name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
PSet.instEmptyCollection | Mathlib.SetTheory.ZFC.PSet | [
"EmptyCollection.mk",
"PSet",
"PSet.empty",
"EmptyCollection"
] | true |
Lean.Elab.Tactic.Do.SplitInfo.matcher.inj | Lean.Elab.Tactic.Do.VCGen.Split | [
"Lean.Meta.MatcherApp",
"Lean.Elab.Tactic.Do.SplitInfo.matcher.noConfusion",
"Lean.Elab.Tactic.Do.SplitInfo",
"Lean.Elab.Tactic.Do.SplitInfo.matcher",
"Eq"
] | true |
CategoryTheory.IsSplitEpi.mk._flat_ctor | Mathlib.CategoryTheory.EpiMono | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsSplitEpi",
"CategoryTheory.IsSplitEpi.mk",
"Nonempty",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.SplitEpi",
"CategoryTheory.Category"
] | false |
Std.Internal.List.Const.getValue?_alterKey | Std.Data.Internal.List.Associative | [
"_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.Const.alterKey.eq_1",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"False",
"Decidable.casesOn",
"congrArg",
"_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.Const.alterKey.match_1.splitter",
"Decidable",
"Bool.false_eq_... | true |
_private.Std.Time.Date.Unit.Weekday.0.Std.Time.Weekday.ofOrdinal.match_1 | Std.Time.Date.Unit.Weekday | [
"Unit.unit",
"False",
"Int.ctorIdx",
"Int.NonNeg",
"Std.Time.Internal.Bounded.LE.ofNatWrapping._proof_5",
"HEq.refl",
"Int.NonNeg.casesOn",
"False.elim",
"Std.Time.Internal.Bounded.LE.instOfNatHAddIntCast._proof_1",
"HSub.hSub",
"Std.Time.Internal.Bounded.LE.ofNatWrapping._proof_6",
"Subtype.c... | false |
_private.Mathlib.SetTheory.ZFC.Rank.0.PSet.rank_eq_wfRank._simp_1_2 | Mathlib.SetTheory.ZFC.Rank | [
"Preorder.toLT",
"Ordinal.partialOrder",
"iSup",
"PartialOrder.toPreorder",
"Exists",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"Ordinal.instConditionallyCompleteLinearOrderBot",
"LT.lt",
"Ordinal.lt_iSup_iff",
"propext",
"ConditionallyCompleteLinearOrderBot.toConditiona... | false |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0._aux_Mathlib_Analysis_SpecialFunctions_Trigonometric_Cotangent___unexpand_Complex_integerComplement_1 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk... | false |
_private.Init.Data.Range.Lemmas.0.Std.Legacy.Range.forM_loop_eq_forM_range'._proof_1_3 | Init.Data.Range.Lemmas | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Std.Legacy.Range.step",
"HMul.hMul",
"Int.natCast_add",
"of_decide_eq_true",
"Std.Legacy.Range.stop",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"H... | false |
Order.IsPredPrelimit.mid.eq_1 | Mathlib.Order.SuccPred.Limit | [
"Preorder.toLT",
"Classical.indefiniteDescription",
"Membership.mem",
"Set.Elem",
"LT.lt",
"Eq.refl",
"Eq",
"Set.instMembership",
"Set.Ioo",
"Order.IsPredPrelimit",
"Order.IsPredPrelimit.mid._proof_1",
"Order.IsPredPrelimit.mid",
"Preorder",
"Set"
] | true |
derivedSeries_succ | Mathlib.GroupTheory.Solvable | [
"Bracket.bracket",
"Group",
"Subgroup",
"instOfNatNat",
"derivedSeries",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Subgroup.commutator",
"Eq",
"rfl"
] | true |
LinearMap.trace.eq_1 | Mathlib.LinearAlgebra.Trace | [
"LinearMap.trace",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Finset",
"LinearMap.traceAux",
"Classical.propDecidable",
"Membership.mem",
"Exists",
"LinearMap.trace._proof_1",
"Subtype",
"Nonempty.some",
"LinearMap.module",
"LinearMap",
"dite",
"smulCommClass_self",
"AddCommMonoi... | true |
Subarray.stop | Init.Data.Array.Subarray | [
"Subarray",
"Std.Slice.internalRepresentation",
"Std.Slice.Internal.SubarrayData",
"Nat",
"Std.Slice.Internal.SubarrayData.stop"
] | true |
ContinuousAlternatingMap.instModule | Mathlib.Topology.Algebra.Module.Alternating.Basic | [
"ContinuousAlternatingMap.instModule._proof_1",
"ContinuousAlternatingMap.instDistribMulAction",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Module.mk",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"ContinuousConstSMul",
"AddCommMonoid",
"TopologicalSpace",
"AddZer... | true |
