name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Set.powersetCard.coe_addActionHom_of_embedding | Mathlib.GroupTheory.GroupAction.SubMulAction.Combination | [
"Finset.univ",
"AddMonoid.toAddSemigroup",
"Finset",
"Function.Embedding.vadd",
"Finset.map",
"Membership.mem",
"Set.powersetCard.instAddActionElemFinset",
"Set.Elem",
"id",
"Fin.fintype",
"Function.Embedding",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddGroup",
"AddSemigroupActio... | true |
_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.map_dual._simp_1_2 | Mathlib.Combinatorics.Matroid.Map | [
"Exists",
"Set.subset_image_iff",
"HasSubset.Subset",
"And",
"propext",
"Set.image",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
_private.Mathlib.Data.Matrix.Basis.0.Matrix.single_mem_matrix._simp_1_1 | Mathlib.Data.Matrix.Basis | [
"Set.mem_matrix",
"Matrix",
"Membership.mem",
"propext",
"Set.matrix",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.Data.ZMod.Basic.0.ZMod.coprime_mod_iff_coprime._proof_1_1 | Mathlib.Data.ZMod.Basic | [
"Nat.gcd",
"False",
"Lean.Grind.iff_eq",
"congrArg",
"Classical.byContradiction",
"id",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"Lean.Grind.eq_congr",
"HMod.hMod",
"Iff",
"Nat",
"Lean.Grind.false_of_not_eq_self",
"Lean.Grind.intro_with_eq",
"Eq.refl",
"Lean.Grind.not_eq_prop",
"... | false |
Lean.Compiler.LCNF.SpecState | Lean.Compiler.LCNF.SpecInfo | [
"Lean.Compiler.LCNF.SpecState.mk"
] | true |
AlgebraicGeometry.Opens.isDominant_homOfLE | Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap | [
"Eq.mpr",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme.homOfLE",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"congrArg",
... | true |
_private.Init.Data.UInt.Lemmas.0.UInt64.toUInt16_le._simp_1_1 | Init.Data.UInt.Lemmas | [
"UInt64",
"LE.le",
"instLENat",
"UInt64.toNat",
"Nat",
"propext",
"UInt64.le_iff_toNat_le",
"instLEUInt64",
"Eq"
] | false |
KaehlerDifferential.submodule_span_range_eq_ideal | Mathlib.RingTheory.Kaehler.Basic | [
"Set.mem_range_self",
"Eq.mpr",
"Submodule",
"Submodule.addSubmonoidClass",
"CommRing",
"Algebra.to_smulCommClass",
"TensorProduct.leftHasSMul",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"AddSubmonoidClass.toAddMemClass",
"Semiring.toModule",
"AlgHom.algHomClass",
"HMul.h... | true |
CategoryTheory.Functor.mapAddMonFunctor._proof_3 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.AddMon.instCategory",
"CategoryTheory.LaxMonoidalFunctor.Hom.hom",
"CategoryTheory.AddMonObj.add",
"CategoryTheory.LaxMonoidalFunctor.toFunctor",
"CategoryTheory.AddMon.addMon",
"CategoryTheory... | false |
TensorAlgebra.equivFreeAlgebra._proof_4 | Mathlib.LinearAlgebra.TensorAlgebra.Basis | [
"CommSemiring.toSemiring",
"RingHomCompTriple",
"CommSemiring",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
Nat.nth_le_of_strictMonoOn_of_mapsTo | Mathlib.Data.Nat.Nth | [
"Mathlib.Tactic.Push.not_forall_eq",
"OrderBot.bddBelow._simp_1",
"Iff.mpr",
"_private.Mathlib.Data.Nat.Nth.0.Nat.nth_le_of_strictMonoOn_of_mapsTo._proof_1_4",
"Eq.mpr",
"Nat.zero_le",
"Preorder.toLT",
"Iff.of_eq",
"congrArg",
"PartialOrder.toPreorder",
"setOf",
"Nat.nth._proof_1",
"Classica... | true |
FreeAlgebra.Rel.add_assoc | Mathlib.Algebra.FreeAlgebra | [
"FreeAlgebra.Pre.hasAdd",
