name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Topology.MetricSpace.HausdorffDistance.0.Metric.hausdorffDist_zero_iff_closure_eq_closure._simp_1_3 | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"Real",
"Real.instZero",
"ENNReal.toReal",
"ENNReal",
"propext",
"Zero.toOfNat0",
"ENNReal.instTop",
"Or",
"ENNReal.instZero",
"Top.top",
"OfNat.ofNat",
"Eq",
"ENNReal.toReal_eq_zero_iff"
] | false |
List.sum_toFinset | Mathlib.Algebra.BigOperators.Group.Finset.Basic | [
"List.brecOn",
"List.map",
"AddMonoid.toAddZeroClass",
"List.sum",
"List.sum_toFinset._f",
"AddZeroClass.toAddZero",
"List.toFinset",
"AddCommMonoid",
"List.Nodup",
"AddZero.toZero",
"List",
"AddZero.toAdd",
"AddCommMonoid.toAddMonoid",
"Eq",
"Finset.sum",
"DecidableEq"
] | true |
decidable_of_decidable_of_eq | Init.Core | [
"Decidable",
"decidable_of_decidable_of_eq._proof_1",
"decidable_of_decidable_of_iff",
"Eq"
] | true |
Lean.Elab.Tactic.Do.SpecAttr.SpecProof.local.inj | Lean.Elab.Tactic.Do.Attr | [
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof.local.noConfusion",
"Lean.FVarId",
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof.local",
"Eq",
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof"
] | true |
YoungDiagram.exists_notMem_col | Mathlib.Combinatorics.Young.YoungDiagram | [
"Eq.mpr",
"YoungDiagram.transpose",
"YoungDiagram",
"congrArg",
"HEq.refl",
"Finset",
"Membership.mem",
"Exists",
"Eq.casesOn",
"YoungDiagram.cells",
"Prod.mk",
"YoungDiagram.exists_notMem_row",
"funext",
"Finset.instSetLike",
"Nat",
"congr",
"True",
"eq_self",
"of_eq_true",
"e... | true |
ModuleCat.instModuleCarrierMkOfSMul'._proof_2 | Mathlib.Algebra.Category.ModuleCat.Basic | [
"ModuleCat.instSMulCarrierMkOfSMul'",
"CategoryTheory.End.one",
"RingHom.instRingHomClass",
"MulOne.toOne",
"instHSMul",
"ModuleCat.mkOfSMul'",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"Monoid.toMulOneClass",
"congrArg",
"CategoryTheory.ConcreteCate... | false |
Int.gcd_eq_zero_iff | Init.Data.Int.Gcd | [
"Nat.gcd",
"Int.gcd",
"congrArg",
"Nat.gcd_eq_zero_iff._simp_1",
"instOfNatNat",
"Int",
"iff_self",
"And",
"Iff",
"instOfNat",
"Nat",
"congr",
"True",
"Int.natAbs",
"of_eq_true",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Int.natAbs_eq_zero._simp_1",
"Eq.trans"
] | true |
IO.Promise.isResolved | Init.System.Promise | [
"IO.hasFinished",
"IO.Promise.result?",
"IO.Promise",
"Bool",
"BaseIO",
"Option"
] | true |
Std.CancellationToken.Consumer.normal.injEq | Std.Sync.CancellationToken | [
"Eq.propIntro",
"Std.CancellationToken.Consumer",
"Unit",
"IO.Promise",
"Eq.ndrec",
"Std.CancellationToken.Consumer.normal",
"Eq.refl",
"Eq",
"Std.CancellationToken.Consumer.normal.inj"
] | true |
_private.Mathlib.Data.List.Permutation.0.List.nodup_permutations'Aux_iff._proof_1_19 | Mathlib.Data.List.Permutation | [
"HSub.hSub",
"Lean.Grind.Nat.lt_eq",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"List",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"List.length"
] | false |
Std.ExtTreeSet.isSome_max?_of_contains | Std.Data.ExtTreeSet.Lemmas | [
"Std.ExtTreeMap.isSome_maxKey?_of_contains",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Bool.true",
"Unit",
"Std.ExtTreeSet",
"Bool",
"Std.ExtTreeSet.contains",
"Std.ExtTreeSet.max?",
"Option.isSome",
"Eq"
] | true |
Aesop.SimpResult.solved | Aesop.Search.Expansion.Simp | [
"Lean.Meta.Simp.UsedSimps",
"Aesop.SimpResult.solved",
"Aesop.SimpResult"
] | true |
_private.Lean.Elab.DocString.Builtin.Postponed.0.Lean.Doc.getHandlerUnsafe | Lean.Elab.DocString.Builtin.Postponed | [
"Lean.instMonadEnvOfMonadLift",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Meta.State",
"Lean.Core.instMonadOptionsCoreM",
"Lean.Name.m... | true |
Vector.push_mk._proof_1 | Init.Data.Vector.Lemmas | [
"Array.push",
"congrArg",
"instOfNatNat",
"Array",
"instHAdd",
"Nat.add_left_cancel_iff._simp_1",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"of_eq_true",