BddBelow.mul | Mathlib.Algebra.Order.Group.Pointwise.Bounds | [
"HMul.hMul",
"Set.Nonempty.mul",
"lowerBounds",
"Preorder.toLE",
"Mul",
"MulLeftMono",
"MulRightMono",
"Set.Nonempty.mono",
"BddBelow",
"subset_lowerBounds_mul",
"Set.mul",
"Preorder",
"instHMul",
"Set"
] | true |
Submonoid.center.commMonoid | Mathlib.GroupTheory.Submonoid.Center | [
"Monoid",
"Monoid.toMulOneClass",
"Subsemigroup.center.commSemigroup",
"Membership.mem",
"MulOne.toMul",
"Subtype",
"Submonoid.toMonoid",
"CommSemigroup",
"MulOneClass.toMulOne",
"Subsemigroup",
"Submonoid.instSetLike",
"Subsemigroup.instSetLike",
"CommMonoid",
"Subsemigroup.center",
"Se... | true |
EuclideanGeometry.oangle_homothety | Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | [
"EuclideanGeometry.oangle",
"LinearMap.id",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"Orientation",
"Real.partialOrder",
"Real",
"instHSMul",
"Preorder.toLT",
"Orientation.oangle",
"AffineMap.instFunLike",
"Real.Angle",
"Orientation.oangle_smul_left_of_neg",
"Mo... | true |
PosMulReflectLT.rec | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs | [
"PosMulReflectLT.mk",
"Preorder.toLT",
"HMul.hMul",
"Preorder.toLE",
"Mul",
"Subtype",
"LE.le",
"PosMulReflectLT",
"LT.lt",
"Zero.toOfNat0",
"OfNat.ofNat",
"Subtype.val",
"ContravariantClass",
"Preorder",
"instHMul",
"Zero"
] | false |
commutatorElement_one_right | Mathlib.GroupTheory.Commutator.Basic | [
"MulOne.toOne",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Bracket.bracket",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"DivInvMonoid.toMonoid",
"commutatorElement",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"One.toOfNat1"... | true |
sSupHom.instInhabited.eq_1 | Mathlib.Order.Hom.CompleteLattice | [
"SupSet",
"sSupHom.id",
"sSupHom.instInhabited",
"sSupHom",
"Inhabited",
"Eq.refl",
"Eq",
"Inhabited.mk"
] | true |
IsPrimitiveRoot.isUnit | Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots | [
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"IsUnit.of_mul_eq_one",
"HSub.hSub",
"IsUnit",
"id",
"MulOne.toMul",
"instSubNat",
"Ne",
"instOfNatNat",
"Nat.sub_one_add_one",
"Monoid.toPow",
"instIsDedekindFiniteMonoid",
"instHAdd",
"MulOneClass.toMulOne... | true |
modularCyclotomicCharacter.toFun | Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter | [
"Int.cast",
"IsDomain",
"Nat.instMulZeroClass",
"CommRing",
"modularCyclotomicCharacter.aux",
"ZMod.commRing",
"CommSemiring.toSemiring",
"Membership.mem",
"Units",
"Fintype.card",
"Subtype",
"Distrib.toAdd",
"Subgroup",
"AddGroupWithOne.toIntCast",
"Units.instGroup",
"rootsOfUnity",
... | true |
Lean.ModuleData.constants | Lean.Environment | [
"Array",
"Lean.ModuleData",
"Lean.ConstantInfo"
] | true |
Finset.sorted_zero_eq_min'_aux | Mathlib.Data.Finset.Sort | [
"Finset.min'",
"Iff.mpr",
"Eq.mpr",
"Nat.zero_le",
"instReflLe",
"congrArg",
"Finset.min'_le",
"Finset.mem_sort",
"Finset",
"List.get",
"LinearOrder",
"PartialOrder.toPreorder",
"List.mem_iff_get",
"Finset.min'_mem",
"Preorder.toLE",
"Finset.pairwise_sort",
"Membership.mem",
"Exist... | true |
Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ctorElimType | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"cond",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ofDiseqSplit",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ofEq",
"Lean.Meta.Grind.Arith.Linear.LinExpr",
"Nat.ble",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ringEq",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ofEqOfNat",
"Lean.Meta.Grind.Ari... | false |
CommBialgCat.Hom.ctorIdx | Mathlib.Algebra.Category.CommBialgCat | [
"CommRing",
"Nat",
"CommBialgCat.Hom",
"CommBialgCat"
] | false |
Std.Rio.isEmpty | Init.Data.Range.Polymorphic.Basic | [
"instDecidableNot",
"Std.PRange.UpwardEnumerable",
"Option.some",
"Std.Rio.upper",
"Option.decidableForallMem",
"Std.Rio",
"LT.lt",
"Bool",
"Std.PRange.Least?",
"Std.PRange.Least?.least?",
"Decidable.decide",
