name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Omega.LinearCombo.coordinate_eval_6 | Init.Omega.LinearCombo | [
"Lean.Omega.Coeffs.get",
"congrArg",
"Lean.Omega.LinearCombo.eval",
"instOfNatNat",
"Int",
"List.cons",
"List",
"instHAdd",
"Lean.Omega.IntList.get",
"HAdd.hAdd",
"Lean.Omega.IntList.get_cons_succ",
"Lean.Omega.Coeffs.ofList",
"Nat",
"True",
"eq_self",
"Lean.Omega.LinearCombo.coordinat... | true |
AddAction.orbitRel_le_fst | Mathlib.GroupTheory.GroupAction.Basic | [
"Setoid.comap",
"Iff.mpr",
"AddAction.fst_mem_orbit_of_mem_orbit",
"Setoid",
"LE.le",
"Prod.fst",
"AddAction",
"Setoid.le_def",
"Setoid.instLE_mathlib",
"AddGroup",
"AddGroup.toSubNegMonoid",
"AddAction.orbitRel",
"SubNegMonoid.toAddMonoid",
"Prod",
"Prod.addAction",
"Setoid.r"
] | true |
Lean.Meta.Diagnostics.synthPendingFailures | Lean.Meta.Basic | [
"Lean.MessageData",
"Lean.Expr.instBEq",
"Lean.PHashMap",
"Lean.Expr",
"Lean.Expr.instHashable",
"Lean.Meta.Diagnostics"
] | true |
CategoryTheory.Dial.associatorImpl._proof_2 | Mathlib.CategoryTheory.Dialectica.Monoidal | [
"CategoryTheory.Limits.limit.π",
"CategoryTheory.Limits.prod.associator._proof_3",
"_private.Mathlib.CategoryTheory.Dialectica.Monoidal.0.CategoryTheory.Dial.associatorImpl._simp_1",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"cong... | false |
Lean.Grind.CommRing.powerRevlex_k.eq_1 | Init.Grind.Ring.CommSolver | [
"Nat.blt",
"Ordering.gt",
"Ordering",
"Ordering.eq",
"Ordering.lt",
"Nat",
"Bool.rec",
"Bool",
"Eq.refl",
"Lean.Grind.CommRing.powerRevlex_k",
"Eq"
] | true |
CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι | Mathlib.CategoryTheory.Abelian.Injective.Resolution | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.single₀",
"congrArg",
"CategoryTheory.InjectiveResolution.ι",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCance... | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.getMsbD_rotateLeftAux_of_ge._proof_1_3 | Init.Data.BitVec.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"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.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"GE.ge",
"id",
... | false |
Nat.lcm_dvd_iff | Init.Data.Nat.Lcm | [
"Nat.lcm",
"Dvd.dvd",
"_private.Init.Data.Nat.Lcm.0.Nat.lcm_dvd_iff.match_1_1",
"Nat.dvd_trans",
"Nat.dvd_lcm_left",
"And",
"Iff",
"Nat.instDvd",
"Nat",
"And.intro",
"Iff.intro",
"Nat.lcm_dvd",
"Nat.dvd_lcm_right"
] | true |
Topology.WithUpperSet.instNonempty | Mathlib.Topology.Order.UpperLowerSetTopology | [
"Topology.WithUpperSet",
"Nonempty"
] | true |
Profinite.NobelingProof.Proj.eq_1 | Mathlib.Topology.Category.Profinite.Nobeling.Basic | [
"Decidable",
"Profinite.NobelingProof.Proj",
"Bool",
"Eq.refl",
"Bool.false",
"Eq",
"ite"
] | true |
_private.Mathlib.RingTheory.AlgebraicIndependent.Basic.0.algebraicIndependent_finset_map_embedding_subtype._simp_1_1 | Mathlib.RingTheory.AlgebraicIndependent.Basic | [
"Subtype.coe_prop",
"Membership.mem",
"Subtype",
"True",
"eq_true",
"Subtype.val",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.Logic.Equiv.Set.0.dite_comp_equiv_update._proof_1_3 | Mathlib.Logic.Equiv.Set | [
"_private.Mathlib.Logic.Equiv.Set.0.dite_comp_equiv_update._proof_1_2",
"False",
"dite_congr",
"Function.update",
"eq_false",
"congrArg",
"HEq.refl",
"Classical.byContradiction",
"Decidable",
"Eq.rec",
"Eq.mp",
"id",
"Subtype",
"Lean.Grind.em",
"Function.update.eq_1",
"dite",
"Or.cas... | false |
Std.DHashMap.Equiv.congr_right | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.Equiv",
"Std.DHashMap.Equiv.symm",
"Iff",
"Iff.intro",
"Hashable",
"Std.DHashMap.Equiv.trans",
"BEq",
"Std.DHashMap"
] | true |
AddGroup.nilpotencyClass.eq_1 | Mathlib.GroupTheory.Nilpotent | [
"AddGroup.IsNilpotent",
"Classical.propDecidable",
