name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Algebra.Group.Submonoid.Membership.0.Submonoid.forall_mem_sup._simp_1_1 | Mathlib.Algebra.Group.Submonoid.Membership | [
"Lattice.toSemilatticeSup",
"HMul.hMul",
"CompleteLattice.toLattice",
"Submonoid.mem_sup",
"Monoid.toMulOneClass",
"Membership.mem",
"Exists",
"SemilatticeSup.toMax",
"MulOne.toMul",
"Submonoid.instCompleteLattice",
"MulOneClass.toMulOne",
"And",
"CommMonoid.toMonoid",
"Max.max",
"propex... | false |
_private.Mathlib.NumberTheory.LSeries.SumCoeff.0.LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_aux₂ | Mathlib.NumberTheory.LSeries.SumCoeff | [
"MeasureTheory.ae",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Iff.mpr",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real.instIsOrderedRing",
"Norm.norm",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"Not.intro"... | true |
AlgebraicTopology.isZero_singularHomologyFunctor_of_totallyDisconnectedSpace | Mathlib.AlgebraicTopology.SingularHomology.Basic | [
"CategoryTheory.Functor",
"AlgebraicTopology.singularChainComplexFunctor_exactAt_of_totallyDisconnectedSpace",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne",
"TopCat.instCategory",
"CategoryTheory.Limits.HasZeroObject.mk",
"CategoryTheory.Functor.category",
"AddRightCancelSemigrou... | true |
Ideal.fiberIsoOfBijectiveResidueField._proof_6 | Mathlib.RingTheory.Etale.QuasiFinite | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Localization.AtPrime",
"Localization.AtPrime.algebraOfLiesOver",
"IsLocalRing.ResidueField.algebra",
"AddMonoid.... | false |
EuclideanGeometry.Sphere.instNonemptySubtypeMemAffineSubspaceRealOrthRadius | Mathlib.Geometry.Euclidean.Sphere.OrthRadius | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
"Real.instRCLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AffineSubspace.mk'",
"EuclideanGeometry.Sphere",
"AddCommGroup.toAddGroup",
"Membership.mem",
"inferInstance",
"Real.semiring",
"Set.instSingletonSet... | true |
Lean.Omega.LinearCombo.coordinate_eval | Init.Omega.LinearCombo | [
"Int.sub_zero",
"HMul.hMul",
"Lean.Omega.Coeffs.get",
"Lean.Omega.LinearCombo.coeffs",
"congrArg",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Int.one_mul",
"Int",
"Lean.Omega.IntList.set",
"Int.instMul",
"instHAdd",
"Lean.Omega.IntList.get",
"instHSub",
"instOfNat",
"HAdd.hAdd",
"L... | true |
Group.fg_of_mul_group_fg | Mathlib.GroupTheory.Finiteness | [
"Multiplicative.group",
"Group.FG",
"AddGroup.fg_iff_mul_fg",
"Multiplicative",
"AddGroup",
"Iff.mp",
"AddGroup.FG"
] | true |
CategoryTheory.EnrichedFunctor.forgetComp_hom_app | Mathlib.CategoryTheory.Enriched.Basic | [
"CategoryTheory.categoryForgetEnrichment",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ForgetEnrichment.of",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
... | true |
NonUnitalSubalgebra.nonUnitalNormedRing._proof_2 | Mathlib.Analysis.Normed.Ring.Basic | [
"Norm.norm",
"Real",
"CommRing",
"NonUnitalSubalgebra",
"AddMonoid.toAddSemigroup",
"CommSemiring.toSemiring",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"Membership.mem",
"NonUnitalSeminormedRing.dist_eq",
"NonUnitalRing.toNonUnitalNonAssocRing",
"Subtype",
"NonUnita... | false |
ContinuousMulEquiv.trans | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"MulEquiv.trans",
"Mul",
"ContinuousMulEquiv.trans._proof_2",
"ContinuousMulEquiv.mk",
"TopologicalSpace",
"ContinuousMulEquiv.trans._proof_1",
"MulEquiv",
"ContinuousMulEquiv",
"ContinuousMulEquiv.toMulEquiv"
] | true |
instDecidableEqChar.match_1 | Init.Prelude | [
"Decidable.isTrue",
"Decidable.casesOn",
"Decidable",
"Char.val",
"UInt32",
"Char",
"Decidable.isFalse",
"Eq",
"Not"
] | false |
TrivSqZeroExt.fst_exp | Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt | [
"Eq.mpr",
"TrivSqZeroExt.snd",
"CommRing",