"Eq",
"Not",
"DecidableLT",
"LT",
"Option"
] | true |
SeparableWeaklyLocallyCompactAddGroup.sigmaCompactSpace | Mathlib.Topology.Algebra.Group.Basic | [
"Filter.instMembership",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"instSeparatelyContinuousAddOfContinuousAdd",
"Set.iUnion_eq_univ_iff",
"TopologicalSpace.denseRange_denseSeq",
"Homeomorph.continuous",
"Classical.indefiniteDescription",
"congrArg",
"Set.univ",
"AddMonoid.toAddZeroClass",
"W... | true |
_private.Mathlib.Logic.Nontrivial.Defs.0.not_nontrivial_iff_subsingleton._simp_1_1 | Mathlib.Logic.Nontrivial.Defs | [
"Nontrivial",
"Exists",
"Ne",
"nontrivial_iff",
"propext",
"Eq"
] | false |
EquivFunctorUnique._proof_2 | Mathlib.Control.EquivFunctor.Instances | [
"Equiv.instEquivLike",
"Equiv.uniqueCongr",
"Unique",
"id",
"Equiv",
"Pi.instSubsingleton",
"of_eq_true",
"_private.Mathlib.Control.EquivFunctor.Instances.0.EquivFunctorUnique._simp_1",
"Equiv.refl",
"Eq",
"DFunLike.coe",
"Unique.subsingleton_unique",
"EquivLike.toFunLike"
] | false |
AlgHom.equalizer_eq_top | Mathlib.Algebra.Algebra.Subalgebra.Lattice | [
"Subalgebra.instSetLike",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"PartialOrder.toPreorder",
"iff_true",
"Algebra.instCompleteLatticeSubalgebra",
"Algebra",
"Preorder.toLE",
"Membership.mem",
"Algebra.mem_top._simp_1",
"CompleteLattice.toBoundedOrder",
"AlgHom.eq... | true |
Lean.Parser.Term.doReturn._regBuiltin.Lean.Parser.Term.doReturn_1 | Lean.Parser.Do | [
"Lean.Parser.Term.doReturn",
"IO",
"Unit",
"Lean.Parser.addBuiltinLeadingParser",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | false |
WithBot.unbot_le_unbot_iff | Mathlib.Order.WithBot | [
"WithBot.some",
"WithBot",
"WithBot.coe_unbot",
"congrArg",
"Ne",
"Bot.bot",
"LE.le",
"LE",
"iff_self",
"WithBot.unbot",
"Iff",
"WithBot.le_unbot_iff._simp_2",
"True",
"of_eq_true",
"congrFun'",
"WithBot.instLE",
"WithBot.bot",
"Eq.trans"
] | true |
ContRepresentation.trivial_apply | Mathlib.RepresentationTheory.Continuous.Basic | [
"Monoid",
"MonoidHom.instFunLike",
"ContinuousLinearMap.semiring",
"Monoid.toMulOneClass",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"ContRepresentation",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"ContRepresentation.trivial",
"ContRepresentation._proof_1",
"MulZeroOneCla... | true |
PEquiv.single_apply | Mathlib.Data.PEquiv | [
"PEquiv.instFunLikeOption",
"PEquiv.single",
"Option.some",
"if_pos",
"Option.none",
"PEquiv",
"Eq",
"DFunLike.coe",
"rfl",
"Option",
"DecidableEq"
] | true |
_private.Lean.Elab.Term.TermElabM.0.Lean.Elab.Term.isNoImplicitLambda | Lean.Elab.Term.TermElabM | [
"Lean.Syntax.isOfKind",
"Lean.Syntax",
"instDecidableEqBool",
"instOfNatNat",
"Bool.true",
"Lean.Syntax.getArg",
"Nat",
"Bool",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr4",
"Eq",
"ite"
] | true |
_private.Lean.Meta.Basic.0.Lean.Meta.ConfigWithKey.mk._flat_ctor | Lean.Meta.Basic | [
"UInt64",
"_private.Lean.Meta.Basic.0.Lean.Meta.ConfigWithKey.mk",
"Lean.Meta.ConfigWithKey",
"Lean.Meta.Config"
] | false |
_private.Mathlib.AlgebraicTopology.SimplexCategory.Basic.0.SimplexCategory.eq_const_of_zero.match_1_1 | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"Unit.unit",
"False",
"Fin.casesOn",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Fin.mk",
"Fin.instOfNat",
"instOfNatNat",
"Nat.le.step",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat.le",
"Nat.instNeZeroSucc",
"SimplexCategory.mk",
"Nat",
"LT.lt",
"Eq.ndrec",
"Nat.ctorIdx",
"in... | false |
IsLeftUniformAddGroup.toIsTopologicalAddGroup | Mathlib.Topology.Algebra.IsUniformGroup.Defs | [
"UniformSpace",
"IsLeftUniformAddGroup",
"AddGroup",
"UniformSpace.toTopologicalSpace",
"IsTopologicalAddGroup"
] | true |
_private.Lean.Meta.MethodSpecs.0.Lean.MethodSpecTheorem._sizeOf_1 | Lean.Meta.MethodSpecs | [
"_private.Lean.Meta.MethodSpecs.0.Lean.MethodSpecTheorem.rec",
"_private.Lean.Meta.MethodSpecs.0.Lean.MethodSpecTheorem",
"Lean.Expr",