"AddGroup.nilpotencyClass",
"instOfNatNat",
"dite",
"AddSubgroup",
"AddGroup.IsNilpotent.nilpotent",
"AddGroup",
"Nat",
"AddSubgroup.upperCentralSeries",
"Nat.find",
"Eq.refl",
"Top.top",
"OfNat.ofNat",
"AddSubgroup.instTop",
"Eq",
"... | true |
Std.IterM.toArray_mapM_eq_toArray_mapWithPostcondition | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"LawfulMonadLiftT",
"Std.IterM.toArray",
"Monad.toApplicative",
"Std.Iterators.Types.Map.instIterator",
"MonadLiftT.monadLift",
"WeaklyLawfulMonadAttach",
"Std.Iterators.Finite",
"LawfulMonad",
"Std.Iterators.PostconditionT.attachLift",
"MonadLiftT",
"Std.Iterator",
"Array",
"Std.Iterators.T... | true |
Std.DTreeMap.Internal.Impl.getKey?_filter! | Std.Data.DTreeMap.Internal.Lemmas | [
"Option.pfilter",
"Ord",
"congrArg",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.filter",
"Option.some",
"Eq.mp",
"Std.DTreeMap.Internal.Impl.get",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.mem_of_getKey?_eq_some",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Std.DTreeMap.Inte... | true |
_private.Mathlib.MeasureTheory.VectorMeasure.BoundedVariation.0.BoundedVariationOn.vectorMeasure_Ioi._proof_1_3 | Mathlib.MeasureTheory.VectorMeasure.BoundedVariation | [
"Lean.Grind.Linarith.Expr",
"Lean.RArray.leaf",
"False",
"OrderTopology",
"Set.Ioi",
"Preorder.toLT",
"CompleteSpace",
"Lean.Grind.nestedProof",
"Lean.Grind.Linarith.diseq_unsat",
"NormedAddCommGroup.toMetricSpace",
"AddCommGroup.toAddCommMonoid",
"SecondCountableTopology",
"LinearOrder",
... | false |
Ideal.trivialFiltration._proof_1 | Mathlib.RingTheory.Filtration | [
"Submodule",
"CommRing",
"le_rfl",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup",
"Submodule.instPartialOrder",
"LE.le",
"CommRing.toCommSemiring",
"Nat",
"Module"
] | false |
Module.Relations.tensor_relation | Mathlib.Algebra.Module.Presentation.Tensor | [
"CommRing",
"Sum",
"Module.Relations.relation",
"Module.Relations.R",
"Module.Relations.G",
"Finsupp.embDomain",
"Eq.refl",
"Module.Relations.tensor.match_1",
"Function.Embedding.sectR",
"CommRing.toRing",
"Module.Relations",
"Prod",
"Ring.toSemiring",
"Eq",
"Function.Embedding.sectL",
... | true |
Lean.Compiler.LCNF.ImpureType.erased | Lean.Compiler.LCNF.Types | [
"Lean.Expr.const",
"Lean.Expr",
"Lean.Level",
"Lean.Name.mkStr1",
"List.nil"
] | true |
Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.ConfirmRupHintFoldEntailsMotive | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound | [
"Std.Tactic.BVDecide.LRAT.Internal.Limplies",
"Prod.fst",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula",
"Array",
"Bool.true",
"And",
"Nat",
"Std.Tactic.BVDecide.LRAT.Internal.Assignment.instEntailsPosFinArray",
"Std.Sat.CNF.Clause",
"Bool",
"Std.Tactic.BVDecide.LRAT.Internal.Assignment",
... | true |
Metric.unitClosedBall.instMonoid | Mathlib.Analysis.Normed.Field.UnitBall | [
"Monoid",
"NormOneClass",
"SeminormedRing.toNorm",
"Real",
"One.mk",
"AddGroupWithOne.toAddMonoidWithOne",
"SeminormedRing.toRing",
"Set.Elem",
"Metric.unitClosedBall.instMonoid._proof_3",
"Metric.unitClosedBall.instSemigroup",
"Monoid.mk",
"Metric.unitClosedBall.instMonoid._aux_5",
"Real.in... | true |
nnnorm_cfcₙ_le_iff._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.Omega.Int.ofNat_pos | Init.Omega.Int | [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"Int.ofNat_lt",
"id",
"instOfNatNat",
"Int",
"Nat.cast",
"Int.ofNat_zero",
"Int.instLTInt",
"Iff",
"instOfNat",
"Nat",
"LT.lt",
"propext",
"instNatCastInt",
"instLTNat",
"OfNat.ofNat",
"Eq.symm",
"Eq"
] | true |
SupBotHom.copy_eq | Mathlib.Order.Hom.BoundedLattice | [
"Max",
"Bot",
"SupBotHom",
"DFunLike.ext'",
"Eq",
"DFunLike.coe",
"SupBotHom.instFunLike",
"SupBotHom.copy"
] | true |