"instAddNat",
"Array.size_push",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Array.size",
"Eq.trans"
] | false |
StrictAntiOn.add_const | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"Preorder.toLT",
"add_lt_add_left",
"StrictAntiOn",
"AddRightStrictMono",
"Membership.mem",
"instHAdd",
"HAdd.hAdd",
"LT.lt",
"Set.instMembership",
"Add",
"Preorder",
"Set"
] | true |
ULift.isAddRegular_up._simp_1 | Mathlib.Algebra.Regular.ULift | [
"ULift",
"ULift.add",
"IsAddRegular",
"propext",
"ULift.up",
"Eq",
"Add",
"ULift.isAddRegular_up"
] | false |
_private.Init.Data.String.Iterate.0.String.Slice.RevPosIterator.finitenessRelation._simp_2 | Init.Data.String.Iterate | [
"String.instLTRaw",
"String.Pos.Raw.lt_iff",
"String.Pos.Raw",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"String.Pos.Raw.byteIdx",
"Eq"
] | false |
lpInftySubalgebra | Mathlib.Analysis.Normed.Lp.lpSpace | [
"NormOneClass",
"NormedRing.toRing",
"lpInftySubalgebra._proof_2",
"Ring.toNonAssocRing",
"Subsemigroup.mk",
"setOf",
"AddGroupWithOne.toAddMonoidWithOne",
"PreLp.ring",
"NormedField.toField",
"NormedRing.toNonUnitalNormedRing",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"lpInftyS... | true |
AddSubgroup.isAddQuotientCoveringMap | Mathlib.Topology.Covering.Quotient | [
"QuotientAddGroup.leftRel_apply",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"isQuotientMap_quotient_mk'",
"Topology.IsQuotientMap.isAddQuotientCoveringMap_of_addSubgroupOp",
"Quotient.eq''",
"AddMonoid.toAddZeroClass",
"AddSubgroup.toAddGroup",
"Quotient.mk''",
"Membership.mem",
"Add... | true |
Std.ExtTreeSet.getLED | Std.Data.ExtTreeSet.Basic | [
"Std.ExtTreeMap.getKeyLED",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Unit",
"Std.ExtTreeSet"
] | true |
MeasureTheory.integrable_neg_iff | Mathlib.MeasureTheory.Function.L1Space.Integrable | [
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"MeasureTheory.Measure",
"Pi.instNeg",
"Pi.involutiveNeg",
"MeasureTheory.Integrable.neg",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.Integrable",
"Eq.rec",
"SeminormedAddGroup.toContinuousENorm",
"neg_neg",
"SubtractionMonoid.... | true |
AlgebraicGeometry.Scheme.height_of_isClosed | Mathlib.AlgebraicGeometry.Scheme | [
"_private.Mathlib.AlgebraicGeometry.Scheme.0.AlgebraicGeometry.Scheme.height_of_isClosed._simp_1_1",
"Eq.mpr",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"Specializes",
"CommSemiring.toSemiring",
"CommRi... | true |
Std.DHashMap.Internal.Raw₀.forall_mem_keys_iff_forall_contains_getKey | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.Internal.List.forall_mem_keys_iff_forall_containsKey_getKey",
"Std.DHashMap.Internal.Raw.WF.out",
"congrArg",
"Std.DHashMap.Internal.Raw₀.getKey",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.contains_eq_containsKey",
... | true |
Fin.Icc_sub_one_eq_Ico | Mathlib.Order.Interval.Finset.Fin | [
"Fin.instSub",
"Finset",
"PartialOrder.toPreorder",
"HSub.hSub",
"Fin.instLocallyFiniteOrder",
"Fin.neZero",
"Fin.instOfNat",
"Finset.Ico",
"Finset.Icc",
"instHSub",
"Fin.instPartialOrder",
"Nat",
"LT.lt",
"instLTFin",
"OfNat.ofNat",
"_private.Mathlib.Order.Interval.Finset.Fin.0.Fin.Ic... | true |
ZFSet.mem_prod._simp_1 | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet",
"Membership.mem",
"Exists",
"ZFSet.prod",
"ZFSet.mem_prod",
"And",
"ZFSet.pair",
"propext",
"Eq",
"ZFSet.instSetLike",
"SetLike.instMembership"
] | false |
_private.Lean.Meta.Tactic.Grind.Internalize.0.Lean.Meta.Grind.internalizeImpl | Lean.Meta.Tactic.Grind.Internalize | [
"Inhabited.default",
"Lean.Meta.Grind.instInhabitedGoalM",
"Lean.Expr",
"Option.none",
"Unit",
"Nat",
"optParam",
"Lean.Meta.Grind.GoalM",
"Option"
] | true |
Int.sub_max_sub_left | Init.Data.Int.LemmasAux | [
"_private.Init.Data.Int.LemmasAux.0.Int.sub_max_sub_left._proof_1_1",
"Int.instMax",
"HSub.hSub",
"Int.instDecidableEq",
"Int",
"instHSub",
"Max.max",