"instOfNatNat",
"List",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"List._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Name",
"OfNat.ofNa... | false |
IntermediateField.ctorIdx | Mathlib.FieldTheory.IntermediateField.Basic | [
"IntermediateField",
"Algebra",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"Nat",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemiring",
"Field"
] | false |
MeasureTheory.AEEqFun | Mathlib.MeasureTheory.Function.AEEqFun | [
"MeasureTheory.Measure",
"MeasureTheory.Measure.aeEqSetoid",
"Subtype",
"MeasurableSpace",
"TopologicalSpace",
"Quotient",
"MeasureTheory.AEStronglyMeasurable"
] | true |
_private.Lean.DocString.Parser.0.Lean.Doc.Parser.recoverBlockAtErrPos.match_1 | Lean.DocString.Parser | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Lean.Parser.Error",
"_private.Lean.DocString.Parser.0.Lean.Doc.Parser.recoverBlockAtErrPos._sparseCasesOn_1",
"Option"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.card_nonuniformWitness_sdiff_biUnion_star._simp_1_5 | Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | [
"Finset",
"Membership.mem",
"And",
"Finset.instSetLike",
"DecidablePred",
"propext",
"Finset.mem_filter",
"Finset.filter",
"Eq",
"SetLike.instMembership"
] | false |
ENNReal.coe_strictMono | Mathlib.Data.ENNReal.Basic | [
"Iff.mpr",
"ENNReal.ofNNReal",
"Preorder.toLT",
"StrictMono",
"PartialOrder.toPreorder",
"ENNReal.coe_lt_coe",
"NNReal",
"NNReal.instPartialOrder",
"LT.lt",
"ENNReal",
"ENNReal.instPartialOrder"
] | true |
_private.Lean.Elab.PreDefinition.WF.GuessLex.0.Lean.Elab.WF.GuessLex.RecCallCache.prettyEntry.match_1 | Lean.Elab.PreDefinition.WF.GuessLex | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Lean.Elab.WF.GuessLex.GuessLexRel",
"Unit",
"Option"
] | false |
LSeries.term_smul_apply | Mathlib.NumberTheory.LSeries.Linearity | [
"instHSMul",
"instSMulOfMul",
"HMul.hMul",
"congrArg",
"Complex.instMul",
"Function.hasSMul",
"congrFun",
"Nat",
"True",
"eq_self",
"of_eq_true",
"HSMul.hSMul",
"congrFun'",
"LSeries.term",
"LSeries.term_smul",
"Complex",
"Eq",
"Eq.trans",
"instHMul"
] | true |
NonemptyInterval.neg_pure | Mathlib.Algebra.Order.Interval.Basic | [
"NegZeroClass.toNeg",
"AddCommGroup.toAddCommMonoid",
"instNegNonemptyInterval",
"NonemptyInterval.pure",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMon... | true |
AffineMap.homothety_eq_iff_of_mul_eq_one | Mathlib.LinearAlgebra.AffineSpace.AffineMap | [
"Eq.mpr",
"MulOne.toOne",
"CommRing",
"AffineMap.instFunLike",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AffineMap.homothety_one",
"AffineMap.homothety",
"AddGroupWithOne.toAddMonoidWithOne",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"id",
"Mul... | true |
CategoryTheory.Arrow.mapCechConerve._proof_3 | Mathlib.AlgebraicTopology.CechNerve | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"congrArg",
"CategoryTheory.Limits.widePushout",
"CategoryTheory.Arrow.cechConerve._proof_3",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.cate... | false |
CategoryTheory.PreZeroHypercover.pullbackCoverOfLeft | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.mk",
"CategoryTheory.Limits.pullback",
"CategoryTheory.PreZeroHypercover.pullbackCoverOfLeft._proof_1",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.HasPullback... | true |
Array.instForMOfMonad | Init.Data.Array.Basic | [
"ForM",
"instOfNatNat",
"Array",
"Array.forM",
"PUnit",
"Nat",
"OfNat.ofNat",
"Monad",
"ForM.mk",
"Array.size"
] | true |
Sum.noMaxOrder | Mathlib.Data.Sum.Order | [
"Iff.mpr",
"NoMaxOrder",
"Sum.inr_lt_inr_iff",
"Exists",
"NoMaxOrder.mk",
"_private.Mathlib.Data.Sum.Order.0.Sum.noMaxOrder.match_1",
"Sum",
"Sum.inl",
"NoMaxOrder.exists_gt",
"_private.Mathlib.Data.Sum.Order.0.Sum.noMinOrder.match_3",
"Sum.inr",
"LT.lt",
"Exists.intro",
"Sum.inl_lt_inl_if... | true |
FiniteField.frobeniusAlgHom | Mathlib.FieldTheory.Finite.Basic | [
"CommRing",
"RingHom.mk",