Complex.arg_nonneg_iff._simp_1 | Mathlib.Analysis.SpecialFunctions.Complex.Arg | [
"Real.instLE",
"Real",
"Real.instZero",
"Complex.im",
"Complex.arg",
"LE.le",
"propext",
"Zero.toOfNat0",
"Complex.arg_nonneg_iff",
"Complex",
"OfNat.ofNat",
"Eq"
] | false |
AddMonCat.FilteredColimits.colimitDesc._proof_2 | Mathlib.Algebra.Category.MonCat.FilteredColimits | [
"Eq.mpr",
"AddMonCat.FilteredColimits.M.mk_surjective",
"CategoryTheory.Functor",
"CategoryTheory.IsFiltered.rightToMax",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.mapCocone",
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"AddMonoidHom.instAddMonoidHomClass",
"Equiv.instEquivLik... | false |
Filter.map_atBot_eq_of_gc_preorder | Mathlib.Order.Filter.AtTopBot.Basic | [
"IsCodirectedOrder",
"Filter.map",
"OrderDual.isDirected_le",
"Monotone",
"Preorder.toLE",
"Exists",
"LE.le",
"And",
"Iff",
"Monotone.dual",
"Filter.atBot",
"Filter.map_atTop_eq_of_gc_preorder",
"OrderDual",
"OrderDual.instPreorder",
"Eq",
"Filter",
"Preorder"
] | true |
CategoryTheory.Limits.mapPair.match_5 | Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.Discrete.mk",
"CategoryTheory.discreteCategory",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Discrete.casesOn",
"CategoryTheory.Discrete"
] | false |
LieEquiv.casesOn | Mathlib.Algebra.Lie.Basic | [
"LieHom",
"LieAlgebra.toModule",
"Function.LeftInverse",
"CommRing",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieEquiv",
"LinearMap.toAddHom",
"LieRing",
"CommRing.toCommSemiring",
"LieEquiv.mk",
"Function.RightInverse",
"LieAlgebra",
"AddComm... | false |
Lean.Elab.Tactic.GuardMsgs.FilterSpec | Lean.Elab.GuardMsgs | [
"Lean.Elab.Tactic.GuardMsgs.FilterSpec.pass",
"Lean.Elab.Tactic.GuardMsgs.FilterSpec.check",
"Lean.Elab.Tactic.GuardMsgs.FilterSpec.drop"
] | true |
Std.Ric.eq_succMany?_of_toArray_eq_append_append._proof_2 | Init.Data.Range.Polymorphic.Lemmas | [
"Array.instAppend",
"Array.size_append",
"Nat.zero_lt_succ._simp_1",
"Std.PRange.UpwardEnumerable",
"Array.push",
"congrArg",
"Nat.lt_add_right_iff_pos._simp_1",
"Std.Ric.toArray",
"instOfNatNat",
"LE",
"List.toArray",
"List.cons",
"Std.Ric",
"Array",
"instHAppendOfAppend",
"instHAdd",... | false |
Lean.Lsp.DiagnosticWith.source? | Lean.Data.Lsp.Diagnostics | [
"Lean.Lsp.DiagnosticWith",
"String",
"Option"
] | true |
AddGroupNormClass.toNormedAddCommGroup_norm_eq | Mathlib.Analysis.Normed.Order.Hom.Basic | [
"Norm.norm",
"Real.partialOrder",
"Real",
"AddGroupNormClass.toNormedAddCommGroup",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"NormedAddCommGroup.toNorm",
"Real.instAddCommMonoid",
"AddGroupNormClass",
"Eq",
"DFunLike.coe",
"rfl",
"FunLike"
] | true |
_private.Mathlib.Analysis.CStarAlgebra.Spectrum.0.NonUnitalStarAlgHom.nnnorm_apply_le._simp_1_2 | Mathlib.Analysis.CStarAlgebra.Spectrum | [
"outParam",
"StarHomClass",
"StarHomClass.map_star",
"Star",
"Eq.symm",
"Eq",
"DFunLike.coe",
"FunLike",
"Star.star"
] | false |
Complex.IsExpCmpFilter.mk | Mathlib.Analysis.SpecialFunctions.CompareExp | [
"Real",
"Complex.IsExpCmpFilter",
"Complex.im",
"Asymptotics.IsBigO",
"Real.exp",
"Monoid.toPow",
"Complex.re",
"Filter.atTop",
"Real.instMonoid",
"HPow.hPow",
"Filter.Tendsto",
"Complex.IsExpCmpFilter.mk",
"Nat",
"instHPow",
"Complex",
"Filter",
"Real.instPreorder",
"Real.norm"
] | true |
definition._@.Mathlib.Topology.Algebra.InfiniteSum.Defs.1210274395._hygCtx._hyg.8 | Mathlib.Topology.Algebra.InfiniteSum.Defs | [
"MulOne.toOne",
"Monoid.toMulOneClass",
"SummationFilter",
"Set.mulIndicator",
"Classical.propDecidable",
"Set.Finite",
"HasProd",
"Multipliable",
"Set.instInter",
"SummationFilter.HasSupport",
"dite",
"Inter.inter",
"TopologicalSpace",
"MulOneClass.toMulOne",
"finprod",
"And",
"Comm... | false |