"FreeAlgebra.Pre",
"FreeAlgebra.Rel.add_assoc",
"CommSemiring",
"instHAdd",
"HAdd.hAdd",
"FreeAlgebra.Rel"
] | true |
Std.DTreeMap.Internal.Impl.Const.maxEntry!._unsafe_rec | Std.Data.DTreeMap.Internal.Queries | [
"Std.DTreeMap.Internal.Impl.Const.maxEntry!._unsafe_rec",
"Std.DTreeMap.Internal.Impl.Const.maxEntry?.match_1",
"panicWithPosWithDecl",
"Std.DTreeMap.Internal.Impl.inner",
"Prod.mk",
"instOfNatNat",
"Unit",
"Nat",
"Inhabited",
"Prod",
"OfNat.ofNat",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | false |
Lean.Grind.AC.Seq.concat_k.eq_1 | Init.Grind.AC | [
"Lean.Grind.AC.Seq.cons",
"Lean.Grind.AC.Seq.rec",
"Eq.refl",
"Lean.Grind.AC.Var",
"Lean.Grind.AC.Seq.concat_k",
"Lean.Grind.AC.Seq",
"Eq"
] | true |
_private.Lean.Data.EditDistance.0.Lean.EditDistance.levenshtein._proof_1 | Lean.Data.EditDistance | [
"Std.Legacy.Range.stop",
"Vector.size",
"String",
"Membership.mem",
"inferInstance",
"instOfNatNat",
"Membership",
"instHAdd",
"Std.Legacy.Range.mk",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Std.Legacy.Range",
"String.length",
"Std.Legacy.instMembershipNatRange",
"instAddNat",
"Eq.refl",
"ins... | false |
AddSubmonoid.mem_map_of_mem | Mathlib.Algebra.Group.Submonoid.Operations | [
"Membership.mem",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"AddSubmonoid",
"AddZeroClass",
"SetLike.coe",
"Set.mem_image_of_mem",
"AddSubmonoid.map",
"AddSubmonoid.instSetLike",
"DFunLike.coe",
"SetLike.instMembership",
"FunLike"
] | true |
AddMagmaCat.neg_hom_apply | Mathlib.Algebra.Category.Semigrp.Basic | [
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"AddHom",
"AddMagmaCat.str",
"CategoryTheory.Iso",
"AddHom.funLike",
"CategoryTheory.Iso.hom_inv_id_apply",
"AddMagmaCat.carrier",
"AddMagmaCat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"AddMagmaCat.instConcreteCategoryAddHomCarrier"... | true |
Aesop.SafeRulesResult.succeeded.inj | Aesop.Search.Expansion | [
"Aesop.SafeRulesResult.succeeded",
"Aesop.RappRef",
"Aesop.SafeRulesResult.succeeded.noConfusion",
"Array",
"Aesop.SafeRulesResult",
"Eq"
] | true |
one_leftCoset | Mathlib.GroupTheory.Coset.Basic | [
"Set.ext",
"Monoid",
"MulOne.toOne",
"instHSMul",
"instSMulOfMul",
"Monoid.toMulOneClass",
"congrArg",
"Membership.mem",
"MulOne.toMul",
"one_smul",
"iff_self",
"MulOneClass.toMulOne",
"Iff",
"True",
"of_eq_true",
"Monoid.toMulAction",
"One.toOfNat1",
"HSMul.hSMul",
"congrFun'",
... | true |
Lean.IR.ToIR.BuilderState.joinPoints._default | Lean.Compiler.IR.ToIR | [
"Lean.instBEqFVarId",
"id",
"Lean.FVarId",
"Std.HashMap",
"Std.HashMap.instEmptyCollection",
"Lean.instHashableFVarId",
"Lean.IR.JoinPointId",
"EmptyCollection.emptyCollection"
] | false |
_private.Init.Data.List.Nat.Erase.0.List.eraseIdx_set_lt._proof_1_2 | Init.Data.List.Nat.Erase | [
"Lean.Omega.LinearCombo.coordinate_eval_6",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"List.eraseIdx",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotom... | false |
ENat.sub_iInf | Mathlib.Data.ENat.Lattice | [
"Eq.mpr",
"iInf",
"instCompleteLinearOrderENat",
"instSubENat",
"congrArg",
"CommSemiring.toSemiring",
"iSup",
"CompletelyDistribLattice.toCompleteLattice",
"le_iInf_iff._simp_1",
"PartialOrder.toPreorder",
"HSub.hSub",
"eq_of_forall_ge_iff",
"Preorder.toLE",
"iSup_le_iff._simp_2",
