name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Analysis.Convex.Gauge.0.Convex.uniformContinuous_gauge.match_1_1 | Mathlib.Analysis.Convex.Gauge | [
"Real",
"LipschitzWith",
"SeminormedAddCommGroup",
"gauge",
"NormedSpace",
"NormedSpace.toModule",
"Exists",
"EMetricSpace.toPseudoEMetricSpace",
"NNReal",
"Real.metricSpace",
"Exists.casesOn",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"SeminormedAddCommGroup.toAddCommGroup",
"Exists.i... | false |
_private.Mathlib.Data.List.Basic.0.List.getLastI_eq_getLast?_getD._sparseCasesOn_1_1 | Mathlib.Data.List.Basic | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
CochainComplex.mappingCone.inr_snd_assoc | Mathlib.Algebra.Homology.HomotopyCategory.MappingCone | [
"Eq.mpr",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"CochainComplex.mappingCone.inr",
"Quiver.Hom",
"CochainComplex.HomComplex.Cochain.comp",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
... | true |
NNReal.isometry_coe | Mathlib.Topology.MetricSpace.Isometry | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Real",
"EMetricSpace.toPseudoEMetricSpace",
"NNReal",
"instMetricSpaceNNReal",
"Real.metricSpace",
"WeakPseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniformSpace",
"ENNReal",
"EDist.edist",
"MetricSpace.toEMetricSpace",
"UniformSpace.toTopo... | true |
Sum.instPreorderSum._proof_3 | Mathlib.Data.Sum.Order | [
"Sum.LiftRel.trans",
"Preorder.toLE",
"Sum",
"LE.le",
"instIsTransLe",
"Sum.LiftRel",
"Preorder"
] | false |
DiscreteConvolution.AddConvolutionExistsAt.convolution_vadd | Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution | [
"Eq.mpr",
"instHSMul",
"SemilinearMapClass.toMulActionSemiHomClass",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"DiscreteConvolution.addConvolution",
"Summable.tsum_const_smul",
"AddMonoid.toAddZeroClass",
"SummationFilter",
"LinearMap.instFunLike",
"Membership.me... | true |
Std.IterM.toListRev_filterMap | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"Pure.pure",
"List.filterMap_reverse",
"congrArg",
"Monad.toApplicative",
"MonadLiftT.monadLift",
"instMonadLiftT",
"Std.Iterators.Finite",
"LawfulApplicative.toLawfulFunctor",
"Std.IterM.toListRev",
"Std.Iterators.Types.FilterMap.instFinite",
"LawfulMonad",
"Std.IterM.filterMap",
"Applicati... | true |
_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable.0.EisensteinSeries.aux_tendsto_tsum._simp_1_7 | Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | [
"False",
"eq_false",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"CharZero",
"Nat.cast_add_one_ne_zero",
"AddMonoidWithOne.toOne",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat",
"On... | false |
Ring.krullDimLE_one_iff | Mathlib.RingTheory.KrullDimension.Basic | [
"WithBot.addMonoidWithOne",
"WithBot.instPreorder",
"Eq.mpr",
"WithBot",
"Semiring.toModule",
"Equiv.instEquivLike",
"instAddMonoidWithOneENat",
"ENat.instNatCast",
"congrArg",
"CommSemiring.toSemiring",
"_private.Mathlib.RingTheory.KrullDimension.Basic.0.Ring.krullDimLE_one_iff._simp_1_2",
"I... | true |
DirectLimit.induction₃ | Mathlib.Order.DirectedInverseSystem | [
"DirectLimit.setoid",
"Preorder.toLE",
"Exists",
"LE.le",
"DirectLimit",
"Quotient.mk",
"And.casesOn",
"And",
"Exists.casesOn",
"IsDirectedOrder",
"Eq.ndrec",
"DirectedSystem",
"Sigma.mk",
"Eq.symm",
"Eq",
"DFunLike.coe",
"Sigma",
"DirectLimit.exists_eq_mk₃",
"Preorder",
"FunLi... | true |
_private.Init.Data.List.Nat.TakeDrop.0.List.drop_append._proof_1_1 | Init.Data.List.Nat.TakeDrop | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Om... | false |
TopCat.pathEquiv_apply_apply | Mathlib.Topology.Homotopy.TopCat.Path | [
"Real",
"Equiv.instEquivLike",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"TopCat.Path",
"Set.Elem",
"Equiv",
"TopCat.I.homeomorph",
"TopCat.Path.hom",
"TopCat.str",
"TopCat.pathEquiv",