SeparationQuotient.uniformContinuous_map | Mathlib.Topology.UniformSpace.Separation | [
"UniformContinuous",
"UniformSpace",
"SeparationQuotient.map._proof_1",
"SeparationQuotient.instUniformSpace",
"SeparationQuotient.map",
"SeparationQuotient.uniformContinuous_lift'",
"Function.comp",
"SeparationQuotient",
"SeparationQuotient.mk",
"UniformSpace.toTopologicalSpace"
] | true |
ContinuousLinearMap.prod_ext | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd | [
"ContinuousLinearMap.comp",
"Iff.mpr",
"instTopologicalSpaceProd",
"ContinuousLinearMap.prod_ext_iff",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"ContinuousLinearMap.inr",
"And",
"And.intro",
"Semiring",
"Module",
"ContinuousLinearMap.inl",
"Prod",
"Prod.instModule",
... | true |
Delone.DeloneSet.mapBilipschitz_trans | Mathlib.Analysis.AperiodicOrder.Delone.Basic | [
"Set.ext",
"Eq.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"NNReal.instCommSemiring",
"Semigroup.toMul",
"Real",
"Preorder.toLT",
"LipschitzWith",
"instHDiv",
"Equiv.instEquivLike",
"HMul.hMul",
"Delone.DeloneSet.mapBilipschitz",
"DivisionCommMonoid.toDivisionMo... | true |
ContinuousOn.exists_isMaxOn' | Mathlib.Topology.Order.Compact | [
"ClosedIciTopology",
"LinearOrder",
"IsMaxOn",
"Filter.Eventually",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"Filter.instInf",
"Filter.cocompact",
"IsClosed",
"TopologicalSpace",
"And",... | true |
CategoryTheory.ReflQuiv.adj | Mathlib.CategoryTheory.Category.ReflQuiv | [
"CategoryTheory.ReflQuiv.forget",
"CategoryTheory.ReflQuiv",
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.ReflQuiv.adj.homEquiv",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Equiv.trans",
"CategoryTheory.Cat.str",
"CategoryTheory.Cat.instQuiver",
"Categor... | true |
WithTop.ofDual | Mathlib.Order.WithBot | [
"WithBot",
"Equiv",
"OrderDual",
"Equiv.refl",
"WithTop"
] | true |
_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.c | Mathlib.NumberTheory.NumberField.House | [
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Complex.commRing",
"Matrix",
"Rat",
"Complex.instNormedField",
"RingHom",
"Rat.commSemiring",
"Field.toDivisionRing",
"Algebra.toModule... | true |
_private.Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop.0.Std.IterM.DefaultConsumers.forIn'_eq_match_step.match_1.eq_1 | Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop | [
"ForInStep.done",
"Subtype",
"ForInStep",
"Subtype.mk",
"Std.IterM.DefaultConsumers.forIn'_eq_match_step.match_1",
"Eq.refl",
"Eq",
"ForInStep.yield"
] | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.msb_one._simp_1_1 | Init.Data.BitVec.Lemmas | [
"Decidable",
"Bool.decide_and",
"Bool.and",
"And",
"Bool",
"Eq.symm",
"Decidable.decide",
"Eq"
] | false |
ISize.ofInt_int64ToInt | Init.Data.SInt.Lemmas | [
"Int64.toInt",
"ISize.ofInt",
"Int64",
"ISize",
"Eq",
"Int64.toISize",
"rfl"
] | true |
Lean.StructureDescr.noConfusion | Lean.Structure | [
"Lean.StructureDescr.noConfusionType",
"Lean.StructureFieldInfo",
"Array",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Lean.StructureDescr.casesOn",
"Lean.StructureDescr",
"Eq"
] | false |
Ordset.pos_size_of_mem | Mathlib.Data.Ordmap.Ordset | [
"WithBot",
"Ordnode",
"Ordset",
"congrArg",
"Ordnode.Valid'.sz",
"Ordnode.pos_size_of_mem",
"Preorder.toLE",
"Membership.mem",
"Eq.mp",
"Ordnode.mem",
"instOfNatNat",
"Bot.bot",
"Ordnode.mem.decidable",
"Ordset.instMembership",
"Ordnode.Valid",
"Bool.true",
"DecidableLE",
"WithTop.... | true |
Ultrafilter.comap_pure | Mathlib.Order.Filter.Ultrafilter.Defs | [
"Pure.pure",
"Eq.mpr",
"Ultrafilter.coe_pure",
"Set.image_singleton",
"congrArg",
"Membership.mem",
"Set.instSingletonSet",
"id",
"Filter.comap_pure",
"Filter.instPure",
"Set.preimage",
"Filter.principal_singleton",