"Decidable.byContradiction",
"Int.instSub",
"Int.instMin",
"Eq",
"Not",
"Min.min"
] | true |
Set.div_empty | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"instHDiv",
"HDiv.hDiv",
"Div",
"Set.image2_empty_right",
"Set.instEmptyCollection",
"Set.div",
"EmptyCollection.emptyCollection",
"Eq",
"Set"
] | true |
finsum_mem_image' | Mathlib.Algebra.BigOperators.Finprod | [
"Eq.mpr",
"congrArg",
"Finset",
"Set.Finite.mem_toFinset",
"Set.inter_self",
"finsum",
"AddMonoid.toAddZeroClass",
"finsum_mem_eq_sum",
"Classical.propDecidable",
"Set.Finite",
"Function.comp",
"Membership.mem",
"AddZeroClass.toAddZero",
"Finset.coe_image",
"id",
"Set.Finite.coe_toFins... | true |
ContMDiffVAdd | Mathlib.Geometry.Manifold.Algebra.SMul | [
"NormedSpace",
"VAdd",
"TopologicalSpace",
"ModelWithCorners",
"ContMDiffVAdd.mk",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"NormedAddCommGroup",
"WithTop",
"ChartedSpace"
] | true |
ContinuousMultilinearMap.ofSubsingleton._proof_3 | Mathlib.Topology.Algebra.Module.Multilinear.Basic | [
"Continuous",
"Pi.topologicalSpace",
"Continuous.comp",
"ContinuousMultilinearMap",
"Function.comp",
"continuous_pi",
"ContinuousMultilinearMap.funLike",
"AddCommMonoid",
"TopologicalSpace",
"continuous_id",
"Semiring",
"ContinuousMapClass.map_continuous",
"Module",
"ContinuousMultilinearM... | false |
_private.Mathlib.Algebra.CharZero.Defs.0.charZero_of_inj_zero._simp_1_1 | Mathlib.Algebra.CharZero.Defs | [
"IsRightCancelAdd",
"instHAdd",
"HAdd.hAdd",
"add_right_cancel_iff",
"propext",
"Eq",
"Add"
] | false |
OrderDual.instNonAssocSemiring._proof_4 | Mathlib.Algebra.Order.Ring.Synonym | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.toAddSemigroup",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"OrderDual.instAddCommMonoidWithOne",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"NatCast.natCast",
"AddMonoidWithOne.natCast_succ",
"AddMonoidWithOne.toOne",
"instHAdd",
"AddSemi... | false |
ContinuousAddEquiv.trans | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"ContinuousAddEquiv.trans._proof_1",
"ContinuousAddEquiv.toAddEquiv",
"TopologicalSpace",
"AddEquiv.trans",
"AddEquiv",
"ContinuousAddEquiv",
"ContinuousAddEquiv.trans._proof_2",
"Add",
"ContinuousAddEquiv.mk"
] | true |
GroupTopology.casesOn | Mathlib.Topology.Algebra.Group.GroupTopology | [
"GroupTopology.rec",
"Group",
"TopologicalSpace",
"IsTopologicalGroup",
"GroupTopology.mk",
"GroupTopology"
] | false |
Dynamics.mem_ball_dynEntourage_comp | Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage | [
"Dynamics.isSymm_dynEntourage",
"UniformSpace.mem_ball_comp",
"SetRel",
"congrArg",
"Membership.mem",
"Dynamics.dynEntourage",
"Eq.mp",
"Prod.mk",
"Set.instInter",
"UniformSpace.ball",
"SetRel.comp",
"Dynamics.dynEntourage_comp_subset",
"Inter.inter",
"And.casesOn",
"UniformSpace.mem_bal... | true |
MeasureTheory.lintegral_mul_left_eq_self | Mathlib.MeasureTheory.Group.LIntegral | [
"MeasurableEquiv.mulLeft",
"MeasurableEquiv.instEquivLike",
"Eq.mpr",
"MeasureTheory.Measure",
"HMul.hMul",
"MeasureTheory.map_mul_left_eq_self",
"Monoid.toMulOneClass",
"congrArg",
"HEq.refl",
"Group",
"Eq.casesOn",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"MeasurableMul",
"Group.toDivI... | true |
ValuationSubring.ofPrime_idealOfLE | Mathlib.RingTheory.Valuation.ValuationSubring | [
"not_iff_not",
"Iff.mpr",
"ValuationSubring.valuation_lt_one_iff",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"SubmonoidClass.instIsDedekindFiniteMonoidSubtypeMem",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Zero... | true |
Nat.coprime_factorial_iff | Mathlib.Data.Nat.Prime.Factorial | [
"not_le",
"Eq.mpr",
"Nat.Coprime",
"Nat.Prime",
"Preorder.toLT",
"Dvd.dvd",
"iff_not_comm",
"Nat.dvd_factorial",
"congrArg",
"Nat.Prime.dvd_factorial",
"PartialOrder.toPreorder",
"Nat.minFac_le_of_dvd",
"Preorder.toLE",
"Exists",
"id",
"Nat.minFac",
"Nat.minFac_dvd",
"Ne",
"instO... | true |