"MonoidHom",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AlgHom",
"Algebra",
"Fintype.card",
"FiniteField.frobeniusAlgHom._proof_2",
"Field.toSemifield",
"MulOneClass.toMulOne",
"CommRing.toCommSemiring",
"Fintype",
"CommMonoid.toMonoid",
"FiniteField.fr... | true |
CategoryTheory.Functor.LaxMonoidal.left_unitality_assoc | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"CategoryTheory.Functor.LaxMonoidal.ε",
"CategoryTheory.Functor.LaxMonoidal.left_unita... | true |
Lean.Elab.Tactic._aux_Mathlib_Tactic_Inhabit___elabRules_Lean_Elab_Tactic_inhabit_1 | Mathlib.Tactic.Inhabit | [
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Tactic.getMainGoal",
"Lean.Meta.State",
"Lean.Syntax.isOfKind",
"Option.some",
"Lean.Elab.Tactic.Context",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.MVarId",
"Lean.TSyntax.raw",
"Lean.Meta.MetaM",
"IO.R... | false |
_private.Mathlib.Algebra.Group.Defs.0.CommMagma.ext.match_1 | Mathlib.Algebra.Group.Defs | [
"Mul.mk",
"HMul.hMul",
"CommMagma.mk",
"Mul",
"CommMagma",
"CommMagma.casesOn",
"Mul.casesOn",
"Eq",
"instHMul"
] | false |
CategoryTheory.Limits.Types.range_snd_of_isPullback | Mathlib.CategoryTheory.Limits.Types.Pullbacks | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.IsPullback",
"TypeCat.instFunLikeFun",
"id",
"TypeCat.Fun",
"Set.preimage",
"CategoryTheory.IsPullback.flip",
"CategoryTheory.types",
"Eq.refl",
"CategoryThe... | true |
Profinite.NobelingProof.Linear_CC'₀.eq_1 | Mathlib.Topology.Category.Profinite.Nobeling.Successor | [
"Int.instAddCommGroup",
"Int.instAddCommMonoid",
"LocallyConstant.instAddCommGroup",
"Preorder.toLT",
"Semiring.toModule",
"isWellOrder_lt",
"Pi.topologicalSpace",
"Ordinal.partialOrder",
"LocallyConstant.instAddCommMonoid",
"ContinuousMap.mk",
"LinearOrder",
"WellFoundedLT",
"PartialOrder.t... | true |
CategoryTheory.nerve.right_edge | Mathlib.AlgebraicTopology.SimplicialSet.Nerve | [
"Eq.mpr",
"SSet.Edge.tgt_eq",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.ComposableArrows.right",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"CategoryTheory.ComposableArrows",
"id",
"Equiv",
"instOfNatNat",
"instHAdd",
"CategoryTheory.nerveEquiv",
... | true |
ValuativeRel.mul_vle_mul_left | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | [
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"ValuativeRel.vle",
"instDistribOfSemiring",
"CommRing.toCommSemiring",
"Distrib.toMul",
"ValuativeRel",
"instHMul"
] | true |
AddGroup.rank_le | Mathlib.GroupTheory.Rank | [
"AddGroup.fg_iff'",
"Finset",
"Exists",
"Classical.decPred",
"Nat.find_le",
"LE.le",
"instLENat",
"AddSubgroup",
"And",
"AddGroup",
"SetLike.coe",
"Finset.instSetLike",
"Nat",
"And.intro",
"Exists.intro",
"Iff.mp",
"Finset.card",
"AddGroup.rank",
"Top.top",
"AddGroup.FG",
"Ad... | true |
_private.Mathlib.LinearAlgebra.Dual.Lemmas.0.LinearMap.flip_bijective_iff₁._simp_1_2 | Mathlib.LinearAlgebra.Dual.Lemmas | [
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.flip_surjective_iff₁",
"LinearMap.in... | false |
iSupIndep.linearEquiv | Mathlib.LinearAlgebra.DFinsupp | [
"Submodule",
"Pi.addCommMonoid",
"iSupIndep.linearEquiv._proof_4",
"iSupIndep.linearEquiv._proof_3",
"iSupIndep",
"iSup",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Submodule.completeLattice",
"DFinsupp.lsum",
"Pi.module",
"AddMonoid.toAddZeroClass",
"iSupIndep.linearEquiv._... | true |
_private.Lean.Meta.Tactic.Grind.Arith.CommRing.Proof.0.Lean.Meta.Grind.Arith.CommRing.withProofContext | Lean.Meta.Tactic.Grind.Arith.CommRing.Proof | [
"Lean.Meta.Grind.Arith.CommRing.SemiringExpr",
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Grind.CommRing.instBEqPoly",
"Lean.Grind.CommRing.Poly",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Arith.CommRing.RingM",
"Lean.Core.instMonadLiftIOCoreM",
"Lean.Meta.Grind.Arith.CommRing.RingM.Context",
"Le... | true |
SimpleGraph.chromaticNumber_pathGraph | Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions | [
"False",
