AddCancelMonoid.toAddRightC... |
FreeAddGroup.reduceCyclically.reduce_flatten_replicate_succ | Mathlib.GroupTheory.FreeGroup.CyclicallyReduced | [
"FreeAddGroup.reduce_append_reduce_reduce",
"Eq.mpr",
"List.replicate",
"False",
"Nat.instMulZeroClass",
"Nat.recAux",
"instHSMul",
"FreeAddGroup.reduce.sound",
"FreeAddGroup.reduceCyclically.conjugator",
"eq_false",
"Nat.instOne",
"AddMonoid.toAddSemigroup",
"congrArg",
"and_self",
"add... |
SubMulAction.algebraMap_mem | Mathlib.Algebra.Algebra.Operations | [
"SubMulAction.instSetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Algebra.toSMul",
"Membership.mem",
"algebraMap",
"Algebra.toModule",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Algebra.algebraMap_eq_smul_one",
"CommSemirin... |
IsCauSeq | Mathlib.Algebra.Order.CauSeq.Basic | [
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"AddGroupWithOne.toAddGroup",
"LinearOrder",
"PartialOrder.toPreorder",
"HSub.hSub",
"IsStrictOrderedRing",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Exists",
"SemilatticeInf.toPartialOrder",
"... |
_private.Mathlib.Lean.Expr.Basic.0.Lean.Expr.type?._sparseCasesOn_1 | Mathlib.Lean.Expr.Basic | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... |
_private.Mathlib.Order.Sublattice.0.Sublattice.le_prod_iff._simp_1_1 | Mathlib.Order.Sublattice | [
"SetLike",
"SetLike.le_def",
"Membership.mem",
"LE.le",
"LE",
"IsConcreteLE",
"propext",
"Eq",
"SetLike.instMembership"
] |
fderivWithin_csinh | Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | [
"NormedCommRing.toSeminormedCommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"Complex.sinh",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsTopologicalSemiring.toContinuousAdd",
"Semiring.toModule",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"IsTopologicalRing.toIsTopologicalSemiring",
... |
Finsupp.equivFunOnFinite | Mathlib.Data.Finsupp.Defs | [
"Finsupp.instFunLike",
"Finite",
"Finsupp.equivFunOnFinite._proof_3",
"Finsupp.equivFunOnFinite._proof_2",
"Equiv.mk",
"Finsupp.mk",
"Equiv",
"Set.Finite.toFinset",
"Function.support",
"Finsupp.equivFunOnFinite._proof_4",
"Finsupp.equivFunOnFinite._proof_1",
"DFunLike.coe",
"Finsupp",
"Zer... |
SimpleGraph.ConnectedComponent.map_mk | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"SimpleGraph.connectedComponentMk",
"RelHom.instFunLike",
"SimpleGraph.ConnectedComponent.map",
"SimpleGraph.Adj",
"SimpleGraph.ConnectedComponent",
"SimpleGraph",
"SimpleGraph.Hom",
"Eq",
"DFunLike.coe",
"rfl"
] |
Set.bounded_le_inter_lt | Mathlib.Order.Bounded | [
"Eq.mpr",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"_private.Mathlib.Order.Bounded.0.Set.bounded_le_inter_lt._simp_1_2",
"congrArg",
"Set.Bounded",
"LinearOrder",
"_private.Mathlib.Order.Bounded.0.Set.bounded_le_inter_lt._simp_1_1",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Sem... |
Std.Internal.List.length_le_length_insertListConst | Std.Data.Internal.List.Associative | [
"Nat.le_refl",
"Std.Internal.List.insertListConst",
"List.rec",
"LE.le",
"Std.Internal.List.insertEntry",
"instLENat",
"Prod.fst",
"Std.Internal.List.length_le_length_insertEntry",
"List.cons",
"List",
"Nat.le_trans",
"Nat",
"Prod",
"BEq",
"Prod.snd",
"List.length",
"Sigma"
] |
Path.target' | Mathlib.Topology.Path | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"Real.semiring",
"Set.Elem",
"TopologicalSpace",
"Path",
"One.toOfNat1",
"ContinuousMap.toFun",
"Set.Icc.instOne",
"Real.pseudoMetricSpace",
"instTopologicalSpaceSubtype",