Subsemigroup.topEquiv_symm_apply_coe | Mathlib.Algebra.Group.Subsemigroup.Operations | [
"MulEquiv.instEquivLike",
"Subsemigroup.instMulMemClass",
"Mul",
"Membership.mem",
"Subtype",
"Subsemigroup.topEquiv",
"MulMemClass.mul",
"Subsemigroup.instTop",
"Subsemigroup",
"MulEquiv",
"Eq.refl",
"Top.top",
"MulEquiv.symm",
"Subsemigroup.instSetLike",
"Subtype.val",
"Eq",
"DFunL... | true |
_private.Mathlib.Order.Interval.Finset.Fin.0.Fin.map_addNatEmb_Ioi._simp_1_1 | Mathlib.Order.Interval.Finset.Fin | [
"Finset",
"Finset.coe_inj",
"SetLike.coe",
"Finset.instSetLike",
"propext",
"Eq.symm",
"Eq",
"Set"
] | false |
_private.Aesop.Tree.Check.0.Aesop.MVarClusterRef.checkMVars.checkNormMVars.match_1 | Aesop.Tree.Check | [
"Unit.unit",
"Lean.Meta.SavedState",
"Aesop.NormalizationState.provenByNormalization",
"Lean.MVarId",
"Aesop.NormalizationState",
"Aesop.NormalizationState.normal",
"Aesop.DisplayRuleName",
"Array",
"Unit",
"Aesop.NormalizationState.notNormal",
"Prod",
"Aesop.NormalizationState.casesOn",
"Ae... | false |
IncidenceAlgebra.instAddCommGroup._proof_5 | Mathlib.Combinatorics.Enumerative.IncidenceAlgebra | [
"AddGroup.toSubtractionMonoid",
"IncidenceAlgebra.instSub",
"IncidenceAlgebra.coe_sub",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"LE",
"SubNegMonoid.toSub",
"instHSub",
"AddGroup.toSubNegMonoid",
"Incid... | false |
_private.Mathlib.Analysis.BoxIntegral.Box.SubboxInduction.0.BoxIntegral.Box.mem_splitCenterBox._simp_1_4 | Mathlib.Analysis.BoxIntegral.Box.SubboxInduction | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"not_lt",
"LT.lt",
"propext",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
CommRingCat.Under.equalizerFork'._proof_2 | Mathlib.Algebra.Category.Ring.Under.Limits | [
"CommRing",
"AlgHom.algHomClass",
"CommRingCat.carrier",
"CommSemiring.toSemiring",
"CommRingCat",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"AlgHomClass",
"CommRingCat.instCommRingObjForgetRingHomCarrier",
"CommRing.toCommSemiring"
] | false |
CategoryTheory.Limits.hasBinaryProduct_zero_right | Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.Limits.HasBinaryProduct",
"CategoryTheory.discreteCategory",
"CategoryTheory.Limits.HasLimit.mk",
"CategoryTheory.Limits.pair",
"CategoryTheory.Limits.HasZeroObject",
"Zero.toOfNat0",
"CategoryTheory.Limit... | true |
Mathlib.Tactic.DepRewrite.Conv.depRewriteTarget | Mathlib.Tactic.DepRewrite | [
"Mathlib.Tactic.DepRewrite.Config.mk",
"ReaderT",
"monadFunctorRefl",
"Lean.Elab.Tactic.getMainGoal",
"Lean.Meta.State",
"Lean.MVarId.depRewrite",
"instMonadLiftT",
"Lean.Meta.RewriteResult.mvarIds",
"Lean.Elab.Tactic.Context",
"Lean.Syntax",
"Lean.MVarId",
"Lean.Elab.Tactic.elabTerm",
"Lean... | true |
CategoryTheory.Limits.PullbackCone.combine._proof_6 | Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Pullbacks | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.WalkingCospan.Hom.inl",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingCospan.right",
"Option.casesOn",
"Option.some",
"CategoryT... | false |
Array.findIdx?_eq_some_iff_findIdx_eq | Init.Data.Array.Find | [
"congrArg",
"Option.some",
"Array.casesOn",
"List.findIdx?",
"List.findIdx?_toArray",
"Array",
"iff_self",
"List",
"And",
"Iff",
"List.size_toArray",
"Nat",
"congr",
"LT.lt",
"True",
"_private.Init.Data.Array.Find.0.Array.findIdx?_eq_some_iff_findIdx_eq._simp_1_1",
"List.findIdx_toAr... | true |
Std.toList_roo_eq_toList_rco_of_isSome_succ? | Init.Data.Range.Polymorphic.Lemmas | [
"Std.PRange.UpwardEnumerable",
"congrArg",
"_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Roo.Internal.toList_eq_toList_iter",
"Std.PRange.LawfulUpwardEnumerableLT",
"Std.Rxo.instIteratorIteratorIdOfUpwardEnumerableOfDecidableLT",
"Std.Rxo.Iterator",
"Std.Rco.Internal.iter",
"_private.Init.Data.Ra... | true |
CategoryTheory.Equivalence.congrFullSubcategory_inverse | Mathlib.CategoryTheory.ObjectProperty.Equivalence | [
