name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ArchimedeanClass.mk_nonneg_of_le_of_le_of_archimedean | Mathlib.Algebra.Order.Ring.Archimedean | [
"CommRing",
"ArchimedeanClass.min_le_mk_of_le_of_le",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"and_self",
"LinearOrder",
"ArchimedeanClass.instLinearOrder",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"OrderR... | true |
CommRingCat.Colimits.instCommRingColimitType._proof_9 | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"Mul.mk",
"HMul.hMul",
"Quot.sound",
"CommRingCat",
"Quot.map₂",
"AddGroupWithOne.toAddMonoidWithOne",
"Quot.inductionOn",
"CommRingCat.instCategory",
"CategoryTheory.SmallCategory",
"CommRingCat.Colimits.Relation.mul_1",
"CommRingCat.Colimits.ColimitType",
"CommRin... | false |
Quaternion.imJ_star | Mathlib.Algebra.Quaternion | [
"NegZeroClass.toNeg",
"CommRing",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"AddMonoidWithOne.toOne",
"CommRing.toCommSemiring",
"Quaternion.instStar",
"... | true |
List.splitAtD.go._sunfold | Batteries.Data.List.Basic | [
"List.splitAtD.go",
"List.replicate",
"List.reverseAux",
"Prod.mk",
"List.cons",
"List",
"Nat",
"List.reverse",
"List.splitAtD.go.match_1",
"Prod",
"List.nil"
] | false |
Lean.Meta.LazyDiscrTree.recOn | Lean.Meta.LazyDiscrTree | [
"Lean.Meta.LazyDiscrTree",
"Lean.Meta.LazyDiscrTree.instBEqKey",
"Std.HashMap",
"Array",
"Lean.Meta.LazyDiscrTree.rec",
"Lean.Meta.LazyDiscrTree.TrieIndex",
"Lean.Meta.LazyDiscrTree.Key.instHashable",
"Lean.Meta.LazyDiscrTree.Trie",
"Lean.Meta.LazyDiscrTree.mk",
"Lean.Meta.LazyDiscrTree.Key"
] | false |
Mathlib.Tactic.Ring.ringCleanupRef | Mathlib.Tactic.Ring.Basic | [
"Classical.ofNonempty",
"Lean.Expr",
"Lean.Meta.MetaM",
"_private.Mathlib.Tactic.Ring.Basic.0.Mathlib.Tactic.Ring.ringCleanupRef._proof_1",
"IO.Ref"
] | true |
VitaliFamily.FineSubfamilyOn.index | Mathlib.MeasureTheory.Covering.VitaliFamily | [
"MeasureTheory.Measure",
"ChainCompletePartialOrder.instOfCompleteLattice",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Set.PairwiseDisjoint",
"Membership.mem",
"Set.instInter",
"ChainCompletePartialOrder.toPartialOrder",
"Prod.fst",
"Inter.inter",
"MeasurableSpace",
"VitaliFamily.setsAt... | true |
SimpleGraph.Walk.IsHamiltonian.fintype._proof_1 | Mathlib.Combinatorics.SimpleGraph.Hamiltonian | [
"List.mem_toFinset",
"Iff.mpr",
"Finset",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Membership.mem",
"SimpleGraph.Walk.IsHamiltonian.mem_support",
"List.toFinset",
"SimpleGraph",
"List",
"List.instMembership",
"Finset.instSetLike",
"SimpleGraph.Walk.IsHamiltonian",
"SetLike.instMemb... | false |
_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.suggestName.match_4 | Lean.Elab.DocString.Builtin | [
"Lean.Exception"
] | false |
Nat.odd_sub._simp_1 | Mathlib.Algebra.Ring.Parity | [
"Odd",
"HSub.hSub",
"instSubNat",
"LE.le",
"instLENat",
"Iff",
"instHSub",
"Nat",
"Even",
"propext",
"instAddNat",
"Nat.instSemiring",
"Nat.odd_sub",
"Eq"
] | false |
CategoryTheory.Functor.elementsFunctor_map | Mathlib.CategoryTheory.Elements | [
"CategoryTheory.Cat.category",
"CategoryTheory.categoryOfElements",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.toCatHom",
"CategoryTheory.NatTrans.mapElements",
"Cat... | true |
WithZeroMulInt.toNNReal_le_one_iff | Mathlib.Data.Int.WithZero | [
"Eq.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Multiplicative.linearOrder",
"Preorder.toLT",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"congrArg",
"Int.instLinearOrder",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"ne_zero_of_lt",
"PartialOrder.toPreorder",
... | true |
Algebra.transcendental_ringHom_iff_of_comp_eq | Mathlib.RingTheory.Algebraic.Basic | [
"Eq.mpr",
"CommRing",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"Algebra.Transcendental",
"Algebra",
"RingHom",
"RingEquivClass",
"id",
"Distrib.toAdd",
"Algebra.IsAlgebraic",