"TrivSqZeroExt.inr",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"TrivSqZeroExt",
"CommRing.toNonUnitalCommRing",
"ContinuousSMul",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMon... | true |
List.get._unsafe_rec | Init.Prelude | [
"Fin.mk",
"instOfNatNat",
"List.cons",
"List",
"Nat.le_of_succ_le_succ",
"List.get._unsafe_rec",
"Nat",
"LT.lt",
"instLTNat",
"List.get.match_1",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"List.length"
] | false |
MeasurableEmbedding.ae_map_iff | Mathlib.MeasureTheory.Measure.Restrict | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"congrArg",
"Filter.Eventually",
"setOf",
"iff_self",
"MeasurableSpace",
"Iff",
"MeasurableEmbedding.map_apply",
"MeasureTheory.Measure.map",
"congr",
"True",
"ENNReal",
"MeasurableEmbedding",
"of_eq_true",
"_private.Mathlib.MeasureTheory.Me... | true |
Affine.Triangle.circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq | Mathlib.Geometry.Euclidean.Angle.Sphere | [
"EuclideanGeometry.oangle",
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Affine.Simplex.points",
"Real.partialOrder",
"Real",
"instHSMul",
"instHDiv",
"Real.pi",
"Real.lattice",
"Real.Angle",
"Real.Angle.coe",
"AddMonoid.toAddSemigroup",
"invertibleT... | true |
Multiset.decidableMem | Mathlib.Data.Multiset.Defs | [
"Decidable",
"Multiset.decidableMem._aux_1",
"Membership.mem",
"Multiset",
"Quot.recOnSubsingleton",
"Multiset.instMembership",
"List",
"Multiset.decidableMem._proof_1",
"List.isSetoid",
"Setoid.r",
"DecidableEq"
] | true |
List.Forall.imp | Mathlib.Data.List.Basic | [
"List.brecOn",
"List",
"List.Forall.imp._f",
"List.Forall"
] | true |
cast_inj | Mathlib.Logic.Function.Basic | [
"Function.Injective.eq_iff",
"cast",
"Function.Bijective.injective",
"Iff",
"cast_bijective",
"Eq"
] | true |
Fintype.subtypeEq._proof_1 | Mathlib.Data.Fintype.Basic | [
"congrArg",
"Finset",
"Membership.mem",
"Finset.mem_singleton._simp_1",
"iff_self",
"Iff",
"Finset.instSetLike",
"True",
"of_eq_true",
"congrFun'",
"implies_true",
"Finset.instSingleton",
"Singleton.singleton",
"Eq",
"SetLike.instMembership",
"Eq.trans",
"forall_congr"
] | false |
Lean.ParserCompiler.instInhabitedCombinatorAttribute.default | Lean.ParserCompiler.Attribute | [
"Inhabited.default",
"Lean.NameMap",
"Lean.AttributeImpl",
"Lean.instInhabitedAttributeImpl",
"Lean.ParserCompiler.CombinatorAttribute.mk",
"Lean.ParserCompiler.CombinatorAttribute",
"Lean.NameMap.instInhabited",
"Lean.Name",
"Prod",
"Lean.SimplePersistentEnvExtension",
"Lean.SimplePersistentEnv... | true |
_private.Mathlib.Algebra.Polynomial.Degree.Lemmas.0.Polynomial.natDegree_comp._simp_1_2 | Mathlib.Algebra.Polynomial.Degree.Lemmas | [
"Polynomial.leadingCoeff",
"Polynomial",
"propext",
"Semiring",
"Zero.toOfNat0",
"Polynomial.instZero",
"OfNat.ofNat",
"Eq",
"Polynomial.leadingCoeff_eq_zero",
"MulZeroClass.toZero",
"instMulZeroClassOfSemiring"
] | false |
CategoryTheory.WithInitial.map | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.WithInitial.of",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.map",
"CategoryTheory.WithInitial",
"CategoryTheory.WithInitial.id.match_1",
"CategoryTheory.WithInitial.map._proof_7",
"Unit",
... | true |
_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Roo.toList_succ_succ_eq_map._simp_1_5 | Init.Data.Range.Polymorphic.Lemmas | [
"and_comm",
"And",
"propext",
"Eq"
] | false |
_private.Mathlib.MeasureTheory.Measure.MeasuredSets.0.MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRing._simp_1_10 | Mathlib.MeasureTheory.Measure.MeasuredSets | [
"Exists",
"not_exists",
"propext",
"Eq",
"Not"
] | false |
Array.instDecidableExistsAndMemOfDecidablePred | Init.Data.Array.Lemmas | [
"decidable_of_iff",
"Nat.decidableExistsLT'",
"Decidable",
"Array.instMembership",
"Membership.mem",
"Exists",
"Array.instDecidableExistsAndMemOfDecidablePred._proof_3",
"Array",
"GetElem.getElem",