"CategoryTheory.Functor",
"CategoryTheory.ObjectProperty.ι",
"CategoryTheory.Equivalence.congrFullSubcategory",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp",
"CategoryTheory.Equivalence.congrFullSubcategory._proof_2",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.ObjectProperty.... | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.List.getValue_filter_containsKey._simp_1_1 | Std.Data.Internal.List.Associative | [
"Option.some",
"Std.Internal.List.getValue",
"Bool.true",
"List",
"Std.Internal.List.containsKey",
"Std.Internal.List.getValue?",
"Bool",
"Eq.symm",
"BEq",
"Eq",
"Sigma",
"Std.Internal.List.getValue?_eq_some_getValue",
"Option"
] | false |
Submodule.coe_mapIic_apply | Mathlib.Algebra.Module.Submodule.Range | [
"Submodule",
"RingHomSurjective.ids",
"Submodule.mapIic",
"Submodule.addCommMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Set.Elem",
"Subtype",
"OrderIso",
"Submodule.instPartialOrder",
"Submodule.module",
"AddCommMonoid",
"instFunLikeOrderIso",
"Submodule.setLi... | true |
Lean.Meta.SimpCongrTheorems.noConfusionType | Lean.Meta.Tactic.Simp.SimpCongrTheorems | [
"Lean.Meta.SimpCongrTheorems",
"List",
"Lean.SMap",
"Lean.Meta.SimpCongrTheorem",
"Lean.Name",
"Eq",
"Lean.Name.instBEq",
"Lean.Meta.SimpCongrTheorems.casesOn",
"Lean.instHashableName"
] | false |
cfc_comp_re._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.RealImaginaryPart | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Finset.map_disjSum | Mathlib.Data.Finset.Sum | [
"Finset",
"Finset.map",
"Sum",
"Finset.val",
"Function.Embedding.inl",
"Finset.val_injective",
"Function.Embedding",
"Finset.disjUnion",
"Finset.map_disjSum._proof_3",
"Function.Embedding.trans",
"Function.Embedding.inr",
"Finset.disjSum",
"Multiset.map_disjSum",
"Function.instFunLikeEmbed... | true |
CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_comp | Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd_assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CartesianMonoidalCategory.tensorHom_fst",
"CategoryTheory.SemiCartesianMonoidalCategory.snd",
"CategoryTheory.Cartesia... | true |
RootPairing.Equiv.weightEquiv_inv | Mathlib.LinearAlgebra.RootSystem.Hom | [
"CommRing",
"DivInvOneMonoid.toInvOneClass",
"LinearEquiv.toLinearMap_inj",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"AddCommGroup",
"LinearMap",
"RootPairing.Equiv.weightEquiv",
"RootPairing.Aut",
"LinearEquiv.aut... | true |
Polynomial.prod_multiset_X_sub_C_dvd | Mathlib.Algebra.Polynomial.Roots | [
"Multiset.toFinset",
"Eq.mpr",
"Polynomial.C",
"Polynomial.pow_rootMultiplicity_dvd",
"IsDomain",
"FractionRing.field",
"CommRing",
"Polynomial.monic_multisetProd_X_sub_C",
"Polynomial.roots",
"Dvd.dvd",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"Multiset.map",
"Polynomial.map_... | true |
CategoryTheory.IsCofiltered.SmallCofilteredIntermediate._proof_1 | Mathlib.CategoryTheory.Filtered.Small | [
"CategoryTheory.Functor",
"CategoryTheory.IsCofiltered.cofilteredClosure",
"CategoryTheory.IsCofilteredOrEmpty",
"CategoryTheory.EssentiallySmall",
"CategoryTheory.ObjectProperty.FullSubcategory",
"CategoryTheory.ObjectProperty.FullSubcategory.category",
"CategoryTheory.IsCofiltered.instEssentiallySmall... | false |
HNNExtension.NormalWord.ReducedWord.ctorIdx | Mathlib.GroupTheory.HNNExtension | [
"Group",
"Subgroup",
"HNNExtension.NormalWord.ReducedWord",
"Nat"
] | false |
BoxIntegral.TaggedPrepartition.distortion | Mathlib.Analysis.BoxIntegral.Partition.Tagged | [
"BoxIntegral.TaggedPrepartition.toPrepartition",
"NNReal",
"BoxIntegral.Prepartition.distortion",
"Fintype",
"BoxIntegral.TaggedPrepartition",
"BoxIntegral.Box"
] | true |
IsBaseChange.eq_1 | Mathlib.RingTheory.IsTensorProduct | [
"LinearMap.restrictScalars",
"Semiring.toModule",
"instSMulOfMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"IsBaseChange._proof_6",
"AddMonoid.toAddZeroClass",
"Module.End.instSemiring",