"Homeomorph.instEquivLike",
"TopCat.carrier",
"TopCat.Hom.hom",
"Homeomo... | true |
CategoryTheory.Limits.isIso_limit_cone_parallelPair_of_epi | Mathlib.CategoryTheory.Limits.Shapes.Equalizers | [
"CategoryTheory.IsIso",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryTheory.Limits.Fork",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Limits.isIso_limit... | true |
FirstOrder.Language.Theory.IsMaximal | Mathlib.ModelTheory.Satisfiability | [
"FirstOrder.Language.Theory.IsSatisfiable",
"Membership.mem",
"FirstOrder.Language.Theory",
"Empty",
"And",
"FirstOrder.Language.Formula.not",
"FirstOrder.Language.Formula",
"FirstOrder.Language",
"FirstOrder.Language.Sentence",
"Or",
"Set.instMembership"
] | true |
_private.Mathlib.FieldTheory.IntermediateField.Adjoin.Defs.0.IntermediateField.sSup_toSubfield._simp_1_1 | Mathlib.FieldTheory.IntermediateField.Adjoin.Defs | [
"Set.sUnion",
"Membership.mem",
"Exists",
"And",
"propext",
"Set.mem_sUnion",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.Algebra.Ring.Parity.0.Nat.not_even_two_mul_add_one._proof_1_1 | Mathlib.Algebra.Ring.Parity | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"Int.instDiv",
"False",
"instHDiv",
"Lean.Grind.not_not",
"HMul.hMul",
"Lean.Grind.iff_eq",
"Int.Linear.eq_norm",
"Classical.byContradiction",
"Nat.ToInt.add_congr",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.eq_unsat_coeff",
"Nat.ToInt.natCas... | false |
CFC.posPart_eq_zero_iff._auto_1 | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Orientation.inner_mul_inner_add_areaForm_mul_areaForm | Mathlib.Analysis.InnerProductSpace.TwoDim | [
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"Orientation",
"Real.partialOrder",
"Real",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"Inner.inner",
"Real.instRCLike",
"CommSemiring.toSemiring",
"AddCommGroup... | true |
Lean.Parser.Tactic.funInduction | Init.Tactics | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"Lean.ParserDescr.cat",
"Lean.Parser.Tactic.inductionAlts",
"OfNat.ofNat",
"Bool... | true |
NumberField.mixedEmbedding.logMap_real | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone | [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"NumberField.mixedEmbedding.logMap",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"instH... | true |
MonoidAlgebra.mapAddEquiv._proof_5 | Mathlib.Algebra.MonoidAlgebra.MapDomain | [
"MonoidAlgebra.addCommMonoid",
"AddEquivClass.instAddMonoidHomClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoidHomClass.toAddMonoidHom",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Distrib.toAdd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"instDistribOfSemiring",
"MonoidAlg... | false |
Aesop.UnorderedArraySet.instForInOfMonad._private_1 | Aesop.Util.UnorderedArraySet | [
"_private.Aesop.Util.UnorderedArraySet.0.Aesop.UnorderedArraySet.rep",
"instForInOfForIn'",
"Array.instMembership",
"inferInstance",
"ForIn.forIn",
"Membership",
"ForInStep",
"Array",
"Aesop.UnorderedArraySet",
"Array.instForIn'InferInstanceMembershipOfMonad",
"Monad",
"BEq"
] | false |
add_eq_right_iff_le | Mathlib.Algebra.Order.Kleene | [
"add_eq_sup",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"Distrib.toAdd",
"LE.le",
"instDistribOfSemiring",
"IdemSemiring.toSemilatticeSup",
"iff_self",
"instHAdd",
"Iff",
"HAdd.hAdd",
"Max.max",
"IdemSemiring.toSemiring",
"True",
"of_eq_true",
... | true |
Lean.Meta.Closure.MkValueTypeClosureResult.value | Lean.Meta.Closure | [
"Lean.Expr",
"Lean.Meta.Closure.MkValueTypeClosureResult"
] | true |
Fin.image_castLE_Ico | Mathlib.Order.Interval.Set.Fin | [
"Set.image_image",
"congrArg",
"Fin.castLE",
"PartialOrder.toPreorder",
"Membership.mem",
"LE.le",
"instLENat",
"Fin.val",
"Set.Ico",
"Fin.val_injective",
"Fin.instPartialOrder",
"Nat.instPreorder",
"Nat",
"congr",
"True",
"Set.image_congr",