"And",
"Array.instGetElemNatLtSize",
"DecidablePred",
"Nat",
"LT.lt",
"instLTNat",
"Arra... | true |
ContinuousCohomology.Iobj._proof_9 | Mathlib.Algebra.Category.ContinuousCohomology.Basic | [
"TopModuleCat.instCategory",
"CommRing",
"AddMonoid.toAddSemigroup",
"ContinuousMap",
"Group",
"ContinuousMap.instIsTopologicalAddGroup",
"AddCommGroup.toAddGroup",
"DivInvMonoid.toMonoid",
"TopModuleCat.instTopologicalSpaceCarrier",
"IsTopologicalAddGroup.toContinuousAdd",
"TopModuleCat.toModul... | false |
CategoryTheory.Monad.beckCofork_π | Mathlib.CategoryTheory.Monad.Coequalizer | [
"CategoryTheory.Monad",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Monad.Algebra.a",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Func... | true |
_private.Mathlib.Data.List.Cycle.0.Cycle.length_nontrivial._simp_1_2 | Mathlib.Data.List.Cycle | [
"LE.le",
"instLENat",
"Nat.succ_le_succ_iff",
"Nat",
"propext",
"Nat.succ",
"Eq"
] | false |
Subarray | Init.Data.Array.Subarray | [
"Std.Slice.Internal.SubarrayData",
"Std.Slice"
] | true |
Associates.coe_unit_eq_one | Mathlib.Algebra.GroupWithZero.Associated | [
"Units.val",
"MulOne.toOne",
"Associates.instCommMonoid",
"Monoid.toMulOneClass",
"_private.Mathlib.Algebra.GroupWithZero.Associated.0.Associates.coe_unit_eq_one._simp_1_1",
"Units",
"Associates.uniqueUnits",
"Units.instOne",
"Unique.instSubsingleton",
"MulOneClass.toMulOne",
"Associates",
"Co... | true |
HomotopyCategory.Plus.singleFunctors._proof_1 | Mathlib.Algebra.Homology.HomotopyCategory.Plus | [
"Int.instAddCommGroup",
"Eq.mpr",
"HomologicalComplex.instCategory",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"congrArg",
"Int.instLinearOrder",
"CochainComplex.singleFunctor",
"HomotopyCategory.singleFunctor",
"PartialOrder.toPreorder",
"instIsRightCancelAddOfAddRightReflectLE",
"AddGroupWit... | false |
Lean.MessageData.Exprs.rec | Mathlib.Lean.MessageData.ForExprs | [
"Lean.MessageData",
"Lean.MessageData.Exprs.mk",
"Lean.MessageData.Exprs"
] | false |
QuadraticMap.coeFn_smul._simp_1 | Mathlib.LinearAlgebra.QuadraticForm.Basic | [
"Monoid",
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Function.hasSMul",
"DistribSMul.toSMulZeroClass",
"QuadraticMap.instFunLike",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"Semiring.toMonoid",
"... | false |
LowerSet.iicInfHom_apply | Mathlib.Order.UpperLower.Hom | [
"LowerSet.instMin",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"InfHom",
"SemilatticeInf.toMin",
"SemilatticeInf",
"LowerSet.iicInfHom",
"InfHom.instFunLike",
"LowerSet",
"Eq",
"DFunLike.coe",
"rfl",
"LowerSet.Iic"
] | true |
Lean.Compiler.LCNF.TrivialStructureInfo.casesOn | Lean.Compiler.LCNF.Irrelevant | [
"Lean.Compiler.LCNF.TrivialStructureInfo.rec",
"Nat",
"Lean.Compiler.LCNF.TrivialStructureInfo",
"Lean.Name",
"Lean.Compiler.LCNF.TrivialStructureInfo.mk"
] | false |
Lean.Syntax.replaceM | Lean.Syntax | [
"Inhabited.default",
"instInhabitedOfMonad",
"Lean.Syntax",
"Inhabited",
"Monad",
"Inhabited.mk",
"Option"
] | true |
NNRat.lt_def | Mathlib.Data.NNRat.Defs | [
"Nat.cast_mul._simp_1",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Rat.num",
"Preorder.toLT",
"HMul.hMul",
"congrArg",
"Nat.cast_lt._simp_1",
"Iff.rfl",
"Rat",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"NNRat.coe_lt_coe",
"Rat.den",
"SemilatticeInf.toPar... | true |
PiTensorProduct.lifts.eq_1 | Mathlib.LinearAlgebra.PiTensorProduct | [
"AddMonoid.toAddSemigroup",
"addConGen",
"CommSemiring.toSemiring",
"PiTensorProduct.Eqv",
"setOf",
"FreeAddMonoid.instAddCancelMonoid",
"AddCancelMonoid.toAddRightCancelMonoid",
"PiTensorProduct.lifts",
"AddCommMonoid",
"CommSemiring",
"AddSemigroup.toAdd",
"AddRightCancelMonoid.toAddMonoid",... | true |
_private.Mathlib.InformationTheory.KullbackLeibler.Basic.0.InformationTheory.toReal_klDiv_smul_right._simp_1_6 | Mathlib.InformationTheory.KullbackLeibler.Basic | [