"instDistribOfSemiring",
"Algebra.isAlgebraic_ringHom_iff_of_comp_eq",
"_private.Mathlib.Ring... | true |
padicValRat.of_int | Mathlib.NumberTheory.Padics.PadicVal.Basic | [
"Int.instAddCommGroup",
"Int.cast",
"congrArg",
"sub_zero",
"padicValInt",
"AddMonoid.toAddZeroClass",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"Rat.den",
"AddZeroClass.toAddZero",
"Rat.instIntCast",
"padicValNat",
"SubtractionMonoid.toSubNegZeroMonoid",
"instOfNatNat",
... | true |
orderBornology_isBounded._simp_1 | Mathlib.Topology.Order.Bornology | [
"Lattice",
"orderBornology_isBounded",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Bornology.IsBounded",
"orderBornology",
"BddAbove",
"And",
"BddBelow",
"propext",
"Nonempty",
"Eq",
"Lattice.toSemilatticeInf",
"Set"
] | false |
Std.Tactic.BVDecide.LRAT.Internal.Formula.rupAdd_sound | Std.Tactic.BVDecide.LRAT.Internal.Formula.Class | [
"outParam",
"Std.Tactic.BVDecide.LRAT.Internal.Formula.ReadyForRupAdd",
"Std.Tactic.BVDecide.LRAT.Internal.Formula",
"Prod.mk",
"Array",
"Std.Tactic.BVDecide.LRAT.Internal.Entails",
"Bool.true",
"Std.Tactic.BVDecide.LRAT.Internal.Liff",
"Nat",
"Std.Tactic.BVDecide.LRAT.Internal.Clause",
"Bool",
... | true |
CategoryTheory.Precoherent.recOn | Mathlib.CategoryTheory.Sites.Coherent.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finite",
"Exists",
"CategoryTheory.Precoherent.rec",
"CategoryTheory.Precoherent.mk",
"And",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.EffectiveEpiFamily",
"Eq",
"CategoryTheory.Pre... | false |
ProbabilityTheory.Kernel.ae_compProd_iff | Mathlib.Probability.Kernel.Composition.CompProd | [
"MeasureTheory.ae",
"ProbabilityTheory.Kernel.ae_compProd_of_ae_ae",
"MeasureTheory.Measure",
"MeasurableSet",
"Filter.Eventually",
"setOf",
"ProbabilityTheory.Kernel.ae_ae_of_ae_compProd",
"ProbabilityTheory.IsSFiniteKernel",
"ProbabilityTheory.Kernel.instFunLike",
"Prod.mk",
"MeasurableSpace",... | true |
max_mul_mul_left | Mathlib.Algebra.Order.Monoid.Unbundled.MinMax | [
"Lattice.toSemilatticeSup",
"HMul.hMul",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Mul",
"monotone_id",
"Monotone.const_mul'",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"MulLeftMono",
"id",
"Monotone.map_max",
"Max.max",
"Eq.... | true |
Equiv.forall_congr' | Mathlib.Logic.Equiv.Defs | [
"Equiv.instEquivLike",
"congrArg",
"Equiv.forall_congr_left",
"Equiv",
"iff_self",
"Iff",
"True",
"propext",
"Iff.trans",
"of_eq_true",
"congrFun'",
"Equiv.symm",
"DFunLike.coe",
"Eq.trans",
"EquivLike.toFunLike",
"forall_congr"
] | true |
CategoryTheory.congr_app | Mathlib.CategoryTheory.NatTrans | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"_private.Mathlib.CategoryTheory.NatTrans.0.CategoryTheory.congr_app._proof_1_1",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.NatTrans",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.NatTrans.app"... | true |
Fintype.linearIndependent_iffₛ | Mathlib.LinearAlgebra.LinearIndependent.Defs | [
"Eq.mpr",
"Pi.Function.module",
"instHSMul",
"Semiring.toModule",
"Pi.addCommMonoid",
"Finset.univ",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"_private.Mathlib.LinearAlgebra.LinearIndependent.Defs.0.Fintype.linearIndependent_iffₛ._simp_1_... | true |
Group.nilpotencyClass_of_not_nilpotent | Mathlib.GroupTheory.Nilpotent | [
"Subgroup.upperCentralSeries",
"Group",
"Classical.propDecidable",
"Subgroup",
"instOfNatNat",
"Group.nilpotencyClass",
"dif_neg",
"Nat",
"Nat.find",
"Subgroup.instTop",
"Group.IsNilpotent",
"Top.top",
"OfNat.ofNat",
"Eq",
"Not",
"Group.IsNilpotent.nilpotent"
] | true |
CategoryTheory.Functor.PreservesLeftKanExtension.mk._flat_ctor | Mathlib.CategoryTheory.Functor.KanExtension.Preserves | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.PreservesLeftKanExtension",
"CategoryTheory.Functor.IsLeftKanExtension",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.associator",