"Ultrafilter.instPure",
"Ultrafilter.comap",
"Filter.principal",
"Set.... | true |
Group.IsNilpotent.nilpotent | Mathlib.GroupTheory.Nilpotent | [
"Group.IsNilpotent.nilpotent'",
"Subgroup.upperCentralSeries",
"Group",
"Exists",
"Subgroup",
"Nat",
"Subgroup.instTop",
"Group.IsNilpotent",
"Top.top",
"Eq"
] | true |
CategoryTheory.Functor.PreservesPointwiseLeftKanExtensionAt.mk | Mathlib.CategoryTheory.Functor.KanExtension.Preserves | [
"CategoryTheory.Functor.PreservesPointwiseLeftKanExtensionAt",
"CategoryTheory.Functor",
"CategoryTheory.Functor.LeftExtension",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.PreservesPointwiseLeftKanExtensionAt.mk",
"CategoryTheory.Functor.LeftExtension.postc... | true |
UniformOnFun.isUniformEmbedding_toFun_finite | Mathlib.Topology.UniformSpace.UniformConvergenceTopology | [
"Filter.instMembership",
"Iff.mpr",
"Set.Finite.union",
"Pi.uniformSpace",
"UniformSpace",
"Eq.mpr",
"Set.finite_empty",
"Lattice.toSemilatticeSup",
"iInf",
"Equiv.instEquivLike",
"UniformOnFun.gen",
"_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformOnFun.isUniformEmb... | true |
CategoryTheory.Oplax.LaxTrans.OplaxFunctor.bicategory._proof_16 | Mathlib.CategoryTheory.Bicategory.FunctorBicategory.Oplax | [
"CategoryTheory.Oplax.LaxTrans.instCategoryStructOplaxFunctor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Oplax.LaxTrans.whiskerRight",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Oplax.LaxTrans.Modification.app",
"inferInstance",
"Categor... | false |
Cardinal.instLE | Mathlib.SetTheory.Cardinal.Order | [
"Cardinal",
"LE",
"Function.Embedding",
"Cardinal.isEquivalent",
"Cardinal.instLE._proof_1",
"LE.mk",
"Nonempty",
"Quotient.liftOn₂"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.size_insertManyIfNewUnit_list_le._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
instCategoryCompactum._proof_8 | Mathlib.Topology.Category.Compactum | [
"Quiver.mk",
"CategoryTheory.CategoryStruct.mk",
"CategoryTheory.Category.comp_id._autoParam",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"instCategoryCompactum._aux_1",
"CategoryTheory.ofTypeMonad",
"CategoryTheory.CategoryStruct.id",
"autoParam",
"Ultrafilter.monad",
"instCategory... | false |
Quaternion.coeComplex_mul._simp_1 | Mathlib.Analysis.Quaternion | [
"Real",
"Quaternion.coeComplex_mul",
"Quaternion.coeComplex",
"HMul.hMul",
"Real.instZero",
"Complex.instMul",
"DivisionRing.toDivisionSemiring",
"Quaternion.instDivisionRing",
"instDistribOfSemiring",
"Real.instOne",
"Distrib.toMul",
"Real.instNeg",
"DivisionSemiring.toSemiring",
"Complex... | false |
ContinuousLinearMap.coe_prodMap' | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd | [
"ContinuousLinearMap.funLike",
"instTopologicalSpaceProd",
"ContinuousLinearMap.prodMap",
"Prod.map",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"Semiring",
"Module",
"Prod",
"Prod.instModule",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"rfl",
... | true |
Option.mem_toArray | Init.Data.Option.Array | [
"False",
"Option.ctorIdx",
"congrArg",
"False.elim",
"Option.toArray",
"Option.casesOn",
"noConfusion_of_Nat",
"Array.instMembership",
"Option.some.injEq",
"Option.some",
"Membership.mem",
"List.mem_toArray._simp_1",
"List.not_mem_nil._simp_1",
"_private.Init.Data.Option.Array.0.Option.mem... | true |
_private.Lean.Elab.SyntheticMVars.0.Lean.Elab.Term.TacticMVarKind.maybeWithoutRecovery | Lean.Elab.SyntheticMVars | [
"monadFunctorRefl",
"Lean.Elab.Tactic.Context",
"IO.RealWorld",
"StateRefT'.instMonadFunctor",
"instDecidableEqBool",
"ReaderT.instMonadFunctor",
"Lean.Elab.Term.TacticMVarKind",
"Bool.true",
"_private.Lean.Elab.SyntheticMVars.0.Lean.Elab.Term.TacticMVarKind.maybeWithoutRecovery.match_1",
"StateRe... | true |