"False",
"eq_false",
"pow_ne_zero",
"Ne",
"Monoid.toPow",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Nat",
"Zero.toOfNat0",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq",
"MonoidWithZero.toMonoid",
"MulZeroClass.toZero",
"IsReduced"
] | false |
Mathlib.Tactic.BicategoryLike.CoherenceHom.tgt | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.CoherenceHom",
"Mathlib.Tactic.BicategoryLike.Mor₁"
] | true |
SubMulAction.ofStabilizer.conjMap_comp | Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer | [
"SubMulAction.ofStabilizer.conjMap_comp_apply",
"SubMulAction.instSetLike",
"Eq.mpr",
"MulAction.stabilizerEquivStabilizer",
"MulActionHom.comp",
"instHSMul",
"MulEquiv.instEquivLike",
"instSMulOfMul",
"HMul.hMul",
"SubMulAction.ofStabilizer.conjMap",
"Monoid.toMulOneClass",
"MulAction.stabili... | true |
_private.Mathlib.FieldTheory.PerfectClosure.0.PerfectClosure.add_aux_right.match_1_1 | Mathlib.FieldTheory.PerfectClosure | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"Nat.Prime",
"CommSemiring.toSemiring",
"HEq.refl",
"PerfectClosure.R.casesOn",
"PerfectClosure.R.intro",
"AddGroupWithOne.toAddMonoidWithOne",
"RingHom",
"Fact",
"Prod.mk",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"f... | false |
_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper.0.AlgebraicGeometry.Proj.valuativeCriterion_existence_aux._simp_1_9 | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | [
"Algebra.cast",
"CommRing",
"CommSemiring.toSemiring",
"IsFractionRing",
"Algebra",
"IsFractionRing.coe_inj",
"CommRing.toCommSemiring",
"propext",
"Eq"
] | false |
Real.le_sqrt_of_sq_le | Mathlib.Data.Real.Sqrt | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real.instLE",
"Real",
"IsOrderedRing.toPosMulMono",
"PartialOrder.toPreorder",
"Real.sq_le",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Real.semiring",
"DistribLattice.toLattice",
"Real.instAddGroup",
"instOfNatNat",
"LE.le",
"Monoi... | true |
RingPreordering.support_eq_bot | Mathlib.Algebra.Order.Ring.Ordering.Basic | [
"Eq.mpr",
"AddSubgroup.instBot",
"Semiring.toModule",
"CommSemiring.toSemiring",
"_private.Mathlib.Algebra.Order.Ring.Ordering.Basic.0.RingPreordering.support_eq_bot._simp_1_1",
"AddCommGroup.toAddGroup",
"Field.toDivisionRing",
"id",
"DivisionRing.toRing",
"Bot.bot",
"RingPreordering",
"Ideal... | true |
LeftInvariantDerivation.hasIntScalar | Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation | [
"ContMDiffMul",
"Derivation",
"NormedCommRing.toNormedRing",
"Monoid",
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"chartedSpaceSelf",
"NormedSpace",
"LieRing.toAddCommGroup",
"instTopENat",
... | true |
Ordinal.omega_ofNat_lt_lift | Mathlib.SetTheory.Cardinal.Aleph | [
"Preorder.toLT",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ordinal.lift",
"AddMonoidWithOne.toNatCast",
"Ordinal.omega",
"Ordinal.addMonoidWithOne",
"Iff",
"Nat",
"LT.lt",
"Ordinal.omega_natCast_lt_lift",
"OrderEmbedding",
"OfNat.ofNat",
"DFunLike.coe",
"inst... | true |
FirstOrder.Language.BoundedFormula.toPrenexImp.eq_def | Mathlib.ModelTheory.Complexity | [
"_private.Mathlib.ModelTheory.Complexity.0.FirstOrder.Language.BoundedFormula.toPrenexImp.match_1.eq_3",
"FirstOrder.Language.BoundedFormula.imp",
"Eq.mpr",
"False",
"FirstOrder.Language.BoundedFormula.toPrenexImp.match_1",
"congrArg",
"HEq.refl",
"FirstOrder.Language.BoundedFormula.brecOn",
"FirstO... | true |
Lean.Widget.RpcEncodablePacket._@.Lean.Widget.InteractiveGoal.1490754142._hygCtx._hyg.1 | Lean.Widget.InteractiveGoal | [
"Lean.Widget.RpcEncodablePacket.mk._@.Lean.Widget.InteractiveGoal.1490754142._hygCtx._hyg.1"
] | false |
_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.mem_splitSupport_iff_nonzero._simp_1_6 | Mathlib.Data.Finsupp.Basic | [
"Exists",
"exists_eq_right",
"And",