"CategoryTheory.Fu... | false |
_private.Mathlib.Data.List.Cycle.0.List.next_eq_getElem._proof_1_7 | Mathlib.Data.List.Cycle | [
"List.getLast",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"Lean.Grind.nestedProof",
"eq_false",
"Lean.Grind.Order.lt_eq_true_of_lt_k",
"Lean.Grind.CommRing.Expr.var",
"congrArg",
"Lean.Grind.Order.le_of_eq_2_k",
"Lean.Grind.Order.lt_le_trans_k",
"PartialOrder.toPreorder",
"HSub.hSub... | false |
_private.Mathlib.Algebra.IsPrimePow.0.not_isPrimePow_zero._simp_1_4 | Mathlib.Algebra.IsPrimePow | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
AlgebraicGeometry.Scheme.Cover.ColimitGluingData.cocone_ι_transitionMap_assoc | Mathlib.AlgebraicGeometry.ColimitsOver | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeAlongOfIsStableUnderBaseChange",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"AlgebraicGeometry.Scheme.Pullback.instHasPullbacks... | true |
Real.expPartialHomeomorph_target | Mathlib.Analysis.SpecialFunctions.Log.Basic | [
"Real",
"Set.Ioi",
"Real.instZero",
"PartialEquiv.target",
"PseudoMetricSpace.toUniformSpace",
"Zero.toOfNat0",
"Eq.refl",
"Real.pseudoMetricSpace",
"OfNat.ofNat",
"OpenPartialHomeomorph.toPartialEquiv",
"UniformSpace.toTopologicalSpace",
"Eq",
"Real.expPartialHomeomorph",
"Real.instPreord... | true |
IsCompl.compl_eq_iff | Mathlib.Order.BooleanAlgebra.Basic | [
"BooleanAlgebra",
"Compl.compl",
"BooleanAlgebra.toCompl",
"SemilatticeInf.toPartialOrder",
"BooleanAlgebra.toBoundedOrder",
"Eq.rec",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"IsCompl.compl_eq",
"BooleanAlgebra.toBiheytingAlgebra",
"Iff",
"IsCompl",
"Cohey... | true |
Array.all_iff_forall | Init.Data.Array.Lemmas | [
"Iff.mpr",
"Eq.mpr",
"Array.all",
"Bool.not",
"Bool.not_eq_false",
"Iff.of_eq",
"congrArg",
"_private.Init.Data.Array.Lemmas.0.Array.all_iff_forall._simp_1_1",
"Exists",
"Eq.mp",
"id",
"Array.any",
"_private.Init.Data.Array.Lemmas.0.Array.all_iff_forall._simp_1_5",
"LE.le",
"instLENat",
... | true |
AddAction.sigmaFixedByEquivOrbitsProdAddGroup._proof_1 | Mathlib.GroupTheory.GroupAction.Quotient | [
"AddMonoid.toAddSemigroup",
"Iff.rfl",
"Prod.fst",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddGroup",
"Iff",
"AddSemigroupAction.toVAdd",
"AddGroup.toSubNegMonoid",
"instHVAdd",
"SubNegMonoid.toAddMonoid",
"Prod",
"Eq",
"Prod.snd"
] | false |
_private.Mathlib.Data.Rat.Sqrt.0.Rat.exists_mul_self.match_1_1 | Mathlib.Data.Rat.Sqrt | [
"Rat.instMul",
"HMul.hMul",
"Rat",
"Exists",
"Exists.casesOn",
"Exists.intro",
"Eq",
"instHMul"
] | false |
Mathlib.Tactic._aux_Mathlib_Tactic_Core___macroRules_Mathlib_Tactic_tacticRepeat1__1 | Mathlib.Tactic.Core | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr3",
"ReaderT.i... | false |
AlgebraicGeometry.instAddCommGroupObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInType | Mathlib.AlgebraicGeometry.StructureSheaf | [
"AlgebraicGeometry.StructureSheaf.Localizations",
"CategoryTheory.Functor",
"CommRing",
"Semiring.toModule",
"Opposite",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AlgebraicGeometry.StructureSheaf.sectionsSubmodule._proof_2",
"OreLocaliza... | true |
HahnSeries.toOrderTopSubOnePos | Mathlib.RingTheory.HahnSeries.Summable | [
"CommRing",
"HahnSeries.instSemiring",
"Preorder.toLT",
"HahnSeries.toOrderTopSubOnePos._proof_2",
"AddGroupWithOne.toAddGroup",
"WithTop.instPreorder",
"CommSemiring.toSemiring",
"HahnSeries.instSub",
"LinearOrder",
"HahnSeries.orderTop",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",... | true |
infEDist_inv | Mathlib.Analysis.Normed.Group.Pointwise | [
"Eq.mpr",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"SeminormedCommGroup.toPseudoMetricSpace",
"InvolutiveInv.toInv",
"DivisionMonoid.toDivInvOneMonoid",
"id",
"Metric.infEDist",
"CommGroup.toDivisionCommMonoid",
"DivisionMonoid.toInvolutiveInv",
"Inv.... | true |
instBornologyPUnit._proof_1 | Mathlib.Topology.Bornology.Basic | [