"eq_self",
"of_eq_true",
"Eq.refl",
... | true |
Lean.collectLevelMVars | Lean.Util.CollectLevelMVars | [
"Lean.CollectLevelMVars.main",
"Lean.Expr",
"Lean.CollectLevelMVars.State"
] | true |
Qq.Impl._aux_Qq_AssertInstancesCommute___macroRules_Lean_Parser_Term_assert_2 | Qq.AssertInstancesCommute | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr3",
"ReaderT.i... | false |
NormedAlgebra.toAlgebra | Mathlib.Analysis.Normed.Module.Basic | [
"Algebra",
"SeminormedRing.toRing",
"NormedField.toField",
"Field.toSemifield",
"NormedField",
"Semifield.toCommSemiring",
"Ring.toSemiring",
"NormedAlgebra",
"SeminormedRing"
] | true |
Polynomial.X_pow_add_C_ne_zero | Mathlib.Algebra.Polynomial.Degree.Operations | [
"Nontrivial",
"Iff.mpr",
"Eq.mpr",
"Polynomial.C",
"WithBot",
"congrArg",
"Polynomial.degree_X_pow_add_C",
"RingHom",
"mt",
"id",
"Ne",
"instOfNatNat",
"Polynomial.instAdd",
"Bot.bot",
"Polynomial.degree",
"instNatCastNat",
"Nat.cast",
"Polynomial",
"Monoid.toPow",
"instHAdd",
... | true |
_private.Mathlib.LinearAlgebra.Matrix.RowCol.0.Matrix.updateCol_submatrix_equiv._simp_1_1 | Mathlib.LinearAlgebra.Matrix.RowCol | [
"Matrix.submatrix",
"Matrix.transpose_submatrix",
"Matrix",
"Matrix.transpose",
"Eq.symm",
"Eq"
] | false |
_private.Batteries.Data.List.Lemmas.0.List.countPBefore_succ._proof_1_1 | Batteries.Data.List.Lemmas | [
"Iff.mpr",
"Lean.Grind.nestedProof",
"List.length_pos_iff",
"instOfNatNat",
"List",
"Nat",
"LT.lt",
"instLTNat",
"OfNat.ofNat",
"Eq",
"List.length",
"Not",
"List.nil"
] | false |
Matrix.adjugate.congr_simp | Mathlib.LinearAlgebra.Matrix.Adjugate | [
"CommRing",
"instSubsingletonDecidable",
"Matrix",
"Decidable",
"Eq.rec",
"Pi.instSubsingleton",
"Fintype",
"Matrix.adjugate",
"Eq.ndrec",
"Eq.refl",
"Subsingleton.elim",
"Eq",
"DecidableEq"
] | true |
AddMonoidHom.closure_preimage_le | Mathlib.Algebra.Group.Subgroup.Map | [
"AddSubgroup.comap",
"Iff.mpr",
"Eq.mpr",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"HasSubset.Subset",
"LE.le",
"AddSubgroup",
"AddSubgroup.mem_comap",
"AddGroup... | true |
WithLp.prod_continuous_toLp | Mathlib.Analysis.Normed.Lp.ProdLp | [
"Iff.mpr",
"WithLp",
"Continuous",
"WithLp.instProdTopologicalSpace",
"instTopologicalSpaceProd",
"Function.comp",
"WithLp.toLp",
"TopologicalSpace",
"continuous_id",
"TopologicalSpace.induced",
"ENNReal",
"Prod",
"WithLp.ofLp",
"continuous_induced_rng"
] | true |
ListSlice.toArray_mkSlice_roi_eq_toArray_mkSlice_rco | Init.Data.Slice.List.Lemmas | [
"Std.Rci.mk",
"Std.Iterators.Types.Take.instIterator",
"Std.Slice.Internal.ListSliceData",
"Std.Rco.Sliceable.mkSlice",
"ListSlice.instToIterator",
"Std.Iterators.Types.ListIterator.instFinite",
"Std.Iterators.Types.ListIterator",
"Std.Slice.toArray",
"congrArg",
"ListSlice.toArray_mkSlice_rco",
... | true |
_private.Mathlib.Analysis.SpecialFunctions.Gamma.Basic.0.Complex.Gamma_add_one._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Gamma.Basic | [
"False",
"eq_false",
"instOfNatNat",
"two_ne_zero",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
_private.Mathlib.Data.Fin.VecNotation.0.Matrix.cons_swap._proof_1_2 | Mathlib.Data.Fin.VecNotation | [
"instNeZeroNatHAdd_1",
"Zero.ofOfNat0",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"NeZero",
"OfNat.ofNat"
] | false |
Std.Internal.List.List.getValueD_filter_containsKey | Std.Data.Internal.List.Associative | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Decidable.casesOn",
"congrArg",
"Std.Internal.List.containsKey_filter_containsKey_eq_false_of_containsKey_eq_false_right",
"Std.Internal.List.getValueD_eq_fallback",
"Decidable",
"Option.getD",
"Eq.rec",
"id",
"instDecidableEqBool",
"Sigma.fst",
"... | true |
LinearMap.BilinForm.toMatrixAux._proof_1 | Mathlib.LinearAlgebra.Matrix.BilinearForm | [
"Algebra.to_smulCommClass",
"instSMulOfMul",