"propext",
"Eq"
] | false |
CategoryTheory.MorphismProperty.instHasIsosPrecoverageOfContainsIdentitiesOfRespectsIso | Mathlib.CategoryTheory.Sites.MorphismProperty | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Precoverage.HasIsos.mk",
"CategoryTheory.MorphismProperty.of_isIso",
"CategoryTheory.Precoverage.HasIsos",
"CategoryTheory.MorphismProperty.precoverage",
"CategoryTheory... | true |
Lean.IR.EmitLLVM.ShouldForwardControlFlow.no.sizeOf_spec | Lean.Compiler.IR.EmitLLVM | [
"Lean.IR.EmitLLVM.ShouldForwardControlFlow.no",
"instOfNatNat",
"Lean.IR.EmitLLVM.ShouldForwardControlFlow",
"Lean.IR.EmitLLVM.ShouldForwardControlFlow._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
List.getElem?_mapIdx | Init.Data.List.MapIdx | [
"List.mapIdx",
"False",
"List.getElem?_mapIdx_go",
"congrArg",
"List.mapIdx.go",
"HSub.hSub",
"List.instGetElem?NatLtLength",
"Option.some",
"Nat.not_lt_zero._simp_1",
"instSubNat",
"instOfNatNat",
"dite",
"List.toArray",
"Array",
"GetElem.getElem",
"List",
"Option.map",
"List.size... | true |
Std.Iter.Total | Init.Data.Iterators.Consumers.Total | [
"Std.Iter.Total.mk"
] | true |
ODE.FunSpace.mk.injEq | Mathlib.Analysis.ODE.PicardLindelof | [
"Real",
"LipschitzWith",
"ODE.FunSpace",
"Eq.propIntro",
"NormedAddCommGroup.toMetricSpace",
"instPseudoEMetricSpaceSubtype",
"Membership.mem",
"Set.Elem",
"EMetricSpace.toPseudoEMetricSpace",
"NNReal",
"Real.metricSpace",
"Set.Icc",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Eq.ndrec"... | true |
Std.ExtTreeMap.size_filterMap_eq_size_iff | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtDTreeMap.Const.size_filterMap_eq_size_iff",
"GetElem?.toGetElem",
"Std.ExtTreeMap.size",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Std.ExtTreeMap.getKey",
"GetElem.getElem",
"Bool.true",
"Iff",
"Std.ExtTreeMap",
"Std.ExtTreeMap.inner",
"Nat",
"Std.ExtTreeMap.filterMap",
"Boo... | true |
Int16.iSizeMinValue_le_toInt | Init.Data.SInt.Lemmas | [
"instPowNat",
"ISize.minValue",
"Int16",
"of_decide_eq_true",
"Int.decLe",
"Int16.le_toInt",
"id",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Int.instNatPow",
"LE.le",
"Bool.true",
"HPow.hPow",
"instOfNat",
"Nat",
"Int.le_trans",
"Int16.toInt",
"Bool",
"ISize.toInt_minValue_le",... | true |
Std.DHashMap.Raw.isSome_getKey?_iff_mem._simp_1 | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Std.DHashMap.Raw",
"Membership.mem",
"LawfulHashable",
"Bool.true",
"EquivBEq",
"propext",
"Bool",
"Hashable",
"Std.DHashMap.Raw.isSome_getKey?_iff_mem",
"Option.isSome",
"BEq",
"Eq",
"Std.DHashMap.Raw.getKey?"
] | false |
act_rel_of_rel_of_act_rel | Mathlib.Algebra.Order.Monoid.Unbundled.Defs | [
"trans",
"IsTrans",
"act_rel_act_of_rel",
"CovariantClass"
] | true |
Fintype.subtype_card | Mathlib.Data.Fintype.Card | [
"Finset",
"Fintype.subtype._proof_1",
"Membership.mem",
"Fintype.card",
"Subtype",
"Finset.val",
"Subtype.mk",
"Multiset.card_pmap",
"Iff",
"Finset.instSetLike",
"Fintype.subtype",
"Nat",
"Finset.card",
"Eq",
"SetLike.instMembership"
] | true |
isPathConnected_stdSimplex | Mathlib.Analysis.Convex.StdSimplex | [
"Real.instIsOrderedRing",
"IsPathConnected",
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"AddMonoid.toAddSemigroup",
"Pi.topologicalSpace",
"I... | true |
IsDedekindDomain.FiniteAdeleRing.instAlgebra | Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing | [
"IsDedekindDomain.instCommRingFiniteAdeleRing",
"CommRing",
"IsDedekindDomain.FiniteAdeleRing",
"IsDedekindDomain.FiniteAdeleRing.algebraMap",
"CommSemiring.toSemiring",
"IsFractionRing",
"Algebra",
"Field.toSemifield",
"CommRing.toCommSemiring",
"Semifield.toDivisionSemiring",
"DivisionSemiring... | true |
HahnSeries.ofFinsupp._proof_1 | Mathlib.RingTheory.HahnSeries.Basic | [
"Set.IsPWO",
"Finsupp.instFunLike",
"HahnSeries.mk_eq_zero._simp_1",
"PartialOrder.toPreorder",
"PartialOrder",