"Filter.instCompleteLatticeFilter",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"Bot.bot",
"LE.le",
"PUnit",
"BoundedOrder.toOrderBot",
"Filter.cofinite",
"bot_le",
"Filter",
"Filter.instPartialOrder"
] | false |
Lean.SerialMessage.ctorIdx | Lean.Message | [
"Nat",
"Lean.SerialMessage"
] | false |
Char.lt | Init.Data.Char.Basic | [
"Char.val",
"instLTUInt32",
"LT.lt",
"UInt32",
"Char"
] | true |
Lean.Grind.CommRing.Stepwise.div_cert.eq_1 | Init.Grind.Ring.CommSolver | [
"Bool.and'",
"Lean.Grind.CommRing.Poly",
"Bool.not",
"Lean.Grind.CommRing.Poly.beq'",
"Int",
"Lean.Grind.CommRing.Poly.mulConst_k",
"instOfNat",
"Int.beq'",
"Bool",
"Eq.refl",
"Lean.Grind.CommRing.Stepwise.div_cert",
"OfNat.ofNat",
"Eq"
] | true |
_private.Lean.Shell.0.Lean.displayHelp | Lean.Shell | [
"Unit.unit",
"_private.Lean.Shell.0.Lean.Internal.isDebug",
"instMonadLiftT",
"IO",
"IO.getStdout",
"EIO",
"instDecidableEqBool",
"liftM",
"instMonadEIO",
"IO.getStderr",
"Bool.true",
"Unit",
"Bool",
"Monad.toBind",
"Bind.bind",
"PUnit.unit",
"IO.Error",
"instMonadLiftTOfMonadLift"... | true |
_private.Mathlib.FieldTheory.AlgebraicClosure.0.le_algebraicClosure_iff._simp_1_1 | Mathlib.FieldTheory.AlgebraicClosure | [
"IsAlgebraic",
"IntermediateField",
"Algebra",
"Membership.mem",
"Field.toDivisionRing",
"mem_algebraicClosure_iff",
"DivisionRing.toRing",
"Field.toSemifield",
"Field.toCommRing",
"Semifield.toDivisionSemiring",
"algebraicClosure",
"propext",
"DivisionSemiring.toSemiring",
"IntermediateFi... | false |
_private.Mathlib.Topology.CWComplex.Classical.Basic.0.Topology.RelCWComplex.disjoint_base_iUnion_openCell._simp_1_2 | Mathlib.Topology.CWComplex.Classical.Basic | [
"Set.iUnion_eq_empty",
"propext",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Set.iUnion",
"Set"
] | false |
CategoryTheory.instIsDenseFunctorOppositeTypeYoneda | Mathlib.CategoryTheory.Functor.KanExtension.Dense | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.IsDense.mk",
"CategoryTheory.Functor.category",
"CategoryTheory.yoneda",
"Nonempty.intro",
"CategoryTheory.Functor.IsDense",
"CategoryTheory.types",
"CategoryTheory.Category.opposite",
"CategoryTheory.Functor.DenseAt",
"CategoryTheory... | true |
Array.forIn' | Init.Data.Array.Basic | [
"Array.forIn'._proof_2",
"Array.forIn'.loop",
"Array.instMembership",
"Membership.mem",
"ForInStep",
"Array",
"Monad",
"Array.size"
] | true |
Std.ExtDTreeMap.Const.getEntryLT._proof_1 | Std.Data.ExtDTreeMap.Basic | [
"Std.ExtDTreeMap.mk",
"Std.DTreeMap",
"Membership.mem",
"Exists",
"Ordering",
"Eq.rec",
"Std.TransCmp",
"And",
"Ordering.lt",
"Std.ExtDTreeMap",
"Eq",
"Std.ExtDTreeMap.instMembershipOfTransCmp"
] | false |
Real.logb_neg_of_base_lt_one | Mathlib.Analysis.SpecialFunctions.Log.Base | [
"Iff.mpr",
"Real.partialOrder",
"Real",
"Real.instZero",
"Real.instZeroLEOneClass",
"lt_trans",
"Real.instLT",
"Real.logb_neg_iff_of_base_lt_one",
"Real.instFloorRing",
"Real.instRing",
"Real.instOne",
"Real.logb",
"zero_lt_one",
"LT.lt",
"One.toOfNat1",
"Zero.toOfNat0",
"OfNat.ofNat... | true |
CategoryTheory.equivEssImageOfReflective_inverse | Mathlib.CategoryTheory.Adjunction.Reflective | [
"CategoryTheory.Functor.EssImageSubcategory",
"CategoryTheory.Functor",
"CategoryTheory.ObjectProperty.ι",
"CategoryTheory.equivEssImageOfReflective",
"CategoryTheory.reflector",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.essImage",
"Eq.refl",
"CategoryTheory.ObjectProperty.FullSubcatego... | true |
AddEquiv.mk.sizeOf_spec | Mathlib.Algebra.Group.Equiv.Defs | [
"Equiv",
"instOfNatNat",
"Equiv.toFun",
"instHAdd",
"HAdd.hAdd",
"AddEquiv.mk",
"Nat",
"SizeOf.sizeOf",
"Equiv._sizeOf_inst",
"AddEquiv",
"instAddNat",
"Eq.refl",
"SizeOf",
"AddEquiv._sizeOf_inst",
"OfNat.ofNat",
"Eq",
"Add"
] | true |
HomotopicalAlgebra.LeftHomotopyRel.postcomp | Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy | [
"HomotopicalAlgebra.Cylinder.LeftHomotopy",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomotopicalAlgebra.LeftHomotopyRel",
"HomotopicalAlgebra.Cylinder.LeftHomotopy.leftHomotopyRel",
"HomotopicalAlgebra.Cylinder",
"Exists.casesOn",
"HomotopicalAlgebra.CategoryWithWeakEquivalences",
"N... | true |
_private.Init.Data.String.Basic.0.String.Pos.toSlice_le._simp_1_1 | Init.Data.String.Basic | [
"String.instLEPos_1",
"String.Slice.Pos.offset",
"String.Slice",
"LE.le",
"String.Pos.Raw",
"String.Slice.Pos.le_iff",
"String.instLERaw",
"propext",
"String.Slice.Pos",
"Eq"
] | false |
HomologicalComplex₂.D₁_totalShift₂XIso_hom | Mathlib.Algebra.Homology.TotalComplexShift | [
"Int.instAddCommGroup",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Iff.mpr",
"Not.intro",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"MulOne.toOne",
"In... | true |
ByteArray.extract_eq_empty_iff | Init.Data.ByteArray.Lemmas | [
"Eq.mpr",
"_private.Init.Data.ByteArray.Lemmas.0.ByteArray.extract_eq_empty_iff._proof_1_1",
"congrArg",
"ByteArray.extract",
"HSub.hSub",
"id",
"instSubNat",
"ByteArray.empty",
"instOfNatNat",
"LE.le",
"instLENat",
"Iff",
"ByteArray.size_extract",
"instHSub",
"Nat",
"propext",
"Deci... | true |
Lean.instInhabitedAuxParentProjectionInfo.default | Lean.ProjFns | [
"Inhabited.default",
"instInhabitedBool",
"instInhabitedNat",
"Nat",
"Bool",
"Lean.AuxParentProjectionInfo.mk",
"Lean.AuxParentProjectionInfo"
] | true |
_private.Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension.0.IsOpen.exists_contDiff_support_eq._simp_1_1 | Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | [
"Set.singleton_subset_iff",
"Membership.mem",
"Set.instSingletonSet",
"HasSubset.Subset",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set.instHasSubset",
"Set"
] | false |
Mathlib.Tactic.Coherence._aux_Mathlib_Tactic_CategoryTheory_Coherence___elabRules_Mathlib_Tactic_Coherence_pure_coherence_internal_1 | Mathlib.Tactic.CategoryTheory.Coherence | [
"instOrElseOfAlternative",
"Lean.instMonadExceptOfExceptionCoreM",
"StateRefT'.instAlternativeOfMonad",
"ReaderT",
"Lean.Elab.Tactic.getMainGoal",
"Lean.Meta.State",
"Mathlib.Tactic.BicategoryCoherence.bicategory_coherence",
"Lean.Syntax.isOfKind",
"instMonadLiftT",
"Lean.Elab.Tactic.Context",
"... | false |
_private.Aesop.Forward.State.0.Aesop.instBEqRawHyp.beq.match_1 | Aesop.Forward.State | [
"_private.Aesop.Forward.State.0.Aesop.instBEqRawHyp.beq._sparseCasesOn_2",
"Aesop.RawHyp.patSubst",
"Aesop.RawHyp.casesOn",
"Aesop.Substitution",
"Lean.FVarId",
"Nat.hasNotBit",
"Aesop.RawHyp",
"Aesop.RawHyp.fvarId",
"_private.Aesop.Forward.State.0.Aesop.instBEqRawHyp.beq._sparseCasesOn_1",
"Aesop... | false |
CategoryTheory.Monad.id._proof_1 | Mathlib.CategoryTheory.Monad.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.Functor.map",
"CategoryTheory.CategoryStruct.comp",
"Eq.refl"... | false |
ProbabilityTheory.IndepFun.map_mul_eq_map_mconv_map₀ | Mathlib.Probability.Independence.Basic | [
"Monoid",
"MeasureTheory.Measure",
"HMul.hMul",
"AEMeasurable",
"Monoid.toMulOneClass",
"MeasureTheory.SigmaFinite",
"MeasureTheory.Measure.isFiniteMeasure_map",
"MeasureTheory.IsFiniteMeasure.toSigmaFinite",
"MulOne.toMul",
"MeasurableSpace",
"MulOneClass.toMulOne",
"ProbabilityTheory.IndepFu... | true |
multiplicity_addValuation_apply | Mathlib.RingTheory.Valuation.PrimeMultiplicity | [
"IsDomain",
"CommRing",
"CommSemiring.toSemiring",
"multiplicity_addValuation",
"Prime",
"CommSemiring.toCommMonoidWithZero",
"AddValuation.instFunLike",
"AddValuation",
"CommRing.toCommSemiring",
"ENat",
"Semiring.toMonoid",
"CommRing.toRing",
"Eq",
"DFunLike.coe",
"rfl",
"emultiplici... | true |
ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt | Mathlib.Analysis.ODE.PicardLindelof | [
"ContDiffAt",
"IsPicardLindelof.of_contDiffAt_one",
"NormedCommRing.toSeminormedCommRing",
"Set.Ioo_subset_Icc_self",
"Real",
"Preorder.toLT",
"CompleteSpace",