"IsBaseChange._proof_5",
"LinearMap.instFunLike",
"Algebra",
"Algeb... | true |
UInt64.toUSize_sub | Init.Data.UInt.Lemmas | [
"instAddUInt64",
"UInt64.toUSize",
"congrArg",
"UInt64",
"UInt64.toUSize_add",
"HSub.hSub",
"USize.sub_eq_add_neg",
"instHAdd",
"instHSub",
"UInt64.toUSize_neg",
"HAdd.hAdd",
"instSubUInt64",
"congr",
"True",
"instNegUSize",
"eq_self",
"of_eq_true",
"instSubUSize",
"instAddUSize"... | true |
IntermediateField.adjoin_algebraic_toSubalgebra | Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra | [
"IsAlgebraic",
"Algebra",
"Algebra.adjoin",
"Membership.mem",
"Field.toDivisionRing",
"DivisionRing.toRing",
"Field.toSemifield",
"Field.toCommRing",
"Semifield.toDivisionSemiring",
"IntermediateField.adjoin",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemiring",
"Subalgebra",
"Interm... | true |
_private.Mathlib.Analysis.Convex.Side.0.Affine.Simplex.sSameSide_affineSpan_faceOpposite_of_sign_eq._simp_1_1 | Mathlib.Analysis.Convex.Side | [
"Finset.mul_sum",
"HMul.hMul",
"Finset",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"NonUnitalNonAssocSemiring",
"Eq.symm",
"Eq",
"Finset.sum",
"instHMul"
] | false |
RootPairing.coroot_reflectionPerm | Mathlib.LinearAlgebra.RootSystem.Defs | [
"RootPairing.coreflection",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid... | true |
CategoryTheory.PreZeroHypercover.sumInr | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.PreZeroHypercover.sumInr._proof_2",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.PreZeroHypercover.sum",
"CategoryTheory.PreZeroHypercover",
"Sum.inr",
"CategoryTheory.PreZeroHypercover.Hom.mk",
"Cate... | true |
PosMulStrictMono.toPosMulMono | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"Iff.mpr",
"Preorder.toLT",
"HMul.hMul",
"posMulMono_iff_covariant_pos",
"MulZeroClass.toMul",
"PartialOrder.toPreorder",
"Preorder.toLE",
"MulZeroClass",
"PartialOrder",
"Subtype",
"covariantClass_le_of_lt",
"LE.le",
"PosMulStrictMono.to_covariantClass_pos_mul_le",
"PosMulMono",
"LT.lt"... | true |
Lean.Meta.getPropHyps | Lean.Meta.Tactic.Util | [
"Pure.pure",
"Lean.Meta.isProp",
"Lean.Meta.instMonadLCtxMetaM",
"Array.push",
"Lean.Meta.State",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.FVarId",
"instDecidableEqBool",
"Lean.LocalContext.instForInLocalDeclOfMonad",
"ForIn.forIn",
"Applicative.toPure",
"ForInStep",
"List.toArray",
"Arr... | true |
Matrix.module | Mathlib.LinearAlgebra.Matrix.Defs | [
"Matrix",
"Module.mk",
"Matrix.module._proof_1",
"Matrix.module._proof_2",
"Matrix.addCommMonoid",
"AddCommMonoid",
"Semiring.toMonoid",
"Semiring",
"Module.toDistribMulAction",
"AddCommMonoid.toAddMonoid",
"Module",
"Matrix.distribMulAction"
] | true |
CategoryTheory.Limits.Pi.whiskerEquiv | Mathlib.CategoryTheory.Limits.Shapes.Products | [
"CategoryTheory.Limits.HasProduct",
"Equiv.instEquivLike",
"CategoryTheory.Limits.Pi.whiskerEquiv._proof_1",
"CategoryTheory.eqToHom",
"CategoryTheory.Limits.Pi.map'",
"CategoryTheory.Limits.Pi.whiskerEquiv._proof_5",
"Equiv",
"CategoryTheory.Iso",
"CategoryTheory.Limits.Pi.whiskerEquiv._proof_3",
... | true |
ContinuousGeneratedByCat.toGeneratedByTopCat._proof_1 | Mathlib.Topology.Convenient.Category | [
"Eq.mpr",
"Topology.IsGeneratedBy",
"ContinuousGeneratedByCat.instCategory",
"Topology.IsGeneratedBy.instWithGeneratedByTopology",
"congrArg",
"TopCat.instCategory",
"inferInstance",
"id",
"ContinuousGeneratedByCat.str",
"TopologicalSpace",
"TopCat.str",
"TopCat.carrier",
"ContinuousGenerate... | false |
FP.Float.Zero.valid | Mathlib.Data.FP.Basic | [
"add_sub_assoc",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"FP.emin",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"FP.prec",
"congrArg",
"Int.instLinearOrder",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Int.instMax",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAdd... | true |