"id",
"HahnSeries.instZero",
"Pi.instZero",
"HahnSeries.mk",
"Set.Finite.isPWO",
"Function.support",
"True",
"eq_self",
"Finsupp.hasFiniteSupport",
"of_eq_true",
"Eq.ndrec",
... | false |
AddRightCancelMonoid.toIsRightCancelAdd | Mathlib.Algebra.Group.Defs | [
"IsRightCancelAdd",
"AddMonoid.toAddSemigroup",
"AddRightCancelMonoid",
"AddSemigroup.toAdd",
"AddRightCancelMonoid.toAddMonoid"
] | true |
ContinuousMap.sigmaMk._proof_1 | Mathlib.Topology.ContinuousMap.Basic | [
"Continuous",
"continuous_sigmaMk",
"instTopologicalSpaceSigma",
"TopologicalSpace",
"Sigma.mk",
"Sigma"
] | false |
CategoryTheory.ComposableArrows.IsComplex.cokerToKer'._proof_22 | Mathlib.Algebra.Homology.ExactSequenceFour | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ComposableArrows.IsComplex",
"PartialOrder.toPreorder",
"CategoryTheory.ComposableArrows",
"CategoryTheory.ComposableArrows.IsComplex.cokerToKer'._proof_17",
"Fin.mk",
"CategoryTheory.Co... | false |
Std.TreeMap.Raw.getElem?_inter_of_not_mem_left | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.WF.out",
"Membership.mem",
"Ordering",
"Std.TreeMap.Raw.instMembership",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Inter.inter",
"Std.TreeMap.Raw",
"Option.none",
"Std.TreeMap.Raw.instInter",
"Std.TreeMap.Raw.instGetElem?Mem",
"GetElem?.getElem?",
"St... | true |
Lean.ScopedEnvExtension.Entry.scoped.inj | Lean.ScopedEnvExtension | [
"Lean.ScopedEnvExtension.Entry",
"And",
"And.intro",
"eq_of_heq",
"Lean.Name",
"Lean.ScopedEnvExtension.Entry.scoped.noConfusion",
"HEq",
"Lean.ScopedEnvExtension.Entry.scoped",
"Eq"
] | true |
Std.DTreeMap.Internal.Impl.aux_size_modify | Std.Data.DTreeMap.Internal.Operations | [
"Ordering.gt",
"Eq.mpr",
"Ord",
"congrArg",
"_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.alter.match_3.splitter",
"_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.minView!.match_1.splitter",
"cast",
"Ordering",
"Ordering.eq",
"Std.DTreeMa... | true |
AddCommGroup.torsion_sum | Mathlib.GroupTheory.Torsion | [
"IsOfFinAddOrder.prod_iff",
"AddSubgroup.mem_prod",
"congrArg",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"Prod.fst",
"AddSubgroup",
"iff_self",
"IsOfFinAddOrder",
"And",
"Iff",
"AddGroup.toSubNegMonoid",
"AddSubgroup.prod",
"AddSubgroup.instSetLike",
"congr",
"Add... | true |
OrderIso.bddAbove_image | Mathlib.Order.GaloisConnection.Basic | [
"OrderIso.to_galoisConnection",
"GaloisConnection.bddAbove_l_image",
"Preorder.toLE",
"OrderIso",
"OrderIso.symm",
"BddAbove",
"Iff",
"instFunLikeOrderIso",
"Set.image",
"DFunLike.coe",
"Preorder",
"Set"
] | true |
_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deriving.Encodable.S.encode.match_1.splitter | Mathlib.Tactic.DeriveEncodable | [
"_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deriving.Encodable.S.encode.match_1",
"_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deriving.Encodable.S.nat",
"_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deriving.Encodable.S.cons",
"Nat",
"_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deri... | true |
BitVec.ne_of_lt | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"congrArg",
"BitVec",
"id",
"Ne",
"BitVec.toNat",
"BitVec.toNat_eq._simp_1",
"implies_congr",
"instLTBitVec",
"Nat",
"LT.lt",
"BitVec.lt_def._simp_1",
"instLTNat",
"Eq",
"Not",
"Nat.ne_of_lt"
] | true |
Equiv.Perm.toList_eq_nil_iff | Mathlib.GroupTheory.Perm.Cycle.Concrete | [
"Equiv.Perm.instDecidableRelSameCycle",
"List.iterate",
"Equiv.Perm.toList",
"Equiv.Perm.support",
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"Equiv.Perm.support_eq_empty_iff._simp_1",
"congrArg",
"Finset.card_eq_zero._simp_1",
"Finset",
"Membership.mem",
"instOfNatNat",
"Decidable.not_not... | true |
Lean.Meta.Grind.Arith.isRelevantPred | Lean.Meta.Tactic.Grind.Arith.IsRelevant | [
"Inhabited.default",