"CommSemiring.toSemiring",
"Algebra.toSMul",
"Algebra.id",
"instDistribOfSemiring",
"CommSemiring",
"Distrib.toMul",
"SMulCommClass"
] | false |
Bool.or_eq_true | Init.SimpLemmas | [
"of_decide_eq_true",
"id",
"instDecidableEqOfIff",
"instDecidableEqBool",
"Bool.true",
"Bool.casesOn",
"Bool",
"Eq.ndrec",
"Bool.or",
"Eq.refl",
"Or",
"Eq.symm",
"Bool.false",
"Decidable.decide",
"Eq",
"instDecidableOr",
"instDecidableIff"
] | true |
PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_obj | Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf | [
"CategoryTheory.Functor",
"Opposite",
"CommRingCat.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CommSemiring.toSemiring",
"CommRingCat",
"CategoryTheory.Functor.category",
"CommRingCat.instConcreteCategoryRingHomCarrier",
"RingCat.ring",
"CategoryTheory.Funct... | true |
RatFunc.toFractionRingRingEquiv.eq_1 | Mathlib.FieldTheory.RatFunc.Basic | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"RatFunc.toFractionRingRingEquiv._proof_4",
"RatFunc.toFractionRingRingEquiv._proof_1",
"FractionRing",
"nonZeroDivisors",
"RatFunc.toFractionRingRingEquiv._... | true |
Encodable.decodeSubtype.eq_1 | Mathlib.Logic.Encodable.Basic | [
"Encodable.decodeSubtype",
"Option.some",
"Option.bind",
"Subtype",
"dite",
"Subtype.mk",
"Option.none",
"DecidablePred",
"Nat",
"Eq.refl",
"Encodable.decode",
"Eq",
"Not",
"Encodable",
"Option"
] | true |
List.take_eq_append_getElem_of_pos | Init.Data.List.Nat.TakeDrop | [
"_private.Init.Data.List.Nat.TakeDrop.0.List.take_eq_append_getElem_of_pos.match_1_1",
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"List.cons",
"_private.Init.Data.List.Nat.TakeDrop.0.List.take_eq_append_getElem_of_pos._proof_1_3",
"GetElem.getElem",
"instHAppendOfAppend",
"List",
"instHAdd",
"in... | true |
Lean.Meta.ACLt.ReduceMode.reduce.elim | Lean.Meta.ACLt | [
"PULift.up",
"Lean.Meta.ACLt.ReduceMode.ctorIdx",
"Lean.Meta.ACLt.ReduceMode",
"Nat",
"Lean.Meta.ACLt.ReduceMode.ctorElim",
"Eq.symm",
"Lean.Meta.ACLt.ReduceMode.reduce",
"Eq"
] | false |
CategoryTheory.Mon.id | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.Mon.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon.id._proof_1",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Mon.Hom.mk",
"CategoryTheory.Mon",
"CategoryTheory.Mon.X",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Tactic.TacticAnalysis.Declarations.0.Mathlib.TacticAnalysis.TerminalReplacementOutcome.success.noConfusion | Mathlib.Tactic.TacticAnalysis.Declarations | [
"_private.Mathlib.Tactic.TacticAnalysis.Declarations.0.Mathlib.TacticAnalysis.TerminalReplacementOutcome",
"_private.Mathlib.Tactic.TacticAnalysis.Declarations.0.Mathlib.TacticAnalysis.TerminalReplacementOutcome.noConfusion",
"Lean.TSyntax",
"_private.Mathlib.Tactic.TacticAnalysis.Declarations.0.Mathlib.Tacti... | false |
Finsupp.instPosSMulReflectLE | Mathlib.Data.Finsupp.Order | [
"Finsupp.instFunLike",
"Finsupp.smulZeroClass",
"Finsupp.coe_le_coe",
"Pi.preorder",
"SMulZeroClass",
"Preorder.toLE",
"Function.hasSMul",
"Pi.instPosSMulReflectLE",
"Finsupp.coe_smul",
"Finsupp.preorder",
"SMulZeroClass.toSMul",
"PosSMulReflectLE.lift",
"Finsupp.instZero",
"PosSMulReflect... | true |
GaloisCoinsertion.u_biSup_of_lu_eq_self | Mathlib.Order.GaloisConnection.Basic | [
"iSup",
"PartialOrder.toPreorder",
"CompleteSemilatticeSup.toSupSet",
"CompleteLattice.toCompleteSemilatticeSup",
"CompleteSemilatticeSup.toPartialOrder",
"GaloisCoinsertion.u_biSup_of_l_u_eq_self",
"CompleteLattice",
"Eq",
"GaloisCoinsertion"
] | true |
Additive.addCommSemigroup | Mathlib.Algebra.Group.TypeTags.Basic | [
"Additive",
"Additive.addSemigroup",
"AddCommSemigroup.mk",
"AddSemigroup",
"CommSemigroup",
"Additive.addCommSemigroup._proof_1",
"CommSemigroup.toSemigroup",
"AddCommSemigroup"
] | true |
Option._sizeOf_inst | Init.SizeOf | [