"Path.t... |
LinearMap.toMatrixRight'_id | Mathlib.LinearAlgebra.Matrix.ToLin | [
"LinearMap.id",
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"Pi.addCommMonoid",
"Matrix.toLinearMapRight'",
"Matrix.module",
"MulZeroClass.toMul",
"congrArg",
"Matrix",
"MulOpposite",
"Function.smulCommClass",
"NonUnitalNonAssocSemiring.toMulZeroClas... |
differentiableAt_of_isInvertible_fderiv | Mathlib.Analysis.Calculus.FDeriv.Const | [
"AddCommGroup.toAddCommMonoid",
"DifferentiableAt",
"ContinuousLinearMap.IsInvertible",
"NormedField.toField",
"AddCommGroup",
"differentiableAt_of_fderiv_injective",
"fderiv",
"Field.toSemifield",
"TopologicalSpace",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Nontrivially... |
Std.DHashMap.Internal.Raw₀.equiv_iff_toList_perm_toList | Std.Data.DHashMap.Internal.RawLemmas | [
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.toList",
"List.Perm",
"Std.DHashMap.Raw.Equiv",
"_private.Std.Data.DHashMap.Internal.RawLemmas.0.Std.DHashMap.Internal.Raw₀.equiv_iff_toList_perm_toList._simp_1_1",
"iff_self",
"List",
"Iff",
"congr",
"Std.DHashMap.Raw.buckets",
"True",
"Std.... |
_private.Batteries.Data.List.Lemmas.0.List.getElem_findIdxs_eq_findIdxNth_add._proof_1_5 | Batteries.Data.List.Lemmas | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"List.cons",
"List.findIdxs",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"Bool",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"List.length"
] |
Polynomial.MonicDegreeEq.degree | Mathlib.Algebra.Polynomial.Monic | [
"Nontrivial",
"WithBot.addMonoidWithOne",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"WithBot",
"NeZero.one",
"Polynomial.MonicDegreeEq",
"congrArg",
"Polynomial.degree_eq_of_le_of_coeff_ne_zero",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"one_ne_zero._simp_1",
"Eq.le",
"Polynomia... |
Lean.Server.RequestCancellationToken._sizeOf_inst | Lean.Server.RequestCancellation | [
"Lean.Server.RequestCancellationToken._sizeOf_1",
"SizeOf.mk",
"Lean.Server.RequestCancellationToken",
"SizeOf"
] |
DirectLimit.instGroup._proof_5 | Mathlib.Algebra.Colimit.DirectLimit | [
"DirectLimit.setoid",
"map_inv",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"DivInvMonoid.toZPow",
"Group",
"Preorder.toLE",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"DirectLimit.map",
"Eq.rec",
"id",
"DivInvMonoid.toMonoid",
"Setoid",
"Int",
"LE.le",... |
Nat.ceilRoot_eq_zero | Mathlib.Data.Nat.Factorization.Root | [
"Nat.ceilRoot_ne_zero",
"congrArg",
"Nat.ceilRoot",
"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.ceilRoot_eq_zero._simp_1_2",
"Ne",
"instOfNatNat",
"iff_self",
"_private.Mathlib.Data.Nat.Factorization.Root.0.Nat.ceilRoot_eq_zero._simp_1_1",
"And",
"Iff",
"Nat",
"Iff.not_right",
"congr... |
HahnModule.instAddCommGroup._proof_12 | Mathlib.RingTheory.HahnSeries.Multiplication | [
"AddMonoid.toAddSemigroup",
"HahnModule.instAddCommGroup._proof_8",
"AddCommGroup.toAddCommMonoid",
"SubNegMonoid.mk",
"SMul",
"HahnModule.instAddCommGroup._proof_11",
"Neg.mk",
"HahnModule.instAddCommGroup._aux_3",
"HahnModule.instAddCommGroup._aux_6",
"HahnModule.instAddCommGroup._proof_9",
"H... |
AddSubgroupClass.subtype_injective | Mathlib.Algebra.Group.Subgroup.Defs | [
"AddSubgroupClass.subtype",
"SetLike",
"AddSubgroupClass.toAddGroup",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"Subtype.coe_injective",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Function.Injective",
"SubNegMonoid.toAddMonoid",
"AddMonoidHom",
"AddMon... |