"NormedSpace.toIsBoundedSMul",
"instAddMonoidWithOneENat",
"Real.lattice",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero"... | true |
Path.Homotopy.transAssoc._proof_4 | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Path.Homotopy.transAssocReparamAux_mem_I",
"Membership.mem",
"Real.semiring",
"Path.Homotopy.transAssocReparamAux_one",
"Set.Elem",
"Subtype",
"Subtype.mk",
"Path.Homotopy.transAssocReparamAux",
"One.toOfNat1",
"Set.Icc.instOne",
"OfN... | false |
Std.Tactic.BVDecide.Normalize.BitVec.beq_one_eq_ite' | Std.Tactic.BVDecide.Normalize.Bool | [
"cond",
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"BitVec.instDecidableForallBitVec",
"BitVec",
"id",
"instDecidableEqBool",
"instOfNatNat",
"BitVec.ofNat",
"instBEqOfDecidableEq",
"instDecidableEqBitVec",
"Bool.true",
"BEq.beq",
"Nat",
"Bool",
"Eq.refl",
"OfNat... | true |
HasFibers.instFaithfulFibι | Mathlib.CategoryTheory.FiberedCategory.HasFibers | [
"HasFibers",
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.Fiber.fiberInclusion",
"CategoryTheory.Functor.comp",
"HasFibers.category",
"CategoryTheory.Functor.Fiber",
"CategoryTheory.Functor.Fiber.fiberCategory",
"HasFibers.Fib",
"CategoryTheory.Functor.IsEqu... | true |
CategoryTheory.InjectiveResolution.toRightDerivedZero'._proof_2 | Mathlib.CategoryTheory.Abelian.RightDerived | [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.single_obj_d",
"CochainComplex.single₀",
"congrArg",
"CategoryTh... | false |
instCategoryCompactum._proof_9 | Mathlib.Topology.Category.Compactum | [
"Quiver.mk",
"CategoryTheory.CategoryStruct.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"instCategoryCompactum._aux_1",
"CategoryTheory.ofTypeMonad",
"CategoryTheory.Category.assoc._autoParam",
"CategoryTheory.Monad.Algebra.eilenbergMoore._proof_6",
"autoParam",
"Ultrafilter.monad... | false |
CategoryTheory.ParametrizedAdjunction.rec | Mathlib.CategoryTheory.Adjunction.Parametrized | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.Functor.id",
"CategoryTheory.Functor.whiskerLeft",
"CategoryTheory.Fu... | false |
Turing.PartrecToTM2.tr.eq_2 | Mathlib.Computability.TuringMachine.ToPartrec | [
"Inhabited.default",
"Turing.PartrecToTM2.tr",
"Turing.PartrecToTM2.Γ'",
"Turing.PartrecToTM2.Λ'.push",
"Turing.TM2.Stmt.branch",
"Option.getD",
"Turing.PartrecToTM2.instInhabitedΓ'",
"Turing.PartrecToTM2.Λ'",
"Turing.PartrecToTM2.Stmt'",
"Eq.refl",
"Turing.TM2.Stmt.goto",
"Turing.PartrecToTM2... | true |
Std.DTreeMap.getKeyD_minKey! | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.isEmpty",
"Ord.mk",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.Internal.Impl.getKeyD_minKey!",
"Std.DTreeMap.wf",
"Bool",
"Inhabited",
"Std.DTreeMap.minKey!",
"Bool.false",
"Eq",
"Std.DTreeMap.getKeyD"
] | true |
PMF.seq.eq_1 | Mathlib.Probability.ProbabilityMassFunction.Constructions | [
"PMF",
"PMF.bind",
"PMF.seq",
"PMF.pure",
"Eq.refl",
"Eq"
] | true |
Lean.Elab.Tactic.BVDecide.Frontend.SolverMode._sizeOf_1 | Std.Tactic.BVDecide.Syntax | [
"Lean.Elab.Tactic.BVDecide.Frontend.SolverMode",
"instOfNatNat",
"Nat",
"Lean.Elab.Tactic.BVDecide.Frontend.SolverMode.rec",
"OfNat.ofNat"
] | false |
Equiv.addEquiv._proof_1 | Mathlib.Algebra.Group.TransferInstance | [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
"Equiv",
"Equiv.toFun",
"instHAdd",
"HAdd.hAdd",
"Equiv.add",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"DFunLike.coe",
"Add",
"Eq.trans",
"EquivLike.toFunLike"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.take_isSubwalk_take._simp_1_2 | Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | [
"List.IsInfix",
"List",
"List.IsPrefix",
"List.IsPrefix.isInfix",
"True",
"eq_true",
"Eq"
] | false |
CategoryTheory.yonedaAddMon._proof_5 | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.yonedaAddMonObj",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Hom.addMonoid",