"Option._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Option"
] | false |
OrderDual.sbtw | Mathlib.Order.Circular | [
"SBtw.sbtw",
"SBtw.mk",
"SBtw",
"OrderDual"
] | true |
SimpleGraph.Dart.symm_involutive._simp_1 | Mathlib.Combinatorics.SimpleGraph.Dart | [
"SimpleGraph.Dart.symm_involutive",
"SimpleGraph.Dart",
"SimpleGraph",
"SimpleGraph.Dart.symm",
"True",
"Function.Involutive",
"eq_true",
"Eq"
] | false |
FinPartOrd.dual_map | Mathlib.Order.Category.FinPartOrd | [
"Equiv.instEquivLike",
"FinPartOrd.dual",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartOrd.instCategory",
"PartOrd.str",
"PartialOrder.toPreorder",
"Equiv",
"FinPartOrd.isFintype",
"FinPartOrd.largeCategory",
"CategoryTheory.Functor.map",
"FinPartOrd.toPartOrd",
"PartOrd",
... | true |
CommSemiRingCat.fullyFaithfulForget₂ToSemiRingCat._proof_1 | Mathlib.Algebra.Category.Ring.Basic | [
"CommSemiRingCat.instConcreteCategoryRingHomCarrier",
"SemiRingCat.instConcreteCategoryRingHomCarrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"CommSemiRingCat.carrier",
"RingHom",
"CommSemiRingCat.ofHom",
"CommSemiRingCat.hasForgetToSemiRingCat",
"SemiR... | false |
_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.State.casesOn | Lean.Compiler.LCNF.ExplicitRC | [
"_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.State",
"_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.LiveVars",
"_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.State.mk",
"_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.State.rec"
] | false |
Std.IterM.toListRev_filterMapWithPostcondition | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"congrArg",
"Monad.toApplicative",
"MonadLiftT.monadLift",
"Std.Iterators.Finite",
"Std.IterM.toListRev",
"Std.Iterators.Types.FilterMap.instFinite",
"LawfulMonad",
"Id.run",
"Id",
"Applicative.toPure",
"Std.IterM.toListRev_eq",
"Std.Iterator",
"Std.Iterators.PostconditionT.run",
"List",
... | true |
Fin.exists_iff_castSucc | Mathlib.Data.Fin.Tuple.Basic | [
"Exists",
"Fin.lastCases",
"instOfNatNat",
"Or.casesOn",
"instHAdd",
"Iff",
"Exists.casesOn",
"HAdd.hAdd",
"Nat",
"Fin.last",
"Iff.intro",
"Exists.intro",
"Eq.ndrec",
"instAddNat",
"Eq.refl",
"Or.inl",
"Or",
"Fin.castSucc",
"OfNat.ofNat",
"Eq.symm",
"Fin",
"Eq",
"Or.inr"
... | true |
isAddQuotientCoveringMap_quotientMk_of_properlyDiscontinuousVAdd | Mathlib.Topology.Covering.Quotient | [
"AddMonoid.toAddSemigroup",
"isQuotientMap_quotient_mk'",
"ContinuousConstVAdd",
"Quotient.eq''",
"IsAddQuotientCoveringMap",
"instTopologicalSpaceQuotient",
"Topology.IsQuotientMap.isAddQuotientCoveringMap_of_properlyDiscontinuousVAdd",
"Quotient.mk",
"TopologicalSpace",
"AddAction",
"AddAction... | true |
CartanMatrix.A | Mathlib.Data.Matrix.Cartan | [
"Equiv.instEquivLike",
"Matrix",
"Matrix.of",
"instDecidableEqFin",
"Equiv",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Fin.val",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"Nat",
"instAddNat",
"instDecidableEqNat",
"Or",
"OfNat.ofNat",
"Fin",
"Eq",
"DFunLike.coe",
"instDecidableOr... | true |
Submodule.Quotient.equiv._proof_2 | Mathlib.LinearAlgebra.Quotient.Basic | [
"Submodule.Quotient.restrictScalarsEquiv._proof_2",
"Submodule",
"RingHomSurjective.ids",
"AddCommGroup.toAddCommMonoid",
"Membership.mem",
"Eq.rec",
"AddCommGroup",
"LinearEquiv.toLinearMap",
"Submodule.comap",
"RingHomInvPair.ids",
"Submodule.setLike",
"LinearEquiv",
"Submodule.mem_map_of_... | false |
Lean.Meta.GeneralizeArg.noConfusion | Lean.Meta.Tactic.Generalize | [
"Lean.Meta.GeneralizeArg.casesOn",
"Lean.Meta.GeneralizeArg",
"Lean.Meta.GeneralizeArg.noConfusionType",
"Lean.Expr",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Eq",
"Option"
] | false |
ModuleCat.restrictScalarsIsoOfEquiv_inv_apply | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | [
"Semiring.toModule",