FiberwiseLinear.openPartialHomeomorph._proof_4 | Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear | [
"Set.instSProd",
"ContinuousLinearEquiv.symm",
"NormedSpace",
"SProd.sprod",
"Set.univ",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"Prod.mk",
"ContinuousLinearEquiv.equivLike",
"Field.toSemifield",
"Prod.fst",
"ContinuousLinearEqui... |
Lean.Elab.Term.precheckFun._regBuiltin.Lean.Elab.Term.precheckFun_1 | Lean.Elab.Binders | [
"Lean.Elab.Term.precheckFun",
"IO",
"Lean.Elab.Term.Quotation.precheckAttribute",
"Lean.Elab.Term.Quotation.Precheck",
"Unit",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] |
_private.Mathlib.Topology.Compactness.Lindelof.0.IsLindelof.elim_nhds_subcover._simp_1_5 | Mathlib.Topology.Compactness.Lindelof | [
"Exists",
"exists_and_right",
"And",
"propext",
"Eq"
] |
ValuativeRel.supp._proof_2 | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"setOf",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"ValuativeRel.vle",
"instHAdd",
"HAdd.hAdd",
"NonUnitalNonAs... |
Std.ExtTreeSet.get?_max? | Std.Data.ExtTreeSet.Lemmas | [
"Option.some",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Unit",
"Std.ExtTreeSet",
"Std.ExtTreeMap.getKey?_maxKey?",
"Std.ExtTreeSet.max?",
"Eq",
"Std.ExtTreeSet.get?",
"Option"
] |
_private.Mathlib.RingTheory.Nilpotent.Exp.0.IsNilpotent.exp_add_of_commute._proof_1_12 | Mathlib.RingTheory.Nilpotent.Exp | [
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Int.Linear.norm_le",
"eq_false",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Int.Linear.le_neg",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"HSub.hSub",
"Int... |
HNNExtension.NormalWord.TransversalPair.noConfusion | Mathlib.GroupTheory.HNNExtension | [
"HEq.refl",
"Group",
"Units",
"Subgroup",
"Int",
"Int.instMonoid",
"HNNExtension.NormalWord.TransversalPair.casesOn",
"SetLike.coe",
"HNNExtension.toSubgroup",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"HNNExtension.NormalWord.TransversalPair.noConfusionType",
"Subgroup.IsComplement",
"Eq",
"Sub... |
BitVec.getElem_eq_true_of_lt_of_le | Init.Data.BitVec.Lemmas | [
"instPowNat",
"False",
"Nat.pow_lt_pow_of_lt",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.getElem_eq_true_of_lt_of_le._proof_1_1",
"congrArg",
"BitVec.getLsbD_of_ge",
"False.elim",
"true_iff",
"Bool.false_eq_true",
"Exists",
"BitVec",
"GE.ge",
"BitVec.getLsbD",
"Eq.mp",
"instDecidableEqB... |
Metric.ediam_image_le_iff | Mathlib.Topology.EMetricSpace.Diam | [
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"_private.Mathlib.Topology.EMetricSpace.Diam.0.Metric.ediam_image_le_iff._simp_1_1",
"LE.le",
"PseudoEMetricSpace",
"iff_self",
"Metric.ediam",
"Iff",
"PseudoEMetricSpace.toEDist",
"implies_congr",
"True",
"ENNReal",... |
Dense.exists_seq_strictAnti_tendsto_of_lt | Mathlib.Topology.Order.IsLUB | [
"Iff.mpr",
"OrderDual.toDual",
"Eq.mpr",
"OrderTopology",
"Preorder.toLT",
"Equiv.instEquivLike",
"StrictMono",
"OrderDual.ofDual",
"congrArg",
"instFirstCountableTopologyOrderDual",
"LinearOrder",
"OrderDual.denselyOrdered",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"Semi... |
_private.Mathlib.Data.Quot.0.Quot.surjective_lift.match_1_1 | Mathlib.Data.Quot | [
"Exists",
"Exists.casesOn",
"Exists.intro",
"Eq"
] |
_private.Mathlib.NumberTheory.RamificationInertia.Basic.0.Ideal.FinrankQuotientMap.linearIndependent_of_nontrivial._simp_1_6 | Mathlib.NumberTheory.RamificationInertia.Basic | [
"MulActionHomClass",
"instHSMul",
"SMul",
"HSMul.hSMul",