"instCompleteLinearOrderENat",
"Bool.fintype",
"ChainCompletePartialOrder.instOfCompleteLattice",
"ENat.instNatCast",
"SimpleGraph.two_le_chromaticNumber_of_adj",
"congrArg",
"CompletelyDistribLattice.toCompleteLattice",
"SimpleGraph.Adj",
"AddMonoid.toAddZeroClass",
"Nat.instAtLeastTwo... | true |
Bundle.contMDiffAt_section | Mathlib.Geometry.Manifold.VectorBundle.Basic | [
"Eq.mpr",
"Bundle.Trivialization.toFun'",
"Prod.normedSpace",
"chartedSpaceSelf",
"Prod.normedAddCommGroup",
"NormedSpace",
"FiberBundle",
"_private.Mathlib.Geometry.Manifold.VectorBundle.Basic.0.Bundle.contMDiffAt_section._simp_1_1",
"congrArg",
"PseudoMetricSpace.toUniformSpace",
"_private.Mat... | true |
LinearMap.intrinsicStar_eq_comp | Mathlib.Algebra.Star.LinearMap | [
"WithConv.toConv",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LinearMap.intrinsicStar",
"WithConv.ofConv",
"AddMonoid.toAddZeroClass",
"RingHomInvPair.triples₂",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"RingHomInvPair.instStarRingEnd",
"StarAddMonoid.toInvolut... | true |
_private.Mathlib.RingTheory.Valuation.Extension.0.Valuation.HasExtension._aux_Mathlib_RingTheory_Valuation_Extension___macroRules__private_Mathlib_RingTheory_Valuation_Extension_0_Valuation_HasExtension_termL₀_1 | Mathlib.RingTheory.Valuation.Extension | [
"Pure.pure",
"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",
"Lean.Name.mkStr... | false |
CategoryTheory.ShortComplex.SnakeInput.Hom.mk.inj | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.SnakeInput.L₃",
"CategoryTheory.ShortComplex.SnakeInput.L₂",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.SnakeInput.L₀",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.SnakeInput"... | true |
Lean.Meta.Config.transparency._default | Lean.Meta.Basic | [
"id",
"Lean.Meta.TransparencyMode",
"Lean.Meta.TransparencyMode.default"
] | false |
smoothSheafGroup._proof_1 | Mathlib.Geometry.Manifold.Sheaf.Smooth | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"Eq.mpr",
"CategoryTheory.Functor",
"GrpCat",
"MonoidHom.instFunLike",
"GrpCat.forget_reflects_isos",
"Opposite",
"NormedSpace",
"MonoidHom",
"GrpCat.str",
"instTopENat",
"Monoid.toMulOneClass",
"TopologicalSpace.Opens.instPartialOrder",
"cong... | false |
_private.Mathlib.RingTheory.Polynomial.Cyclotomic.Eval.0.Polynomial.sub_one_pow_totient_lt_cyclotomic_eval._simp_1_5 | Mathlib.RingTheory.Polynomial.Cyclotomic.Eval | [
"forall_true_left",
"True",
"propext",
"Eq",
"True.intro"
] | false |
MeromorphicAt.eventually_eq_zero_or_eventually_ne_zero | Mathlib.Analysis.Meromorphic.Basic | [
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"NormedRing.toRing",
"NormedSpace",
"instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors",
"AddGroupWithOne.toAddGroup",
"congrArg",
"sub_eq_zero",
"DistribMulAction.toDistribSMul",
"... | true |
Finset.sum_range_add_sub_sum_range | Mathlib.Algebra.BigOperators.Group.Finset.Basic | [
"AddCommGroup.toAddCommMonoid",
"sub_eq_of_eq_add'",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Finset.range",
"SubNegMonoid.toSub",
"instHAdd",
"instHSub",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"Nat",
"Finset.sum_range_add",
"instAddNat",
"Eq",
"Finset.sum"
] | true |
List.mem_dedup._simp_1 | Mathlib.Data.List.Dedup | [
"List.dedup",
"Membership.mem",
"List.mem_dedup",
"List",
"List.instMembership",
"propext",
"Eq",
"DecidableEq"
] | false |
CategoryTheory.PreGaloisCategory.mulAction_naturality | Mathlib.CategoryTheory.Galois.Basic | [
"CategoryTheory.PreGaloisCategory.instMulActionAutFunctorFintypeCatObjFiniteObj",
"CategoryTheory.NatTrans.naturality_apply",
"CategoryTheory.Functor",
"instHSMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"Finite",
"FintypeCat",
"CategoryTheor... | true |
Lean.mkLambda | Lean.Expr | [
"Lean.Expr",
"Lean.Expr.lam",
"Lean.Name",
"Lean.BinderInfo"
] | true |
Lean.Parser.FirstTokens.merge | Lean.Parser.Types | [
"Lean.Parser.FirstTokens.unknown",