"ModuleCat",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"RingEquiv.instEquivLike",
"RingEquiv.instRingEquivClass",
"LinearMap.instFunLike",
"Distrib.toAdd",
"ModuleCat.instConcreteCategoryLinearMapIdCarrier",
"ModuleCat.restrictScalars",
"LinearMa... | true |
Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.core | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Expr",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.core",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof",
"Int.Linear.Poly"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.average_density_near_total_density | Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | [
"Real.instIsOrderedRing",
"div_le_div₀",
"Eq.mpr",
"le_refl",
"pow_pos",
"SzemerediRegularity.stepBound",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"HMul.hMul",
"Real.lattice",
"Finset.univ",
"MulZeroClass.toMul",
"IsStrictOrderedRing.toMulPosStrictMono",
"Nat.ble",
"Re... | true |
Nat.preimage_Ici | Mathlib.Algebra.Order.Floor.Semiring | [
"Set.ext",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Set.Ici",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Nat... | true |
Mathlib.Command.MinImports.getId | Mathlib.Tactic.MinImports | [
"_private.Mathlib.Tactic.MinImports.0.Mathlib.Command.MinImports.getId.match_3",
"Pure.pure",
"Lean.TSyntax",
"Lean.Elab.DefView.declId",
"Lean.Elab.Command.mkDefViewOfInstance",
"Lean.Syntax.missing",
"Lean.Syntax.isOfKind",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Elab.Visibility.regular",
"IO.... | true |
Lean.Elab.Tactic.GuardMsgs.WhitespaceMode.toCtorIdx | Lean.Elab.GuardMsgs | [
"Lean.Elab.Tactic.GuardMsgs.WhitespaceMode",
"Lean.Elab.Tactic.GuardMsgs.WhitespaceMode.ctorIdx",
"Nat"
] | false |
Dynamics.netMaxcard.eq_1 | Mathlib.Dynamics.TopologicalEntropy.NetEntropy | [
"instCompleteLinearOrderENat",
"SetRel",
"ENat.instNatCast",
"iSup",
"Finset",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"Nat.cast",
"CompleteLinearOrder.toConditionallyCompleteLinearOrderBot",
"SetLike.coe",
"Finset.instSetLike",
"Nat",
"ENat",
"Dynamics.IsDynNetIn"... | true |
_private.Mathlib.Algebra.Group.Pointwise.Set.Basic.0.Set.preimage_nsmul_subset.match_1_1 | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
_private.Init.Data.UInt.Lemmas.0.UInt16.ofNat_add._simp_1_1 | Init.Data.UInt.Lemmas | [
"instPowNat",
"UInt16.ofNat_eq_iff_mod_eq_toNat",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"instNatPowNat",
"UInt16.ofNat",
"HMod.hMod",
"UInt16",
"HPow.hPow",
"Nat",
"propext",
"UInt16.toNat",
"instHPow",
"OfNat.ofNat",
"Eq"
] | false |
MeasureTheory.Lp.instModule._proof_1 | Mathlib.MeasureTheory.Function.LpSpace.Basic | [
"Submodule",
"Submodule.module._proof_1",
"Semigroup.toMul",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"NormedRing.toRing",
"MeasureTheory.Lp.LpSubmodule",
"HMul.hMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMo... | false |
Lean.Export.alloc | Mathlib.Util.Export | [
"Pure.pure",
"modify",
"Monad.toApplicative",
"Lean.Export.OfState.get",
"Lean.Export.Alloc",
"MonadState.get",
"Lean.Export.OfState",
"instOfNatNat",
"Applicative.toPure",
"Lean.ExportM",
"instHAdd",
"Lean.Core.CoreM",
"Lean.Export.Alloc.map",
"Lean.Export.State",
"instMonadStateOfState... | true |
_private.Mathlib.MeasureTheory.Measure.Regular.0.Set.measure_eq_iInf_isOpen._simp_1_2 | Mathlib.MeasureTheory.Measure.Regular | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
CategoryTheory.IsCofiltered.of_hasInitial | Mathlib.CategoryTheory.Filtered.Basic | [
"CategoryTheory.IsCofiltered.of_isInitial",
"CategoryTheory.IsCofiltered",
"CategoryTheory.Limits.initialIsInitial",
"CategoryTheory.Limits.initial",
"CategoryTheory.Limits.HasInitial",
"CategoryTheory.Category"
] | true |