DividedPowers.mk.congr_simp | Mathlib.RingTheory.DividedPowers.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.choose",
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toSemiring",
"Nat.instAddMonoid",
"Membership.mem",
"Eq.rec",
"Distrib.toAdd",
"AddMonoidWithOne.toNatCast",
"Ne",
"instMulNat",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne... | true |
_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.getThenInsertIfNew?.match_1.eq_2 | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"Option.some",
"Option.none",
"Unit",
"Std.DTreeMap.Internal.Impl.getThenInsertIfNew?.match_1",
"Eq.refl",
"Eq",
"Option"
] | true |
Lean.Firefox.SamplesTable.weight | Lean.Util.Profiler | [
"Lean.Firefox.SamplesTable",
"Array",
"Lean.Firefox.Milliseconds"
] | true |
instMonadFinallyEIO._aux_1 | Init.System.IO | [
"EST.Out.ok",
"EST",
"Option.some",
"IO.RealWorld",
"EIO",
"Prod.mk",
"instMonadFinallyEST.match_1",
"Option.none",
"Void",
"EST.Out.error",
"Prod",
"Option",
"EST.Out"
] | false |
Set.BijOn.iterate | Mathlib.Data.Set.Function | [
"Nat.brecOn",
"Nat.iterate",
"Nat",
"Set.BijOn",
"Set.BijOn.iterate._f",
"Set"
] | true |
AddSubgroupClass.normedAddCommGroup | Mathlib.Analysis.Normed.Group.Subgroup | [
"SetLike",
"Subtype.metricSpace",
"NormedAddCommGroup.toMetricSpace",
"AddSubgroupClass.normedAddCommGroup._proof_1",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddSubgroupClass.seminormedAddCommGroup",
"Subtype",
"SeminormedAddCommGroup.toNorm",
"AddGroup.toSubNegMonoid",
"SeminormedAddCommG... | true |
Vector.flatMap_empty._proof_1 | Init.Data.Vector.Lemmas | [
"HMul.hMul",
"congrArg",
"instMulNat",
"instOfNatNat",
"Nat.zero_mul",
"Nat",
"True",
"eq_self",
"of_eq_true",
"OfNat.ofNat",
"Eq",
"Eq.trans",
"instHMul"
] | false |
IsAlgClosed.instInfinite | Mathlib.FieldTheory.IsAlgClosed.Basic | [
"Fintype.card_le_of_injective",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Polynomial.C",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"Polynomial.instOne",
"Polynomial.C_1",
"NeZero.one",
"Polynomial.natDegree_X_pow_sub_C",
"AddMonoid.toAddSemigroup",
"Algebra.algebraMap",
"AddGroupW... | true |
_private.Mathlib.Data.Nat.Digits.Lemmas.0.List.fixedLengthDigits_one._proof_1_1 | Mathlib.Data.Nat.Digits.Lemmas | [
"Lean.Grind.of_eq_eq_true",
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"forall_not_of_not_exists",
"Lean.Grind.not_not",
"Lean.Grind.not_and",
"eq_false",
"Lean.Grind.iff_eq",
"Lean.Grind.CommRing.Expr.var",
"Finset.mem_im... | false |
Set.union_distrib_iInter_left | Mathlib.Data.Set.Lattice | [
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Set.iInter",
"Set.instUnion",
"CompleteDistribLattice.toCoframe",
"Union.union",
"Eq",
"sup_iInf_eq",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
"Set.instCompleteAtomicBooleanAlgebra",
"Set"
] | true |
Matrix.seminormedAddCommGroup._proof_3 | Mathlib.Analysis.Matrix.Normed | [
"NNDist.nndist",
"Real.instLE",
"Real",
"pseudoMetricSpacePi._proof_2",
"SeminormedAddCommGroup",
"Finset.univ",
"Dist.mk",
"PseudoEMetricSpace.toPseudoMetricSpaceOfDist",
"Matrix",
"PseudoMetricSpace.toNNDist",
"pseudoMetricSpacePi._proof_1",
"PseudoMetricSpace.dist_triangle",
"NNReal.instS... | false |
_private.Mathlib.Data.EReal.Basic.0.EReal.coe_ennreal_mul.match_1_1 | Mathlib.Data.EReal.Basic | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"NNReal",
"Option.none",
"Unit",
"ENNReal"
] | false |
_private.Lean.Meta.Tactic.Grind.Arith.Linear.Inv.0.Lean.Grind.Linarith.Poly.isSorted.go.match_1 | Lean.Meta.Tactic.Grind.Arith.Linear.Inv | [
"Option.casesOn",
"Option.some",
"Int",
"Lean.Grind.Linarith.Var",
"Lean.Grind.Linarith.Poly.casesOn",
"Option.none",
"Lean.Grind.Linarith.Poly.nil",