"inst... | true |
PowerBasis.map | Mathlib.RingTheory.PowerBasis | [
"PowerBasis",
"PowerBasis.mk",
"CommRing",
"PowerBasis.dim",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"PowerBasis.gen",
"Module.Basis.map",
"Algebra",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"PowerBasis.basis",
"NonAssocRing.toNonUnitalNonAssocRing",... | true |
_private.Batteries.Data.List.Basic.0.List.forall₂_cons.match_1_1 | Batteries.Data.List.Basic | [
"List.Forall₂.cons",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"List.Forall₂.nil",
"List.Forall₂.casesOn",
"List.cons",
"List",
"List.Forall₂",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"List.ctorIdx",
"List.cons.noConfusion",
"List.nil"
] | false |
Lean.Server.RequestError.rec | Lean.Server.Requests | [
"Lean.Server.RequestError.mk",
"Lean.JsonRpc.ErrorCode",
"Lean.Server.RequestError",
"String"
] | false |
NonemptyInterval.toDualProd_injective | Mathlib.Order.Interval.Basic | [
"NonemptyInterval.toDualProd",
"NonemptyInterval.toProd_injective",
"LE",
"Function.Injective",
"OrderDual",
"Prod",
"NonemptyInterval"
] | true |
_private.Batteries.Data.List.Lemmas.0.List.mem_findIdxs_iff_getElem_sub_pos._proof_1_7 | Batteries.Data.List.Lemmas | [
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"Lean.Grind.CommRing.Expr.var",
"Int.Linear.Expr.eq_of_norm_eq",
"congrArg",
"List.length_cons",
"Lean.Grind.Order.le_of_eq_2_k",
"Std.IsL... | false |
CategoryTheory.Equivalence.symmEquivInverse_obj_functor | Mathlib.CategoryTheory.Equivalence.Symmetry | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Equivalence",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.Equivalence.instCategory",
"CategoryTheory.Equivalence.symmEquivInverse",
"CategoryTheory.Category.opposite",
"Eq.refl",
"Eq",
"Opposite.unop",
"CategoryTheory.Functor.obj",
... | true |
Std.Http.Internal.ChunkedBuffer.instCoeArrayByteArray | Std.Internal.Http.Internal.ChunkedBuffer | [
"Std.Http.Internal.ChunkedBuffer.ofArray",
"Coe.mk",
"Array",
"ByteArray",
"Std.Http.Internal.ChunkedBuffer",
"Coe"
] | true |
_private.Mathlib.Data.Finset.SymmDiff.0.Finset.mem_symmDiff._simp_1_1 | Mathlib.Data.Finset.SymmDiff | [
"Finset.instUnion",
"Finset",
"Membership.mem",
"Finset.instSetLike",
"propext",
"Finset.mem_union",
"Or",
"Union.union",
"Eq",
"SetLike.instMembership",
"DecidableEq"
] | false |
Std.DHashMap.Raw.Const.all_keys | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"List.all",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.Const.all_keys",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"LawfulHashable",
"Subtype.mk",
"Std.DHashMap.Raw.keys",
"EquivBEq",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Bool",
"Std.DHashM... | true |
Int.fmod_fmod | Init.Data.Int.DivMod.Lemmas | [
"Dvd.dvd",
"congrArg",
"Int",
"Int.fmod",
"Int.dvd_refl._simp_1",
"Int.instDvd",
"Int.fmod_fmod_of_dvd",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans"
] | true |
CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux | Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify | [
"PresheafOfModules.map",
"PresheafOfModules.Sheafify.app_eq_of_isLocallyInjective",
"Eq.mpr",
"CategoryTheory.NatTrans.naturality_apply",
"CategoryTheory.Functor",
"instHSMul",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"ModuleCat",