"Eq.symm",
"Eq",
"DFunLike.coe",
"FunLike",
"map_smul"
] |
Lean.Compiler.LCNF.Simp.State.simplified | Lean.Compiler.LCNF.Simp.SimpM | [
"Lean.Compiler.LCNF.Simp.State",
"Bool"
] |
Real.one_le_exp | Mathlib.Analysis.Complex.Exponential | [
"Real.instIsOrderedRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorder.toLT",
"HMul.hMul",
"Nat.rawCast",
"AddMonoid.toAddSemigroup",
"Ring.toNonAssocRing",
"Real.instZero",
"Real.instAddMonoid",
"Mathlib.Tactic.Linarith.sub_nonpos_of_le",
... |
ergodic_mul_left_of_denseRange_zpow | Mathlib.Dynamics.Ergodic.Action.OfMinimal | [
"Ergodic",
"MeasureTheory.Measure",
"MeasureTheory.instSFiniteOfSigmaFinite",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"SecondCountableTopology",
"DivInvMonoid.toZPow",
"Group",
"ContinuousInv.measurableInv",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMon... |
Language.map | Mathlib.Computability.Language | [
"MulOne.toOne",
"RingHom.mk",
"List.map",
"OneHom.mk",
"Language.map._proof_1",
"RingHom",
"MonoidHom.mk",
"NonAssocSemiring.toMulZeroOneClass",
"Language.map._proof_4",
"Language.instSemiring",
"MulZeroOneClass.toMulOneClass",
"Language.map._proof_2",
"List",
"MulOneClass.toMulOne",
"La... |
Polynomial.iterate_derivative_mul | Mathlib.Algebra.Polynomial.Derivative | [
"Multiset.sum",
"Polynomial.derivative",
"NonUnitalNonAssocSemiring.nat_isScalarTower",
"Function.iterate_succ_apply'",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Polynomial.derivative_mul",
"Polynomial.instNSMul",
"Nat.instMulZeroClass",
"Nat.instOrde... |
Lean.Server.Test.Runner.Client.HighlightedSubexprInfo.ctorElim | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.HighlightedSubexprInfo.subexpr",
"Lean.Server.Test.Runner.Client.SubexprInfo",
"Lean.Server.Test.Runner.Client.HighlightedSubexprInfo",
"Lean.Server.Test.Runner.Client.HighlightedSubexprInfo.ctorElimType",
"Nat",
"Lean.Server.Test.Runner.Client.HighlightedSubexprInfo.highli... |
List.cyclicPermutations_of_ne_nil | Mathlib.Data.List.Rotate | [
"List.zipWith",
"Exists",
"Ne",
"List.dropLast",
"List.cyclicPermutations",
"List.cons",
"instHAppendOfAppend",
"List",
"List.exists_cons_of_ne_nil",
"Exists.casesOn",
"List.cyclicPermutations_cons",
"Eq.ndrec",
"List.instAppend",
"Eq.symm",
"Eq",
"HAppend.hAppend",
"List.tails",
"... |
IsCoprime.isRelPrime | Mathlib.RingTheory.Coprime.Basic | [
"CommSemiring.toSemiring",
"IsCoprime.isUnit_of_dvd'",
"IsRelPrime",
"CommSemiring",
"MonoidWithZero.toMonoid",
"Semiring.toMonoidWithZero",
"IsCoprime"
] |
Lean.Compiler.LCNF.Simp.instInhabitedFunDeclInfo | Lean.Compiler.LCNF.Simp.FunDeclInfo | [
"Lean.Compiler.LCNF.Simp.FunDeclInfo",
"Inhabited",
"Lean.Compiler.LCNF.Simp.instInhabitedFunDeclInfo.default",
"Inhabited.mk"
] |
_private.Mathlib.Analysis.SpecialFunctions.Complex.CircleMap.0.eq_of_circleMap_eq._simp_1_3 | Mathlib.Analysis.SpecialFunctions.Complex.CircleMap | [
"False",
"eq_false",
"Complex.instZero",
"Complex.I_ne_zero",
"Zero.toOfNat0",
"Complex",
"OfNat.ofNat",
"Eq",
"Complex.I"
] |
List.mem_reverse | Init.Data.List.Lemmas | [
"False",
"congrArg",
"List.reverseAux",
"Membership.mem",
"List.not_mem_nil._simp_1",
"_private.Init.Data.List.Lemmas.0.List.mem_reverse._simp_1_1",
"iff_self",
"List",
"Iff",
"List.instMembership",
"True",
"List.reverse",
"of_eq_true",
"congrFun'",
"or_false",
"Or",
"Eq.trans",
"L... |
Std.DTreeMap.Raw.WF.emptyc | Std.Data.DTreeMap.Raw.WF | [
"Ordering",
"Std.DTreeMap.Raw.WF.empty",