_private.Mathlib.NumberTheory.Divisors.0.Int.mem_divisors_iff_natAbs_mem_divisors_natAbs._proof_1_4 | Mathlib.NumberTheory.Divisors | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"of_eq_false",
"Lean.RArray.leaf",
"False",
"Lean.Grind.CommRing.Mon.mult",
"Lean.Grind.not_not",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"HMul.hMul",
"Le... | false |
CategoryTheory.Preadditive.ofFullyFaithful._proof_3 | Mathlib.CategoryTheory.Preadditive.Transfer | [
"CategoryTheory.Functor.FullyFaithful.map_injective",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Functor.FullyFaithful.homEquiv",
"Equiv.addCommGroup",
"CategoryTheory.Preadditive",
"instHAdd",
"HAdd.hAdd",
"C... | false |
LLVM.Builder | Lean.Compiler.IR.LLVMBindings | [
"_private.Lean.Compiler.IR.LLVMBindings.0.LLVM.Builder.mk"
] | true |
AdicCompletion.mkₐ_apply_coe | Mathlib.RingTheory.AdicCompletion.Algebra | [
"Submodule",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"instHSMul",
"Semiring.toModule",
"AdicCompletion.instAlgebraAdicCauchySequence",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"AddCommGroup.toAddCommMonoid",
"AlgHom",
"AlgHom.funLike",
"AdicCompletion.instCommRingAdicCauchySeque... | true |
AdjoinRoot.adjoinRoot_eq_top | Mathlib.RingTheory.AdjoinRoot | [
"Subalgebra.instSetLike",
"Iff.mpr",
"CommRing",
"Lattice.toSemilatticeSup",
"AdjoinRoot",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"Polynomial.algebraOfAlgebra",
"PartialOrder.toPreorder",
"Algebra.instCompleteLatticeSubalgebra",
"Preorder.toLE",
"Algebra.adjoin",
"RingHom",
... | true |
ProbabilityTheory.partitionFiltration | Mathlib.Probability.Process.PartitionFiltration | [
"MeasureTheory.Filtration.mk",
"MeasurableSet",
"MeasurableSpace.generateFrom_memPartition_le",
"memPartition",
"MeasureTheory.Filtration",
"ProbabilityTheory.partitionFiltration._proof_1",
"MeasurableSpace.generateFrom",
"MeasurableSpace",
"Nat.instPreorder",
"Nat",
"Set"
] | true |
_private.Mathlib.GroupTheory.Coxeter.Inversion.0.CoxeterSystem.rightInvSeq_concat._simp_1_5 | Mathlib.GroupTheory.Coxeter.Inversion | [
"zpow_add",
"HMul.hMul",
"Monoid.toMulOneClass",
"DivInvMonoid.toZPow",
"Group",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Int",
"Group.toDivInvMonoid",
"instHAdd",
"MulOneClass.toMulOne",
"HPow.hPow",
"HAdd.hAdd",
"Int.instAdd",
"instHPow",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Pi.instNoMaxOrderLexForallOfWellFoundedLTOfNonempty | Mathlib.Order.PiLex | [
"_private.Mathlib.Order.PiLex.0.Pi.instNoMaxOrderLexForallOfWellFoundedLTOfNonempty.match_1",
"Pi.preorder",
"Preorder.toLT",
"Equiv.instEquivLike",
"Lex",
"NoMaxOrder",
"LinearOrder",
"WellFoundedLT",
"PartialOrder.toPreorder",
"Exists",
"NoMaxOrder.mk",
"SemilatticeInf.toPartialOrder",
"Pa... | true |
jacobsonSpace_iff | Mathlib.Topology.JacobsonSpace | [
"JacobsonSpace",
"JacobsonSpace.casesOn",
"JacobsonSpace.mk",
"closedPoints",
"Set.instInter",
"Inter.inter",
"IsClosed",
"TopologicalSpace",
"Iff",
"closure",
"Iff.intro",
"Eq",
"Set"
] | true |
instAddMonoidUniformFun._proof_2 | Mathlib.Topology.Algebra.UniformConvergence | [
"instAddUniformFun",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"instAddMonoidUniformFun._proof_1",
"AddSemigroup.mk",
"instZeroUniformFun",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"UniformFun",
"AddMonoid",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofN... | false |
Fin.rec._@.Mathlib.Util.CompileInductive.3197476844._hygCtx._hyg.355 | Mathlib.Util.CompileInductive | [
"Fin.mk",
"Nat",
"LT.lt",
"instLTNat",
"Fin"
] | false |
Order.Ideal.mem_sup._simp_1 | Mathlib.Order.Ideal | [
"IsCodirectedOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Order.Ideal.instMax",
"SemilatticeSup.toMax",
"LE.le",
"And",
"Max.max",
"propext",
"Order.Ideal.mem_sup",
"SemilatticeSup.toPartialOrder",
"Order.Ideal.instSetLike",
"Order.Ideal",
"Eq",
"S... | false |