"Categ... | true |
CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo | [
"CategoryTheory.Pseudofunctor.StrongTrans.naturality",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Pseudofunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"... | true |
CategoryTheory.ShortComplex.Splitting.ofIsIsoOfIsZero._proof_4 | Mathlib.Algebra.Homology.ShortComplex.Exact | [
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Limits.comp_zero",
"AddCommGroup.toAddGroup",
"CategoryTheory.I... | false |
_private.Lean.Compiler.LCNF.StructProjCases.0.Lean.Compiler.LCNF.StructProjCases.findStructCtorInfo?._sparseCasesOn_9 | Lean.Compiler.LCNF.StructProjCases | [
"Lean.ConstantInfo.recInfo",
"Lean.ConstantInfo.defnInfo",
"Lean.ConstructorVal",
"Nat.ne_of_beq_eq_false",
"Lean.QuotVal",
"Lean.ConstantInfo.inductInfo",
"Lean.ConstantInfo.opaqueInfo",
"Nat.shiftRight",
"Lean.ConstantInfo.thmInfo",
"Nat.hasNotBit",
"Lean.ConstantInfo.rec",
"instOfNatNat",
... | false |
CategoryTheory.MorphismProperty.Comma.Hom.ext' | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MorphismProperty.Comma.instCategory",
"CategoryTheory.Comma.left",
"CategoryTheory.Comma",
"CategoryTheory.commaCategory",
... | true |
Finset.filter_le_eq_Ici | Mathlib.Order.Interval.Finset.Basic | [
"Finset.mem_filter._simp_1",
"LocallyFiniteOrderTop",
"Finset.univ",
"congrArg",
"Finset",
"Finset.mem_Ici._simp_2",
"Finset.ext",
"Preorder.toLE",
"Membership.mem",
"Finset.Ici",
"LE.le",
"iff_self",
"And",
"Iff",
"Fintype",
"Finset.instSetLike",
"DecidablePred",
"congr",
"True"... | true |
SzemerediRegularity.stepBound_mono | Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | [
"MulOne.toOne",
"SzemerediRegularity.stepBound",
"of_decide_eq_true",
"Monoid.toMulOneClass",
"Nat.instMonoid",
"Monotone",
"Preorder.toLE",
"id",
"instMulNat",
"instOfNatNat",
"Nat.instMulLeftMono",
"LE.le",
"Monoid.toPow",
"Bool.true",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat.inst... | true |
contDiff_id | Mathlib.Analysis.Calculus.ContDiff.Basic | [
"IsBoundedLinearMap.contDiff",
"NormedSpace",
"NormedSpace.toModule",
"NormedField.toField",
"id",
"ContDiff",
"Field.toSemifield",
"IsBoundedLinearMap.id",
"Semifield.toDivisionSemiring",
"ENat",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedFiel... | true |
_private.Mathlib.Algebra.ContinuedFractions.Computation.Approximations.0.GenContFract.fib_le_of_contsAux_b._proof_1_1 | Mathlib.Algebra.ContinuedFractions.Computation.Approximations | [
"False",
"Lean.Grind.not_not",
"of_decide_eq_true",
"Nat.Simproc.add_le_gt",
"Classical.byContradiction",
"False.casesOn",
"instOfNatNat",
"LE.le",
"instLENat",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Lean.Grind.intro_with_eq",
"instAddNat",
"E... | false |
Std.DTreeMap.getKey!_eq_of_mem | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.getKey!",
"Ord.mk",
"Membership.mem",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.instMembership",
"Std.LawfulEqCmp",
"Std.DTreeMap.wf",
"Inhabited",
"Std.DTreeMap.Internal.Impl.getKey!_eq_of_mem",
"Eq"
] | true |
Subring.copy._proof_4 | Mathlib.Algebra.Ring.Subring.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Subring.toSubsemiring",
"Subring.instSetLike",
"AddMonoid.toAddZeroClass",