"Std.DTreeMap.Raw.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Std.DTreeMap.Raw.WF",
"Std.DTreeMap.Raw"
] |
finsum_eq_indicator_apply | Mathlib.Algebra.BigOperators.Finprod | [
"Eq.mpr",
"Set.indicator",
"HEq.refl",
"finsum",
"AddMonoid.toAddZeroClass",
"Classical.propDecidable",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.casesOn",
"finsum_eq_if",
"AddCommMonoid",
"AddZero.toZero",
"eq_of_heq",
"Eq.ndrec",
"Zero.toOfNat0",
"Eq.refl",
"HEq",
"AddCommM... |
_private.Mathlib.NumberTheory.Padics.PadicIntegers.0.PadicInt.coe_sum._simp_1_1 | Mathlib.NumberTheory.Padics.PadicIntegers | [
"Nat.Prime",
"Subring.instSetLike",
"PadicInt",
"PadicInt.Coe.ringHom",
"CommSemiring.toSemiring",
"RingHom",
"Membership.mem",
"Fact",
"Subtype",
"PadicInt.Coe.ringHom_apply",
"PadicInt.instCommRing",
"CommRing.toNonAssocCommRing",
"Field.toSemifield",
"CommRing.toCommSemiring",
"RingHo... |
Lean.Elab.Term.LetIdDeclView.binders | Lean.Elab.Binders | [
"Lean.Syntax",
"Array",
"Lean.Elab.Term.LetIdDeclView"
] |
UpperSemicontinuousOn.add | Mathlib.Topology.Semicontinuity.Basic | [
"OrderTopology",
"LinearOrder",
"UpperSemicontinuousOn.add'",
"PartialOrder.toPreorder",
"instTopologicalSpaceProd",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Prod.mk",
"Prod.fst",
"AddCommMonoid",
"Continuous.continuousAt",
"TopologicalSpace",
"instHA... |
_private.Init.Data.List.Pairwise.0.List.Pairwise.imp.match_1_1 | Init.Data.List.Pairwise | [
"Unit.unit",
"List.Pairwise.cons",
"List.Pairwise",
"HEq.refl",
"Membership.mem",
"List.cons",
"List",
"List.Pairwise.nil",
"Unit",
"List.instMembership",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"List.Pairwise.casesOn",
"List.nil"
] |
Lean.Name.MatchUpToIndexSuffix.suffixMatch.elim | Batteries.Lean.Meta.UnusedNames | [
"PULift.up",
"Lean.Name.MatchUpToIndexSuffix.ctorElim",
"Lean.Name.MatchUpToIndexSuffix.ctorIdx",
"Lean.Name.MatchUpToIndexSuffix",
"Nat",
"Eq.symm",
"Eq",
"Lean.Name.MatchUpToIndexSuffix.suffixMatch"
] |
_private.Mathlib.Lean.Meta.RefinedDiscrTree.Encode.0.Lean.Meta.RefinedDiscrTree.encodingStepAux.match_5 | Mathlib.Lean.Meta.RefinedDiscrTree.Encode | [
"_private.Mathlib.Lean.Meta.RefinedDiscrTree.Encode.0.Lean.Meta.RefinedDiscrTree.encodingStepAux._sparseCasesOn_5",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"Lean.Expr.sort",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.fvar... |
Stream'.Seq.update_cons_succ | Mathlib.Data.Seq.Basic | [
"Stream'.Seq",
"False",
"Nat.instMulZeroClass",
"Nat.instOne",
"congrArg",
"Stream'.Seq.ext",
"Nat.add_eq_zero_iff._simp_1",
"Stream'.Seq.update",
"Option.some",
"one_ne_zero._simp_1",
"instOfNatNat",
"Nat.casesAuxOn",
"instHAdd",
"Option.map",
"And",
"Nat.right_eq_add._simp_1",
"HAd... |
_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Defs.0.EisensteinSeries.denom_aux | Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Defs | [
"Mathlib.Tactic.Ring.mul_pp_pf_overlap",
"Int.cast",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MonoidHom.instMonoidHomClass",
"Mathlib.Meta.NormNum.isNat_add",
"Real",
"Matrix.SpecialLinearGroup",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
... |
Set.image_sub_const_uIcc | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"sub_eq_add_neg",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Semilattic... |
LibraryNote.continuity_lemma_statement | Mathlib.Topology.Continuous | [
"Inhabited.default",
"Batteries.Util.instInhabitedLibraryNote",
"Batteries.Util.LibraryNote"
] |
FaithfulSMul.of_injective | Mathlib.GroupTheory.GroupAction.Hom | [