TopCat.toSSetObj₀Equiv_symm_apply | Mathlib.AlgebraicTopology.SimplicialSet.TopAdj | [
"Real.partialOrder",
"Real",
"Opposite",
"Equiv.instEquivLike",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Pi.topologicalSpace",
"TopCat.toSSet",
"TopCat.instCategory",
"ContinuousMap.mk",
"ContinuousMap",
"TopCat.toSSetObjEquiv",
"CategoryTheory.Functor.category",
"Pseu... | true |
_private.Lean.Compiler.LCNF.FloatLetIn.0.Lean.Compiler.LCNF.FloatLetIn.initialDecisions.visitArg | Lean.Compiler.LCNF.FloatLetIn | [
"Pure.pure",
"Lean.instBEqFVarId",
"Lean.Compiler.LCNF.Arg",
"_private.Lean.Compiler.LCNF.FloatLetIn.0.Lean.Compiler.LCNF.FloatLetIn.initialDecisions.visitArg.match_1",
"Lean.Core.instMonadLiftIOCoreM",
"IO.instMonadLiftSTRealWorldBaseIO",
"modify",
"Monad.toApplicative",
"instMonadLiftT",
"Std.Ha... | true |
_private.Mathlib.RingTheory.Jacobson.Ring.0.MvPolynomial.quotient_mk_comp_C_isIntegral_of_isJacobsonRing' | Mathlib.RingTheory.Jacobson.Ring | [
"MvPolynomial.isJacobsonRing",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Nat.recAux",
"Semiring.toModule",
"Algebra.algebraMap",
"AlgEquiv.symm",
"AddMonoidAlgebra.commRing",
"CommSemiring.toSemiring",
"AddMonoidAlgebra.algebra",
"Polynomial.algebraOfAlgebra",
"Finsup... | true |
_private.Lean.Meta.Tactic.Split.0.Lean.Meta.Split.applyMatchSplitter.match_1 | Lean.Meta.Tactic.Split | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"_private.Lean.Meta.Tactic.Split.0.Lean.Meta.Split.generalizeMatchDiscrs.withNewAltEqs.go._sparseCasesOn_3",
"Nat",
"Option"
] | false |
ENat.lt_add_one_iff' | Mathlib.Data.ENat.Basic | [
"Eq.mpr",
"instAddMonoidWithOneENat",
"instTopENat",
"ENat.one_ne_top",
"congrArg",
"Iff.rfl",
"ENat.add_one_le_iff",
"instAddENat",
"id",
"Ne",
"LE.le",
"instLEENat",
"AddMonoidWithOne.toOne",
"instHAdd",
"Iff",
"HAdd.hAdd",
"ENat",
"LT.lt",
"ENat.add_le_add_iff_right",
"prope... | true |
Nat.pred_lt_self | Init.Data.Nat.Basic | [
"Nat.lt_succ_self",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"_private.Init.Data.Nat.Basic.0.Nat.pred_lt_self.match_1_1",
"Nat.pred"
] | true |
Mathlib.Tactic.BicategoryLike.instInhabitedHorizontalComp | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | [
"Mathlib.Tactic.BicategoryLike.instInhabitedHorizontalComp.default",
"Inhabited",
"Mathlib.Tactic.BicategoryLike.HorizontalComp",
"Inhabited.mk"
] | true |
_private.Init.Data.Int.Lemmas.0.Int.neg_ofNat_eq_negSucc_add_one_iff._simp_1_1 | Init.Data.Int.Lemmas | [
"eq_comm",
"propext",
"Eq"
] | false |
_private.Lean.Meta.Tactic.Simp.Types.0.Lean.Meta.Simp.mkImpCongr._sparseCasesOn_1 | Lean.Meta.Tactic.Simp.Types | [
"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"
] | false |
_private.Mathlib.Data.Set.Card.0.Set.encard_eq_four.match_1_1 | Mathlib.Data.Set.Card | [
"Exists",
"Set.instSingletonSet",
"Insert.insert",
"Ne",
"And.casesOn",
"And",
"Exists.casesOn",
"Set.instInsert",
"And.intro",
"Exists.intro",
"Singleton.singleton",
"Eq",
"Set"
] | false |
MonoidAlgebra.support_gen_of_gen' | Mathlib.RingTheory.FiniteType | [
"MonoidAlgebra.semiring",
"Monoid",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"MonoidHom.instFunLike",
"MonoidHom",
"CompleteLattice.toLattice",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"PartialOrder.toPreorder",
"Algebra.instCompleteLatticeSubalgebra",
"Preorde... | true |
Nat.bit_cases_on_inj._simp_1 | Mathlib.Data.Nat.Bits | [
"Nat.bit",
"Nat.bitCasesOn",
"Nat.bit_cases_on_inj",
"Nat",
"propext",
"Bool",
"Eq"
] | false |
_private.Lean.Meta.Tactic.Grind.Arith.CommRing.Poly.0.Lean.Grind.CommRing.Mon.toExpr.go | Lean.Meta.Tactic.Grind.Arith.CommRing.Poly | [
"Lean.Grind.CommRing.Expr",
"_private.Lean.Meta.Tactic.Grind.Arith.CommRing.Poly.0.Lean.Grind.CommRing.Mon.toExpr.go._f",
"Lean.Grind.CommRing.Mon",
"Lean.Grind.CommRing.Mon.brecOn"
] | true |
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