"Lean.Parser.Token",
"Lean.Parser.FirstTokens.tokens",
"Lean.Parser.FirstTokens.optTokens",
"instHAppendOfAppend",
"List",
"Lean.Parser.FirstTokens.toOptional",
"_private.Lean.Parser.Types.0.Lean.Parser.FirstTokens.merge.match_1",
"Lean.Parser.FirstTokens",
"List... | true |
Lean.mkLabelExt | Lean.LabelAttribute | [
"Array.push",
"IO",
"Option.some",
"Lean.registerSimpleScopedEnvExtension",
"id",
"instDecidableEqBool",
"autoParam",
"List.toArray",
"Array",
"Bool.true",
"Lean.mkLabelExt._auto_1",
"Bool",
"Lean.Name",
"Lean.SimpleScopedEnvExtension.Descr.mk",
"Lean.OLeanLevel",
"Lean.LabelExtension"... | true |
_private.Mathlib.LinearAlgebra.QuadraticForm.Prod.0.QuadraticMap.posDef_prod_iff._simp_1_1 | Mathlib.LinearAlgebra.QuadraticForm.Prod | [
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"QuadraticMap.Anisotropic",
"QuadraticMap.PosDef",
"QuadraticMap.instFunLike",
"LE.le",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"And",
"... | false |
HomologicalComplex.XIsoOfEq_inv_naturality | Mathlib.Algebra.Homology.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HomologicalComplex",
"Eq.rec",
"HomologicalComplex.XIsoOfEq",
"CategoryTheory.Category.comp_id",
"ComplexShape",
"congr"... | true |
addSubgroupOfIdempotent._proof_2 | Mathlib.GroupTheory.OrderOfElement | [
"Finite",
"AddMonoid.toAddZeroClass",
"AddSubsemigroup.carrier",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubmonoid.toAddSubsemigroup",
"AddCancelMonoid.toAddLeftCancelMonoid",
"AddSubsemigroup.add_mem'",
"instHAdd",
"Set.add",
"AddGroup",
"Set.Nonempty",
"AddGroup.toSubNegMonoid",
... | false |
IsMulApplyEqComp.mul_apply_eq_comp | Mathlib.Data.FunLike.IsApply | [
"HMul.hMul",
"outParam",
"Mul",
"IsMulApplyEqComp",
"Eq",
"DFunLike.coe",
"FunLike",
"instHMul"
] | true |
Std.Tactic.BVDecide.instHashableBVBit.hash | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"UInt64.instOfNat",
"mixHash",
"UInt64",
"instHashableNat",
"instHashableFin",
"Hashable.hash",
"Nat",
"_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Basic.0.Std.Tactic.BVDecide.instHashableBVBit.hash.match_1",
"OfNat.ofNat",
"Fin",
"Std.Tactic.BVDecide.BVBit"
] | true |
rTensor.inverse_of_rightInverse._proof_4 | Mathlib.LinearAlgebra.TensorProduct.RightExactness | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"CommRing.toCommSemiring",
"CommMonoid.toMonoid",
"TensorProduct.instSMul._proof_1",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMonoid.t... | false |
Cubic.coeff_eq_zero | Mathlib.Algebra.CubicDiscriminant | [
"Cubic.c",
"instOfNatNat",
"Cubic.toPoly",
"Cubic.d",
"Polynomial.coeff",
"GT.gt",
"And",
"And.left",
"Cubic.b",
"Nat",
"LT.lt",
"Cubic.a",
"Semiring",
"Cubic",
"_private.Mathlib.Algebra.CubicDiscriminant.0.Cubic.coeffs",
"Zero.toOfNat0",
"instLTNat",
"OfNat.ofNat",
"Eq",
"MulZ... | true |
Polynomial.monicEquivDegreeLT._proof_2 | Mathlib.RingTheory.Polynomial.Basic | [
"Nontrivial",
"Polynomial.Monic.ne_zero_of_polynomial_ne",
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.degreeLT",
"Submodule",
"Polynomial.instOne",
"WithBot",
"Preorder.toLT",
"_private.Mathlib.RingTheory.Polynomial.Basic.0.Polynomial.monicEquivDegreeLT._simp_1",
"NeZero.one",
"Semiring.toM... | false |
Sigma.instAddAction._proof_1 | Mathlib.Algebra.Group.Action.Sigma | [
"Eq.mpr",
"AddMonoid.toAddSemigroup",
"congrArg",
"AddSemigroupAction.add_vadd",
"id",
"Sigma.fst",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"instHAdd",
"AddSemigroup.toAdd",
"Sigma.vadd_mk",
"AddSemigroupAction.toVAdd",
"HAdd.hAdd",
"AddMonoid",
"instHVAdd",
"Eq... | false |
ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat | Mathlib.Probability.Kernel.Disintegration.CDFToKernel | [
"Iff.mpr",
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"_private.Mathlib.Probability.Kernel.Disintegration.CDFToKernel.0.ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat.match_1_1",
"instClosedIicTopology",
"Real.partialOrder",