"Lean.Meta.Grind.instInhabitedGoalM",
"Lean.Expr",
"Bool",
"Lean.Meta.Grind.GoalM"
] | true |
ContMDiff.sumElim | Mathlib.Geometry.Manifold.ContMDiff.Constructions | [
"ChartedSpace.sum",
"ChartedSpace.sum_chartAt_inr",
"Eq.mpr",
"extChartAt",
"NormedSpace",
"chartAt",
"ContMDiff.continuous",
"congrArg",
"ContinuousAt",
"ContMDiff",
"PartialEquiv",
"nhdsWithin",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Function.comp",
"Membership.mem",
"Partia... | true |
Std.TreeSet.merge | Std.Data.TreeSet.Basic | [
"Std.TreeSet",
"Unit.unit",
"Ordering",
"Std.TreeSet.inner",
"Std.TreeMap.mergeWith",
"Std.TreeSet.mk",
"Unit"
] | true |
_private.Mathlib.Combinatorics.Graph.Basic.0.Graph.banana_inc._simp_1_2 | Mathlib.Combinatorics.Graph.Basic | [
"Exists",
"exists_and_left",
"And",
"propext",
"Eq"
] | false |
RegularExpression.map_pow._f | Mathlib.Computability.RegularExpressions | [
"RegularExpression.matches'.match_1",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"RegularExpression",
"RegularExpression.char",
"RegularExpression.instPowNat",
"id",
"RegularExpression.map",
"instOfNatNat",
"RegularExpression.instMul",
"congr_arg",
"Nat.below",
"RegularExpression.instZero",
"ins... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Equiv.insert._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
Coalgebra.coassoc | Mathlib.RingTheory.Coalgebra.Basic | [
"Coalgebra.toCoalgebraStruct",
"Coalgebra",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"LinearMap.lTensor",
"LinearMap",
"AddCommMonoid",
"CoalgebraStruct.comul",
"CommSemiring",
"LinearMap.comp",
"LinearEquiv.toLinearMap",
"RingHomInvPair.ids",
"TensorProduct.assoc",
"Tenso... | true |
RootPairing.isSimpleModule_weylGroupRootRep | Mathlib.LinearAlgebra.RootSystem.Irreducible | [
"Nontrivial",
"Iff.mpr",
"Sublattice",
"RootPairing.IsIrreducible.nontrivial",
"Submodule",
"CommRing",
"RootPairing.weylGroup",
"Representation.instModuleMonoidAlgebraAsModule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"MonoidAlgebra.ring",
"Me... | true |
Std.LawfulRightIdentity.recOn | Init.Core | [
"Std.LawfulRightIdentity",
"Std.RightIdentity",
"Std.LawfulRightIdentity.rec",
"Std.LawfulRightIdentity.mk",
"Eq"
] | false |
Lean.Server.FileWorker.SemanticTokensState.mk.sizeOf_spec | Lean.Server.FileWorker.SemanticHighlighting | [
"Lean.Server.FileWorker.SemanticTokensState.mk",
"instOfNatNat",
"Lean.Server.FileWorker.SemanticTokensState",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Server.FileWorker.SemanticTokensState._sizeOf_inst"
] | true |
Nat.stirlingFirst_one_right | Mathlib.Combinatorics.Enumerative.Stirling | [
"Eq.mpr",
"Nat.recAux",
"HMul.hMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"id",
"instMulNat",
"instOfNatNat",
"Nat.stirlingFirst",
"zero_add",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"Nat.factorial",
"Nat",
"True",
"eq_self",
... | true |
CategoryTheory.GrothendieckTopology.OneHypercover.id_h₁ | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.PreOneHypercover.I₁",
"CategoryTheory.PreOneHypercover.toPreZeroHypercover",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.PreOneHypercover.Y",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.GrothendieckTopology.OneH... | true |
ModuleCat.instModuleCarrierMkOfSMul' | Mathlib.Algebra.Category.ModuleCat.Basic | [
"ModuleCat.instSMulCarrierMkOfSMul'",
"ModuleCat.mkOfSMul'",
"AddCommGrpCat.instCategory",
"AddCommGroup.toAddCommMonoid",
"ModuleCat.instModuleCarrierMkOfSMul'._proof_4",
"Module.mk",
"RingHom",
"DistribMulAction.mk",
"SemigroupAction.mk",
"CategoryTheory.End",
"AddCommGrpCat.carrier",
"Modul... | true |
_private.Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics.0.isLittleO_exp_neg_mul_rpow_atTop._simp_1_6 | Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics | [
"GroupWithZero.toMonoidWithZero",
"False",