"Submonoid.toSubsemigroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"NonAssocRing",
"AddCommMonoidWithOne.toAddMonoidWi... | false |
HNNExtension.toSubgroup_neg_one | Mathlib.GroupTheory.HNNExtension | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Group",
"Units.instNeg",
"Units",
"Subgroup",
"Int",
"Units.instOne",
"Int.instMonoid",
"NonUnitalNonAssocRing.toHasDistribNeg",
"Int.instCommRing",
"HNNExtension.toSubgroup",
"NonUnitalNonAssocCommRing.toNonUn... | true |
_private.Mathlib.MeasureTheory.Measure.Tight.0.MeasureTheory.exists_measure_iUnion_gt_of_isCompact_closure._simp_1_12 | Mathlib.MeasureTheory.Measure.Tight | [
"NNReal.instTopologicalSpace",
"Preorder.toLE",
"nhds",
"MeasureTheory.ProbabilityMeasure",
"NNReal",
"MeasureTheory.ProbabilityMeasure.tendsto_measure_iUnion_accumulate",
"Filter.atTop",
"MeasurableSpace",
"Set.accumulate",
"Filter.Tendsto",
"Filter.IsCountablyGenerated",
"MeasureTheory.Proba... | false |
ZMod.val_neg_of_ne_zero | Mathlib.Data.ZMod.Basic | [
"NegZeroClass.toNeg",
"Nat.instMulZeroClass",
"ZMod.commRing",
"eq_false",
"congrArg",
"CommSemiring.toSemiring",
"ZMod.decidableEq",
"HSub.hSub",
"ZMod.neg_val",
"instSubNat",
"SubtractionMonoid.toSubNegZeroMonoid",
"instOfNatNat",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid... | true |
String.ofList_eq_empty_iff | Init.Data.String.Basic | [
"String.toList_ofList",
"Eq.mpr",
"String.toList_inj",
"congrArg",
"String",
"Iff.rfl",
"id",
"String.toList_empty",
"List",
"Iff",
"String.toList",
"propext",
"Char",
"Eq.symm",
"Eq",
"String.ofList",
"List.nil"
] | true |
_private.Batteries.Data.String.Lemmas.0.Substring.Raw.Valid.prevn.match_1_3 | Batteries.Data.String.Lemmas | [
"Exists",
"Substring.Raw.ValidFor",
"Substring.Raw",
"List",
"Exists.casesOn",
"Exists.intro",
"Char"
] | false |
Module.End.instDivisionRing._proof_12 | Mathlib.RingTheory.SimpleModule.Basic | [
"Module.End.instRing",
"Semiring.toNatCast",
"NNRat.castRec",
"LinearEquiv.symm",
"Semigroup.toMul",
"HMul.hMul",
"AddCommGroup.toAddCommMonoid",
"Module.End.instDivisionRing._proof_8",
"AddCommGroup",
"NNRatCast.mk",
"IsSimpleModule",
"NNRat",
"DivInvMonoid.div'",
"Div.mk",
"dite",
"L... | false |
CompleteDistribLattice.toSDiff | Mathlib.Order.CompleteBooleanAlgebra | [
"CompleteDistribLattice",
"SDiff"
] | true |
CategoryTheory.Limits.IsLimit.whiskerEquivalence | Mathlib.CategoryTheory.Limits.IsLimit | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.IsLimit.ofRightAdjoint",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Limits.Cone.whiskeringEquivalence",
"CategoryThe... | true |
Lean.Meta.Grind.AC.EqCnstrProof.core.injEq | Lean.Meta.Tactic.Grind.AC.Types | [
"Eq.propIntro",
"Lean.Grind.AC.Expr",
"Lean.injEq_helper",
"Lean.Expr",
"Lean.Meta.Grind.AC.EqCnstrProof",
"Lean.Meta.Grind.AC.EqCnstrProof.core",
"And",
"Eq.ndrec",
"Eq.refl",
"Lean.Meta.Grind.AC.EqCnstrProof.core.inj",
"Eq"
] | true |
instFintypeAddEquivInt._proof_2 | Mathlib.GroupTheory.ArchimedeanDensely | [
"Int.instAddCommGroup",
"NegZeroClass.toNeg",
"False",
"Int.ctorIdx",
"AddMonoid.toAddSemigroup",
"congrArg",
"Finset",
"False.elim",
"noConfusion_of_Nat",
"Membership.mem",
"AddEquiv.neg",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"Int.instAddMonoid",