"Lean.Grind.Linarith.Poly.add",
"Lean.Grind.Linarith.Poly",
"Option"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.size_filter_le_size._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
Polynomial.map_list_prod | Mathlib.Algebra.Polynomial.Eval.Defs | [
"MonoidHom.instMonoidHomClass",
"Polynomial.instOne",
"MonoidHom.instFunLike",
"MonoidHom",
"List.map",
"RingHom",
"NonAssocSemiring.toMulZeroOneClass",
"Polynomial",
"MulZeroOneClass.toMulOneClass",
"List",
"MulOneClass.toMulOne",
"Polynomial.mapRingHom",
"Polynomial.semiring",
"Semiring.... | true |
_private.Mathlib.LinearAlgebra.Matrix.ToLinearEquiv.0.Matrix.exists_vecMul_eq_zero_iff._simp_1_1 | Mathlib.LinearAlgebra.Matrix.ToLinearEquiv | [
"Matrix.mulVec_transpose",
"Matrix",
"Matrix.vecMul",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalCommSemiring.toNonUnitalSemiring",
"Fintype",
"Matrix.transpose",
"NonUnitalCommSemiring",
"Eq.symm",
"Matrix.mulVec",
"Eq"
] | false |
Ordnode.span._unsafe_rec | Mathlib.Data.Ordmap.Ordnode | [
"Ordnode.partition.match_1",
"Ordnode",
"Ordnode.span._unsafe_rec",
"Prod.mk",
"Unit",
"Ordnode.size.match_1",
"DecidablePred",
"Nat",
"Ordnode.nil",
"Prod",
"Ordnode.link",
"ite"
] | false |
Metric.cthickening_eq_preimage_infEdist | Mathlib.Topology.MetricSpace.Thickening | [
"Real",
"ENNReal.ofReal",
"PartialOrder.toPreorder",
"Metric.cthickening_eq_preimage_infEDist",
"Metric.infEDist",
"PseudoEMetricSpace",
"Set.preimage",
"ENNReal",
"ENNReal.instPartialOrder",
"Set.Iic",
"Eq",
"Metric.cthickening",
"Set"
] | true |
NonAssocSemiring.one_mul | Mathlib.Algebra.Ring.Defs | [
"HMul.hMul",
"NonAssocSemiring.toOne",
"NonUnitalNonAssocSemiring.toMul",
"NonAssocSemiring",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"instHMul"
] | true |
Matroid.IsRestriction.exists_eq_restrict | Mathlib.Combinatorics.Matroid.Minor.Restrict | [
"Matroid.E",
"Exists",
"HasSubset.Subset",
"Matroid.IsRestriction",
"And",
"Matroid.restrict",
"Eq",
"Matroid",
"Set.instHasSubset",
"Set"
] | true |
Int.Linear.Poly.isZero | Lean.Meta.Tactic.Grind.Arith.Cutsat.Util | [
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Util.0.Int.Linear.Poly.isZero.match_1",
"Bool.true",
"Unit",
"Bool",
"Bool.false",
"Int.Linear.Poly"
] | true |
ULift.addCommGroup._proof_5 | Mathlib.Algebra.Group.ULift | [
"instHSMul",
"Equiv.instEquivLike",
"ULift",
"AddMonoid.toNSMul",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Equiv.ulift",
"Equiv",
"ULift.smul",
"AddGroup.toSubNegMonoid",
"Nat",
"HSMul.hSMul",
"SubNegMonoid.toAddMonoid",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | false |
RingCat.Hom.ext_iff | Mathlib.Algebra.Category.Ring.Basic | [
"RingCat.Hom.hom'",
"HEq.refl",
"RingCat.ring",
"RingHom",
"Eq.casesOn",
"RingCat",
"Iff",
"Iff.intro",
"RingCat.Hom.ext",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Eq",
"RingCat.carrier",
"RingCat.Hom"
] | true |
IsStronglyAtomic.casesOn | Mathlib.Order.Atoms | [
"Preorder.toLT",
"IsStronglyAtomic",
"IsStronglyAtomic.rec",
"CovBy",
"Preorder.toLE",
"Exists",
"LE.le",
"And",
"LT.lt",
"IsStronglyAtomic.mk",
"Preorder"
] | false |
Finset.forall_mem_cons | Mathlib.Data.Finset.Insert | [
"Finset.cons",
"Finset",
"Membership.mem",
"And",
"Iff",
"Finset.instSetLike",
"_private.Mathlib.Data.Finset.Insert.0.Finset.forall_mem_cons._proof_1_1",
"Not",
"SetLike.instMembership"
] | true |
Homotopy.dNext_cochainComplex | Mathlib.Algebra.Homology.Homotopy | [
"CategoryTheory.Limits.HasZeroMorphisms",
"Nat.instIsOrderedAddMonoid",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"instIsRightCancelAddOfAddRightReflectLE",
... | true |
InnerProductSpace.toDualMap._proof_4 | Mathlib.Analysis.InnerProductSpace.Dual | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"SeparatelyContinuousMul.to_continuousSMul",