"AddMonCat.hom_ext",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"AddMonCat.ofHom",
... | false |
SupIrred.ne_bot | Mathlib.Order.Irreducible | [
"False",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"not_supIrred_bot",
"Ne",
"Bot.bot",
"Eq.ndrec",
"SemilatticeSup.toPartialOrder",
"Eq.symm",
"Eq",
"SemilatticeSup",
"SupIrred"
] | true |
HomologicalComplex.mapBifunctor₂₃.d₃_eq | Mathlib.Algebra.Homology.BifunctorAssociator | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"instHSMul",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"Units.instSMul",
"AddCommGroup.toAddGroup",
"HomologicalComplex",
"Units"... | true |
Set.nonempty_sInter._simp_1 | Mathlib.Data.Set.Lattice | [
"Membership.mem",
"Exists",
"Set.nonempty_sInter",
"Set.Nonempty",
"propext",
"Eq",
"Set.sInter",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.ofPrime_idealOfLE._simp_1_2 | Mathlib.RingTheory.Valuation.ValuationSubring | [
"MulOne.toOne",
"Membership.mem",
"MulOne.toMul",
"Submonoid.mem_mk",
"MulOneClass.toMulOne",
"Subsemigroup",
"propext",
"Subsemigroup.carrier",
"One.toOfNat1",
"Submonoid.mk",
"Submonoid.instSetLike",
"MulOneClass",
"OfNat.ofNat",
"Subsemigroup.instSetLike",
"Eq",
"Set.instMembership"... | false |
DirSupInaccOn | Mathlib.Order.DirSupClosed | [
"Preorder.toLE",
"DirectedOn",
"Membership.mem",
"LE.le",
"Set.instInter",
"Inter.inter",
"Set.Nonempty",
"IsLUB",
"Set.instMembership",
"Preorder",
"Set"
] | true |
extDeriv_apply_vectorField_of_pairwise_commute | Mathlib.Analysis.Calculus.DifferentialForm.VectorField | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"ContinuousAlternatingMap.instAddCommGroup._proof_7",
"instHSMul",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"Finset.univ",
"NormedSpace",
"congrArg",
... | true |
Convexity.StdSimplex | Mathlib.Geometry.Convex.ConvexSpace.Defs | [
"One",
"LE",
"AddCommMonoid",
"Convexity.StdSimplex.mk"
] | true |
_private.Mathlib.Analysis.SpecialFunctions.Complex.Circle.0.Circle.not_isPreconnected_compl_pair._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Complex.Circle | [
"isPreconnected_iff_subset_of_disjoint_closed",
"Set.instUnion",
"HasSubset.Subset",
"Set.instInter",
"Inter.inter",
"IsClosed",
"TopologicalSpace",
"propext",
"Set.instEmptyCollection",
"Or",
"Union.union",
"EmptyCollection.emptyCollection",
"Eq",
"IsPreconnected",
"Set.instHasSubset",
... | false |
BitVec.toNat_cpop_concat | Init.Data.BitVec.Lemmas | [
"instPowNat",
"Eq.mpr",
"BitVec.setWidth",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.toNat_cpop_concat._proof_1_2",
"congrArg",
"BitVec.toNat_cpop_le",
"Bool.toNat",
"BitVec.instAdd",
"BitVec",
"id",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"BitVec.toNat",
"LE.le",
"BitVec.ofNat",
... | true |
Polynomial.recOnHorner._unary._proof_15 | Mathlib.Algebra.Polynomial.Inductions | [
"Polynomial.C",
"HMul.hMul",
"congrArg",
"Polynomial.C_0",
"RingHom",
"id",
"Polynomial.instAdd",
"Polynomial.divX",
"Polynomial",
"instHAdd",
"RingHom.instFunLike",
"HAdd.hAdd",
"Polynomial.semiring",
"Semiring",
"Zero.toOfNat0",
"Polynomial.instMul",
"Polynomial.instZero",
"OfNat... | false |
Aesop.instInhabitedNormalizationState.default | Aesop.Tree.Data | [
"Aesop.NormalizationState",
"Aesop.NormalizationState.notNormal"
] | true |
_private.Std.Data.DHashMap.Lemmas.0.Std.DHashMap.mem_alter._simp_1_1 | Std.Data.DHashMap.Lemmas | [
"Membership.mem",
"Std.DHashMap.instMembership",
"Std.DHashMap.mem_iff_contains",
"Bool.true",
"Std.DHashMap.contains",
"propext",
"Bool",
"Hashable",
"BEq",
"Eq",
"Std.DHashMap"
] | false |
DifferentiableOn.mul_const | Mathlib.Analysis.Calculus.FDeriv.Mul | [
"NormedRing.toRing",
"HMul.hMul",
"NormedSpace",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedRing.toNonUnitalNormedRing",
"instDistribOfSemiring",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Distrib.toMul",
"NormedAlgebra.toNormedSpace",
"Ring.toAddC... | true |