CliffordAlgebra.equivExterior._proof_2 | Mathlib.LinearAlgebra.CliffordAlgebra.Contraction | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CommRing.toCommSemiring",
"CommMonoid.toMonoid",
"Ring.toAddCommGroup",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMonoid.toAddMon... | false |
Nat.shiftRight_succ_inside._f | Init.Data.Nat.Lemmas | [
"Eq.mpr",
"instHDiv",
"congrArg",
"id",
"HDiv.hDiv",
"Nat.shiftRight_succ",
"instOfNatNat",
"instHShiftRightOfShiftRight",
"Nat.below",
"instHAdd",
"Nat.instShiftRight",
"HAdd.hAdd",
"HShiftRight.hShiftRight",
"Nat",
"Nat.instDiv",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Nat.suc... | false |
Lean.Parser.nameLit | Lean.Parser.Extra | [
"Lean.Parser.nameLitNoAntiquot",
"Lean.Parser.Parser",
"Lean.nameLitKind",
"Lean.Parser.withAntiquot",
"Bool.true",
"Lean.Parser.mkAntiquot",
"Bool.false"
] | true |
WeierstrassCurve.Affine.Point.instInvolutiveNeg | Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | [
"CommRing",
"InvolutiveNeg",
"InvolutiveNeg.mk",
"WeierstrassCurve.Affine",
"WeierstrassCurve.Affine.Point",
"WeierstrassCurve.Affine.Point.instInvolutiveNeg._proof_1",
"WeierstrassCurve.Affine.Point.instNeg"
] | true |
BoundedContinuousFunction.instRing | Mathlib.Topology.ContinuousMap.Bounded.Normed | [
"Ring.mk",
"BoundedContinuousFunction.instRing._proof_7",
"ContinuousMap.instZSMul",
"BoundedContinuousFunction.instRing._proof_9",
"instHSMul",
"AddGroupWithOne.toAddGroup",
"ContinuousMap",
"BoundedContinuousFunction.instRing._proof_5",
"PseudoMetricSpace.toUniformSpace",
"SeminormedRing.toRing"... | true |
CategoryTheory.InjectiveResolution.ofCocomplex._proof_2 | Mathlib.CategoryTheory.Abelian.Injective.Resolution | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian",
"CategoryTheory.Limits.HasCokernels.has_colimit",
"CategoryTheory.Limits.HasCokernel",
"CategoryTheory.Abelian.has_cokernels",
"CategoryTheory.Preadditive.preadditiveHasZeroMorphis... | false |
Std.Sat.CNF.Mem | Std.Sat.CNF.Basic | [
"Std.Sat.CNF",
"Array.instMembership",
"Membership.mem",
"Array",
"Std.Sat.CNF.Clause",
"Std.Sat.CNF.clauses"
] | true |
Filter.Tendsto.compCM | Mathlib.Topology.CompactOpen | [
"ContinuousMap",
"instTopologicalSpaceProd",
"ContinuousMap.comp",
"nhds",
"Prod.mk",
"Prod.fst",
"LocallyCompactPair",
"Continuous.tendsto",
"TopologicalSpace",
"Filter.Tendsto",
"ContinuousMap.continuous_comp'",
"Filter.Tendsto.comp",
"Prod",
"ContinuousMap.compactOpen",
"Prod.snd",
... | true |
CategoryTheory.MorphismProperty.inf_iff._simp_1 | Mathlib.CategoryTheory.MorphismProperty.Basic | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CompleteLattice.toLattice",
"CategoryTheory.MorphismProperty.inf_iff",
"SemilatticeInf.toMin",
"And",
"propext",
"CompleteBooleanAlgebra.toCompl... | false |
zpow_lt_zpow_right | Mathlib.Algebra.Order.Group.Basic | [
"Preorder.toLT",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"IsOrderedMonoid",
"PartialOrder.toPreorder",
"zpow_right_strictMono",
"DivInvMonoid.toZPow",
"DivisionMonoid.toDivInvOneMonoid",
"PartialOrder",
"Int",
"CommGroup",
"CommGroup.toDiv... | true |
TypeCat.Hom.casesOn | Mathlib.CategoryTheory.Types.Basic | [
"TypeCat.Hom",
"_private.Mathlib.CategoryTheory.Types.Basic.0.TypeCat.Hom.mk",
"TypeCat.Fun",
"TypeCat.Hom.rec"
] | false |
MeasureTheory.StronglyMeasurable.approxBounded | Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic | [
"Norm.norm",
"MeasureTheory.StronglyMeasurable.approx",
"Real",
"instHSMul",
"instHDiv",
"Real.instDivInvMonoid",
"SMul",
"MeasureTheory.SimpleFunc",
"Norm",
"HDiv.hDiv",
"Real.instMin",
"Real.instOne",
"MeasurableSpace",
"TopologicalSpace",
"Nat",
"DivInvMonoid.toDiv",
"One.toOfNat1... | true |
_private.Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors.0.MvPowerSeries.instNoZeroDivisors._simp_2 | Mathlib.RingTheory.MvPowerSeries.NoZeroDivisors | [
"WithTop.add_eq_top",
"instHAdd",
"WithTop.top",
"HAdd.hAdd",
"propext",
"Or",
"Top.top",
"Eq",
"WithTop.add",
"Add",