"ConditionallyCompleteLinearOrder.to... | true |
Std.Http.Headers.mk.noConfusion | Std.Internal.Http.Data.Headers | [
"Std.Http.Header.Name.instBEq",
"id",
"Std.Http.Header.Name",
"Std.Http.Header.Value",
"Std.Http.Header.Name.instHashable",
"Std.Http.Headers.mk",
"Std.Http.Headers",
"Std.Internal.IndexMultiMap",
"Eq",
"Std.Http.Headers.noConfusion"
] | false |
Lean.registerEnvExtension | Lean.Environment | [
"Pure.pure",
"instMonadExceptOfMonadExceptOf",
"Array.push",
"IO.instMonadLiftSTRealWorldBaseIO",
"Monad.toApplicative",
"ST.Ref.modify",
"MonadExcept.throw",
"instMonadLiftT",
"IO",
"instMonadExceptOfEIO",
"ST.Ref.get",
"Lean.initializing",
"_private.Lean.Environment.0.Lean.EnvExtension.env... | true |
Mathlib.Tactic.Ring.Common.pow_one_cast_of_isNat | Mathlib.Tactic.Ring.Common | [
"Mathlib.Meta.NormNum.IsNat",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"Nat.instAddMonoidWithOne",
"Nat.cast",
"Monoid.toPow",
"CommSemiring",
"AddMonoidWithOne.toOne",
"HPow.hPow",
"pow_one",
"Nat",
"True",
"eq_self",
"Semiring.toMonoid",
... | true |
instPartialOrderHomogeneousSubmodule_1 | Mathlib.RingTheory.GradedAlgebra.Homogeneous.Submodule | [
"PartialOrder.ofSetLike",
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"DirectSum.Decomposition",
"HomogeneousSubmodule.setLike",
"DistribMulAction.toDistribSMul",
"SetLike.GradedSMul",
"AddMonoid.toAddZeroClass",
"HomogeneousSubmodule",
"AddSubmonoidClass",
"AddZeroClass.toAddZero",
... | true |
_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.ofPrime_le_of_le.match_1_1 | Mathlib.RingTheory.Valuation.ValuationSubring | [
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"RingHom",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Exists",
"Subtype",
"Ideal",
"CommRing.toNonAssocCommRing",
"Field.toSemifield",
"Field.to... | false |
_private.Std.Internal.Http.Internal.IndexMultiMap.0.Std.Internal.IndexMultiMap.insert._proof_2 | Std.Internal.Http.Internal.IndexMultiMap | [
"Iff.mpr",
"Std.HashMap.alter",
"Std.Internal.IndexMultiMap.indexes",
"Array.push",
"Iff.of_eq",
"Option.some",
"Membership.mem",
"Std.Internal.IndexMultiMap.entries",
"Std.HashMap",
"List.cons",
"Array",
"_private.Std.Internal.Http.Internal.IndexMultiMap.0.Std.Internal.IndexMultiMap.insert.ma... | false |
LieAlgebra.HasCentralRadical.casesOn | Mathlib.Algebra.Lie.Semisimple.Defs | [
"CommRing",
"LieAlgebra.HasCentralRadical.mk",
"LieRing",
"LieAlgebra.HasCentralRadical.rec",
"LieIdeal",
"LieAlgebra",
"LieAlgebra.center",
"Eq",
"LieAlgebra.radical",
"LieAlgebra.HasCentralRadical"
] | false |
Std.Http.Version.recOn | Std.Internal.Http.Data.Version | [
"Std.Http.Version.v30",
"Std.Http.Version.v10",
"Std.Http.Version",
"Std.Http.Version.v11",
"Std.Http.Version.v20",
"Std.Http.Version.rec"
] | false |
ProbabilityTheory.Kernel.snd_compProd_prodMkLeft | Mathlib.Probability.Kernel.Composition.KernelLemmas | [
"ProbabilityTheory.Kernel.comp",
"ProbabilityTheory.Kernel.comp_eq_snd_compProd",
"ProbabilityTheory.IsSFiniteKernel",
"MeasurableSpace",
"ProbabilityTheory.Kernel.snd",
"Eq.symm",
"Eq",
"ProbabilityTheory.Kernel",
"ProbabilityTheory.Kernel.prodMkLeft",
"ProbabilityTheory.Kernel.compProd"
] | true |
_private.Mathlib.MeasureTheory.Measure.Support.0.MeasureTheory.Measure.isClosed_support._proof_1_2 | Mathlib.MeasureTheory.Measure.Support | [
"False",
"MeasureTheory.Measure",
"Preorder.toLT",
"eq_false",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Lean.Grind.eq_false_of_imp_eq_true",
"Lean.Grind.and_eq_of_eq_true_left",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"And.casesOn",
"MeasurableSpace",
"TopologicalSpace... | false |
_private.Mathlib.Analysis.Normed.Field.Ultra.0.IsUltrametricDist.isUltrametricDist_of_forall_pow_norm_le_nsmul_pow_max_one_norm._simp_1_2 | Mathlib.Analysis.Normed.Field.Ultra | [
"False",
"Preorder.toLT",
"lt_self_iff_false",
"LT.lt",
"propext",
"Eq",
"Preorder"
] | false |
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