"MulActionHomClass",
"Eq.mpr",
"instHSMul",
"FaithfulSMul.eq_of_smul_eq_smul",
"congrArg",
"SMul",
"id",
"FaithfulSMul",
"FaithfulSMul.mk",
"congr",
"True",
"eq_self",
"of_eq_true",
"HSMul.hSMul",
"congrFun'",
"Function.Injective",
"Eq",
"DFunLike.coe",
"Eq.trans",
"FunLike",
... |
szemeredi_regularity | Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma | [
"instPowNat",
"NormedCommRing.toNormedRing",
"Rat.instOfNat",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Distrib.leftDistribClass",
"Real.instIsOrderedRing",
"Function.iterate_succ_apply'",
"Finset.card_univ",
"Eq.mpr",
"SzemerediRegularity.energy_increment",
"GroupWithZero.to... |
Vector.finIdxOf?_mk | Init.Data.Vector.Lemmas | [
"Vector.finIdxOf?",
"Array",
"Fin.cast",
"Option.map",
"Vector.mk",
"Nat",
"Array.finIdxOf?",
"Fin",
"BEq",
"Eq",
"Array.size",
"rfl",
"Option"
] |
Finset.toRight | Mathlib.Data.Finset.Sum | [
"Finset.toRight._proof_2",
"Finset",
"Option.some",
"Sum",
"Finset.filterMap",
"Option.none",
"Sum.elim",
"Option"
] |
DirectedOn.le_of_minimal | Mathlib.Order.Bounds.Basic | [
"Preorder.toLE",
"DirectedOn",
"Membership.mem",
"Exists",
"LE.le",
"And.casesOn",
"And",
"Exists.casesOn",
"And.right",
"And.left",
"LE.le.trans",
"Minimal",
"Set.instMembership",
"Preorder",
"Set"
] |
WittVector.instIsocrystalStandardOneDimIsocrystal._proof_2 | Mathlib.RingTheory.WittVector.Isocrystal | [
"PerfectRing",
"CommRing",
"Nat.Prime",
"WittVector.FractionRing.frobenius",
"WittVector.instCommRing",
"CommSemiring.toSemiring",
"RingEquiv.instEquivLike",
"RingEquiv.instRingEquivClass",
"AddGroupWithOne.toAddMonoidWithOne",
"FractionRing",
"nonZeroDivisors",
"Fact",
"RingHomCompTriple",
... |
Sum.instLocallyFiniteOrder._proof_1 | Mathlib.Data.Sum.Interval | [
"False",
"Sum.ctorIdx",
"iff_false",
"congrArg",
"and_self",
"Sum.inr.injEq",
"Finset",
"False.elim",
"Sum.instPreorderSum",
"false_and",
"noConfusion_of_Nat",
"Preorder.toLE",
"Finset.map",
"Membership.mem",
"Exists",
"Sum",
"Sum.inl",
"Sum.inl.injEq",
"LE.le",
"Finset.Icc",
... |
CanonicallyOrderedAddCommMonoid.toAddCancelCommMonoid | Mathlib.Algebra.Order.Sub.Basic | [
"AddCancelCommMonoid.mk",
"AddCancelCommMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"inferInstance",
"PartialOrder",
"OrderedSub",
"AddCommMonoid",
"CanonicallyOrderedAddCommMonoid.toAddCancelCommMonoid._proof_2",
"AddLeftReflectLE",
"AddCommSemigroup.toAddCommMagma",
"AddCommMonoid.t... |
Submodule.rank_sup_add_rank_inf_eq | Mathlib.LinearAlgebra.Dimension.RankNullity | [
"Submodule.comap_inf",
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"Lattice.toSemilatticeSup",
"Cardinal",
"Submodule.Quotient.addCommGroup",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.rank_quotient_add_rank",
"Submodule.addCommMonoid",
"Submodule.c... |
comp_partialSups | Mathlib.Order.PartialSups | [
"partialSups._proof_2",
"congrArg",
"Finset",
"map_finset_sup'",
"PartialOrder.toPreorder",
"Monotone",
"Function.comp",
"Membership.mem",
"LocallyFiniteOrderBot",
"Eq.rec",
"SemilatticeSup.toMax",
"partialSups",
"SupHomClass",
"funext",
"OrderHom.instFunLike",
"Finset.instSetLike",
... |
Module.End.UnifEigenvalues.val | Mathlib.LinearAlgebra.Eigenspace.Basic | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Module.End.HasUnifEigenvalue",
"AddCommGroup",
"CommRing.toCommSemiring",
"ENat",
"Module.End.UnifEigenvalues",
"Module.End",
"Module",
"Subtype.val"
] |
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