"WithTop"
] | false |
AlgEquivClass.casesOn | Mathlib.Algebra.Algebra.Equiv | [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"RingEquivClass",
"Distrib.toAdd",
"instDistribOfSemiring",
"CommSemiring",
"AlgEquivClass.mk",
"RingHom.instFunLike",
"AlgEquivClass.rec",
"EquivLike",
"Distrib.toMul",
"Semiring",
"Semiring.toNonAssocSemiring",
"E... | false |
Lean.Parser.numLitNoAntiquot | Lean.Parser.Basic | [
"Lean.Parser.Parser",
"Lean.Parser.mkAtomicInfo",
"Lean.Parser.Parser.mk",
"Lean.Parser.numLitFn"
] | true |
_private.Mathlib.FieldTheory.Separable.0.Associated.separable._proof_1_1 | Mathlib.FieldTheory.Separable | [
"False",
"Dvd.dvd",
"eq_false",
"CommSemiring.toNonUnitalCommSemiring",
"CommSemiring.toSemiring",
"Classical.byContradiction",
"semigroupDvd",
"Lean.Grind.eq_false_of_imp_eq_true",
"SemigroupWithZero.toSemigroup",
"Eq.mp",
"id",
"NonUnitalSemiring.toSemigroupWithZero",
"Polynomial",
"NonU... | false |
Subalgebra.unop_op | Mathlib.Algebra.Algebra.Subalgebra.MulOpposite | [
"Subalgebra.unop",
"Algebra",
"Subalgebra.op",
"CommSemiring",
"Semiring",
"Subalgebra",
"Eq",
"rfl"
] | true |
Valuation.RankOne.restrict_RankOne._proof_3 | Mathlib.RingTheory.Valuation.RankOne | [
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"ValuationClass.toMonoidWithZeroHomClass",
"MonoidWithZeroHomClass.toMonoidWithZeroHom",
"MonoidWithZeroHom.ValueGroup₀.instLinearOrderedCommGroupWithZero",
"MonoidWithZeroHom.funLike",
"MonoidWithZeroH... | false |
QuotSMulTop.equivQuotTensor._proof_3 | Mathlib.RingTheory.QuotSMulTop | [
"Submodule.pointwiseDistribMulAction",
"Submodule",
"CommRing",
"instHSMul",
"Submodule.ideal_span_singleton_smul",
"Semiring.toModule",
"QuotSMulTop.equivQuotTensor._proof_1",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass"... | false |
Array.foldrM.fold._unsafe_rec | Init.Data.Array.Basic | [
"Pure.pure",
"Monad.toApplicative",
"Nat.lt_succ_self",
"instDecidableEqBool",
"instOfNatNat",
"LE.le",
"instLENat",
"Applicative.toPure",
"Nat.le_of_lt",
"instBEqOfDecidableEq",
"Array",
"Array.foldrM.fold._unsafe_rec",
"GetElem.getElem",
"Bool.true",
"instHAdd",
"BEq.beq",
"Array.i... | false |
IsPredArchimedean.mk | Mathlib.Order.SuccPred.Archimedean | [
"Preorder.toLE",
"Exists",
"LE.le",
"Nat.iterate",
"IsPredArchimedean",
"Nat",
"Order.pred",
"IsPredArchimedean.mk",
"PredOrder",
"Eq",
"Preorder"
] | true |
TopCat.Presheaf.EtaleSpace.base | Mathlib.Topology.Sheaves.EtaleSpace | [
"TopCat.Presheaf",
"CategoryTheory.ConcreteCategory",
"TopCat.carrier",
"CategoryTheory.Limits.HasColimits",
"TopCat",
"TopCat.Presheaf.EtaleSpace",
"FunLike",
"CategoryTheory.Category"
] | true |
Lean.Expr.ProdTree._sizeOf_1 | Mathlib.Tactic.ProdAssoc | [
"Lean.Expr.ProdTree.rec",
"Lean.Level._sizeOf_inst",
"Lean.Expr",
"Lean.Expr.ProdTree",
"instOfNatNat",
"Lean.Level",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"OfNat.ofNat",
"Lean.Expr._sizeOf_inst"
] | false |
Polynomial.toFinsupp_C_mul_X | Mathlib.Algebra.Polynomial.Basic | [
"Eq.mpr",
"Polynomial.C",
"Polynomial.C_mul_X_eq_monomial",
"Semiring.toModule",
"Polynomial.toFinsupp",
"HMul.hMul",
"Polynomial.toFinsupp_monomial",
"congrArg",
"LinearMap.instFunLike",
"RingHom",
"Polynomial.monomial",
"id",
"instOfNatNat",
"LinearMap",
"Polynomial",
"NonUnitalNonAs... | true |
Set.Finite.toFinset_nontrivial._simp_1 | Mathlib.Data.Set.Finite.Basic | [
"Set.Finite",
"Set.Finite.toFinset_nontrivial",
"Set.Finite.toFinset",
"Finset.Nontrivial",
"propext",
"Set.Nontrivial",
"Eq",
"Set"
] | false |
Prod.instMonoidWithZero | Mathlib.Algebra.GroupWithZero.Prod | [
"Prod.instMonoidWithZero._proof_2",
"Prod.instMonoid",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"Prod.instZero",
"MulZeroOneClass.toMulZeroClass",
"Prod",
"Prod.instMonoidWithZero._proof_1",
"MonoidWithZero.toMonoid",
"MulZeroClass.toZero",
"MonoidWithZero.mk"
] | true |
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