"IsTopologicalDivisionRing.toIsTopologicalRing",
"PseudoMetricSpace.toUniformSpace",
"NormedDivisio... | false |
Qq.QuotedLevelDefEq | Qq.Typ | [
"Qq.QuotedLevelDefEq.unsafeIntro",
"Lean.Level"
] | true |
Int.cast_lt_zero | Mathlib.Algebra.Order.Ring.Cast | [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"Preorder.toLT",
"AddCommGroupWithOne",
"AddCommMonoidWithOne.toAddCommMonoid",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Int.cast_zero",
"Iff.rfl",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"AddLeftMono",
"Preor... | true |
WeierstrassCurve.Affine.Equation.map | Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic | [
"Eq.mpr",
"RingHom.instRingHomClass",
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"WeierstrassCurve.Affine.map",
"RingHom",
"map_zero",
"id",
"RingHomClass.toMonoidWithZeroHomClass",
"NonAssocSemiring.toMulZeroOneClass",
"Polynomial.map_mapRingHom_evalEval",
"Polynomial",
"Weierstra... | true |
CategoryTheory.ObjectProperty.instIsClosedUnderExtensionsTop | Mathlib.CategoryTheory.ObjectProperty.Extensions | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex",
"imp_self._simp_1",
"BooleanAlgebra.toTop",
"implies_congr",
"True",
"CategoryTheory.ObjectProperty.IsClosedUnderExtensions",
"CategoryTheory.ShortComplex.ShortExact",
"of_eq_true",
"Eq.refl",
"CategoryTheory.Category.toCat... | true |
_private.Mathlib.Analysis.Analytic.ConvergenceRadius.0.FormalMultilinearSeries.isLittleO_of_lt_radius._simp_1_8 | Mathlib.Analysis.Analytic.ConvergenceRadius | [
"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 |
differentIdeal._proof_4 | Mathlib.RingTheory.DedekindDomain.Different | [
"IsDomain",
"FractionRing.field",
"IsDedekindDomain.toIsDomain",
"FractionRing.instIsScalarTower",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"IsScalarTower",
"Mod... | false |
HomologicalComplex.instPreservesColimitsOfShapeEvalOfHasColimitsOfShape | Mathlib.Algebra.Homology.HomologicalComplexLimits | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.Functor.comp",
"HomologicalComplex",
"HomologicalComplex.eval",
"inferInstance",
... | true |
Rat.abs_nonneg | Init.Data.Rat.Lemmas | [
"Rat.instOfNat",
"Rat.instDecidableLe",
"Eq.mpr",
"Decidable.casesOn",
"Rat.abs",
"congrArg",
"Rat",
"Decidable",
"Rat.le_of_lt",
"Eq.mp",
"id",
"LE.le",
"Rat.instLE",
"if_pos",
"_private.Init.Data.Rat.Lemmas.0.Rat.abs_nonneg._simp_1_2",
"LT.lt",
"propext",
"Rat.instLT",
"Rat.lt_... | true |
FreeGroup.lift_mk | Mathlib.GroupTheory.FreeGroup.Basic | [
"cond",
"MonoidHom.instFunLike",
"InvOneClass.toOne",
"Equiv.instEquivLike",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"List.map",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Equiv",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"FreeGro... | true |
TopologicalSpace.Compacts.regularSpace_iff | Mathlib.Topology.Sets.VietorisTopology | [
"TopologicalSpace.Compacts.instSingleton",
"RegularSpace",
"inferInstance",
"TopologicalSpace",
"Iff",
"TopologicalSpace.Compacts.topology",
"Iff.intro",
"Topology.IsEmbedding.toIsInducing",
"Topology.IsInducing.regularSpace",
"Singleton.singleton",
"TopologicalSpace.Compacts.isEmbedding_singlet... | true |
_private.Mathlib.Data.List.AList.0.AList.insertRec.match_1.eq_1 | Mathlib.Data.List.AList | [
"AList.mk",
"List.cons",
"List",
"AList",
"Eq.refl",
"List.NodupKeys",
"Eq",
"AList.insertRec.match_1",
"Sigma",
"List.nil"
] | true |
Aesop.Script.StaticStructureM.State.mk.inj | Aesop.Script.StructureStatic | [
"Aesop.Script.StaticStructureM.State.mk.noConfusion",
"Aesop.Script.StaticStructureM.State.mk",
"Aesop.Script.StaticStructureM.State",
"Bool",
"Eq"
] | true |
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