CategoryTheory.Limits.KernelFork.IsLimit.ofιUnop._proof_4 | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Kernels | [
"CategoryTheory.Limits.HasZeroMorphisms",
"Opposite",
"CategoryTheory.Limits.KernelFork.ofι",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.CategoryStruct.opposite",
"Quiver.Hom.op",
"Quiver.Hom.op_inj",
"Q... | false |
FiniteField.frobeniusAlgEquiv._proof_1 | Mathlib.FieldTheory.Finite.Basic | [
"PNat.val",
"Nontrivial",
"PerfectRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"Nat.Prime",
"Algebra.algebraMap",
"bijective_iterateFrobenius",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"Nat.instMonoid",
"AlgHom.funLike",
"AddGroupWithOne.toAddMonoidWith... | false |
UniformSpace.Completion.extensionHom._proof_2 | Mathlib.Topology.Algebra.UniformRing | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"RingHomClass.toAddMonoidHomClass",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"RingHom.instFunLike",
"AddMonoidWithOne.toAddMonoid",
"Semi... | false |
_private.Mathlib.Order.Cover.0.WithTop.covBy_top_iff._simp_1_2 | Mathlib.Order.Cover | [
"WithTop.forall",
"WithTop.some",
"And",
"WithTop.top",
"propext",
"Top.top",
"Eq",
"WithTop"
] | false |
_private.Batteries.Data.List.Lemmas.0.List.pos_findIdxNth_getElem._proof_1_12 | Batteries.Data.List.Lemmas | [
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"List.findIdxNth",
"List",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"_private.Batteries.Data.List.Lemmas.0.List.pos_findIdxNth_getElem._proof_1_2",
"Bool",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"List.l... | false |
_private.Lean.Data.FuzzyMatching.0.Lean.FuzzyMatching.Score | Lean.Data.FuzzyMatching | [
"_private.Lean.Data.FuzzyMatching.0.Lean.FuzzyMatching.Score.mk"
] | true |
_private.Qq.Macro.0.Qq.Impl.quoteExpr.match_1 | Qq.Macro | [
"Qq.Impl.ExprBackSubstResult.casesOn",
"Lean.Expr",
"Qq.Impl.ExprBackSubstResult",
"Qq.Impl.ExprBackSubstResult.quoted",
"Qq.Impl.ExprBackSubstResult.unquoted"
] | false |
FreeLieAlgebra.lift_of_apply | Mathlib.Algebra.Lie.Free | [
"LieHom",
"Eq.mpr",
"CommRing",
"Equiv.instEquivLike",
"FreeLieAlgebra.instLieRing",
"FreeLieAlgebra.of_comp_lift",
"congrArg",
"FreeLieAlgebra.of",
"Function.comp",
"FreeLieAlgebra.lift",
"id",
"Equiv",
"LieRing",
"FreeLieAlgebra",
"FreeLieAlgebra.instLieAlgebra",
"Eq.refl",
"Functi... | true |
CategoryTheory.SplitMono | Mathlib.CategoryTheory.EpiMono | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SplitMono.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
instAlgebraUniversalEnvelopingAlgebra._aux_1 | Mathlib.Algebra.Lie.UniversalEnveloping | [
"LieAlgebra.toModule",
"UniversalEnvelopingAlgebra.Rel",
"CommRing",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"RingQuot.smul",
"Algebra.id",
"UniversalEnvelopingAlgebra",
"TensorAlgebra",
"instSemiringTensorAlgebra",
"IsScalarTower.left",
"instAlge... | false |
MDifferentiableWithinAt.prodMap' | Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | [
"Set.instSProd",
"Prod.normedSpace",
"Prod.normedAddCommGroup",
"NormedSpace",
"SProd.sprod",
"instTopologicalSpaceProd",
"Set.prod_subset_preimage_fst",
"Function.comp",
"instTopologicalSpaceModelProd",
"Prod.map",
"MDifferentiableWithinAt.prodMk",
"Prod.fst",
"TopologicalSpace",
"ModelWi... | true |
CategoryTheory.Localization.Construction.morphismProperty_eq_top' | Mathlib.CategoryTheory.Localization.Construction | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismProperty.Q",
"CategoryTheory.MorphismProperty.IsStableUnderComposition",
"CategoryTheory.Iso",
"CategoryTheory.MorphismProper... | true |
FreeGroup.of_ne_one._simp_2 | Mathlib.GroupTheory.FreeGroup.Reduce | [
"FreeGroup.of",
"False",
"eq_false",
"FreeGroup.instOne",
"FreeGroup.of_ne_one",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"FreeGroup"
] | false |
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