"GroupWithZero.toDivInvMonoid",
"eq_false",
"GroupWithZero",
"DivInvMonoid.toZPow",
"Ne",
"Int",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Zero.toOfNat0",
"zpow_ne_zero",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq... | false |
_private.Lean.Meta.Basic.0.Lean.Meta.realizeValue.match_7 | Lean.Meta.Basic | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"_private.Lean.Meta.Basic.0.Lean.Meta.RealizeValueResult",
"_private.Lean.Meta.Basic.0.Lean.Meta.withRestoreOrSaveFull._sparseCasesOn_1",
"Option"
] | false |
Nat.Linear.ExprCnstr.denote_toPoly | Init.Data.Nat.Linear | [
"cond",
"Eq.mpr",
"Nat.Linear.Poly.denote",
"congrArg",
"eq_iff_iff._simp_1",
"Nat.Linear.PolyCnstr.denote",
"Nat.Linear.Poly",
"Nat.Linear.Expr",
"id",
"instDecidableEqBool",
"Prod.mk",
"LE.le",
"instLENat",
"Nat.Linear.ExprCnstr",
"Prod.fst",
"dite",
"Nat.Linear.Expr.denote",
"if... | true |
HeytAlg.Hom.recOn | Mathlib.Order.Category.HeytAlg | [
"_private.Mathlib.Order.Category.HeytAlg.0.HeytAlg.Hom.mk",
"HeytAlg",
"HeytAlg.Hom.rec",
"HeytAlg.carrier",
"HeytAlg.Hom",
"HeytingHom",
"HeytAlg.str"
] | false |
Aesop.Options'.ctorIdx | Aesop.Options.Internal | [
"Aesop.Options'",
"Nat"
] | false |
_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iUnion_Ioo_coe_nat._simp_1_1 | Mathlib.Data.ENNReal.Basic | [
"Set.Ioi",
"Set.instInter",
"Inter.inter",
"Set.Ioi_inter_Iio",
"Eq.symm",
"Set.Iio",
"Eq",
"Set.Ioo",
"Preorder",
"Set"
] | false |
_private.Mathlib.Tactic.Linarith.Verification.0.Mathlib.Tactic.Linarith.mkLTZeroProof.match_1 | Mathlib.Tactic.Linarith.Verification | [
"Unit.unit",
"Lean.Expr",
"Nat.hasNotBit",
"Prod.mk",
"List.cons",
"List",
"Unit",
"Nat",
"List.casesOn",
"Prod",
"Prod.casesOn",
"List.ctorIdx",
"_private.Mathlib.Tactic.Linarith.Verification.0.Mathlib.Tactic.Linarith.addExprs'.go._sparseCasesOn_1",
"List.nil"
] | false |
Lean.Meta.Grind.AC.getOpId | Lean.Meta.Tactic.Grind.AC.Util | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Goal",
"instMonadReaderOfReaderTOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Sym.Context",
"MonadReader.read",
"ReaderT.instMonad",
"Lean.Meta.Grind.Context",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Meta.Grind.AC.ACM.Contex... | true |
Multiset.singleton_inj | Mathlib.Data.Multiset.ZeroCons | [
"Multiset",
"id",
"Multiset.instSingleton",
"Iff",
"Zero.toOfNat0",
"Multiset.cons_inj_left",
"Singleton.singleton",
"OfNat.ofNat",
"Eq",
"Multiset.instZero"
] | true |
Lean.Lsp.instToJsonWorkspaceClientCapabilities | Lean.Data.Lsp.Capabilities | [
"Lean.Lsp.instToJsonWorkspaceClientCapabilities.toJson",
"Lean.ToJson.mk",
"Lean.ToJson",
"Lean.Lsp.WorkspaceClientCapabilities"
] | true |
IsBoundedBilinearMap.isBigO' | Mathlib.Analysis.Normed.Operator.BoundedLinearMaps | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"SeminormedAddCommGroup",
"HMul.hMul",
"AddCommGroup.toAddCommMonoid",
"NormedDivisionRing.toNormMulClass",
"Prod.toNorm",
"Asymptotics.IsBigO",
"Asymptotics.isBigO_fst_prod'",
"Asymptotics.IsBigO.norm_n... | true |
_private.Mathlib.NumberTheory.LSeries.Nonvanishing.0.DirichletCharacter.one_lt_re_one_add | Mathlib.NumberTheory.LSeries.Nonvanishing | [
"Complex.mul_im",
"Real.partialOrder",
"Real",
"Complex.mul_re",
"HMul.hMul",
"sub_self",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
"and_self",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Complex.im",
"Real.instSub",
"MulZeroClass.zero_mul",
"AddMonoid.toAddZeroClass",
"PartialO... | true |
_private.Init.Data.String.Iterator.0.String.Legacy.Iterator.hasNext.eq_1 | Init.Data.String.Iterator | [
"String.Legacy.Iterator.mk",
"String",
"String.Legacy.Iterator.hasNext",
"String.Pos.Raw",
"String.rawEndPos",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"String.Pos.Raw.byteIdx",
"Decidable.decide",
"Eq"
] | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.