"SubNegZeroMonoid.toNegZeroCla... | false |
ProperSpace.mk._flat_ctor | Mathlib.Topology.MetricSpace.ProperSpace | [
"Real",
"PseudoMetricSpace.toUniformSpace",
"ProperSpace",
"PseudoMetricSpace",
"ProperSpace.mk",
"Metric.closedBall",
"UniformSpace.toTopologicalSpace",
"IsCompact"
] | false |
isRelLowerSet_self._simp_1 | Mathlib.Order.UpperLower.Relative | [
"IsRelLowerSet",
"Membership.mem",
"LE",
"True",
"eq_true",
"isRelLowerSet_self",
"Eq",
"Set.instMembership",
"Set"
] | false |
Equiv.commSemigroup.eq_1 | Mathlib.Algebra.Group.TransferInstance | [
"Equiv.instEquivLike",
"Equiv",
"Equiv.commSemigroup",
"CommMagma.toMul",
"CommSemigroup",
"Equiv.commSemigroup._proof_1",
"Function.Injective.commSemigroup",
"Equiv.mul",
"CommSemigroup.toCommMagma",
"Eq.refl",
"Equiv.injective",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
tsum_eq_sum' | Mathlib.Topology.Algebra.InfiniteSum.Basic | [
"Eq.mpr",
"congrArg",
"Finset",
"finsum",
"AddMonoid.toAddZeroClass",
"SummationFilter",
"tsum_eq_finsum",
"AddZeroClass.toAddZero",
"id",
"HasSubset.Subset",
"Set.Finite.subset",
"AddCommMonoid",
"TopologicalSpace",
"AddZero.toZero",
"SetLike.coe",
"Finset.instSetLike",
"tsum",
"f... | true |
AlgebraicGeometry.Scheme.germToFunctionField._proof_1 | Mathlib.AlgebraicGeometry.FunctionField | [
"Eq.mpr",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"congrArg",
"CommRingCat",
"Set.univ",
"TopologicalSpace.Opens",
"Eq.mp",
"CommRingCat.instCategory",
"id",
"Set.instInter",
"Set.univ_inter... | false |
Finset.Nonempty.norm_prod_le_sup'_norm | Mathlib.Analysis.Normed.Group.Ultra | [
"_private.Mathlib.Analysis.Normed.Group.Ultra.0.Finset.Nonempty.norm_prod_le_sup'_norm._simp_1_5",
"Norm.norm",
"Eq.mpr",
"Exists.choose_spec",
"Real.instLE",
"Real",
"HMul.hMul",
"Finset.prod_singleton",
"Monoid.toMulOneClass",
"Finset.cons",
"congrArg",
"Finset",
"Real.instSemilatticeSup",... | true |
Prefunctor.IsCovering.comp | Mathlib.Combinatorics.Quiver.Covering | [
"Prefunctor.costar",
"Prefunctor.IsCovering.star_bijective",
"Prefunctor.comp",
"Quiver.Star",
"Prefunctor.IsCovering.costar_bijective",
"Prefunctor.IsCovering",
"Prefunctor",
"Quiver",
"Prefunctor.IsCovering.mk",
"Quiver.Costar",
"Function.Bijective.comp",
"Prefunctor.star",
"Prefunctor.obj... | true |
Int.existsUnique_equiv | Mathlib.Data.Int.ModEq | [
"Int.emod_lt_abs",
"Dvd.dvd",
"abs",
"congrArg",
"PartialOrder.toPreorder",
"semigroupDvd",
"Exists",
"SemilatticeInf.toPartialOrder",
"Eq.mp",
"ne_of_gt",
"instHMod",
"dvd_refl._simp_1",
"Int",
"LE.le",
"Int.instMonoid",
"Int.instLTInt",
"HMod.hMod",
"And",
"instOfNat",
"Int.M... | true |
padicNormE._proof_4 | Mathlib.NumberTheory.Padics.PadicNumbers | [
"padicNorm.instIsAbsoluteValueRat",
"NormedCommRing.toNormedRing",
"Nat.Prime",
"NormedRing.toRing",
"PadicSeq.norm_nonneg",
"Rat",
"PartialOrder.toPreorder",
"Rat.linearOrder",
"Preorder.toLE",
"Fact",
"LE.le",
"Quotient.inductionOn",
"Rat.instNormedField",
"Rat.instField",
"Nat",
"Ca... | false |
List.head?_range' | Init.Data.List.Range | [
"List.head?",
"False",
"Nat.recAux",
"congrArg",
"False.elim",
"List.range'",
"noConfusion_of_Nat",
"Option.some",
"instOfNatNat",
"ite_cond_eq_true",
"Option.none",
"instHAdd",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Nat.ctorIdx",
"instAddNat",
"instDecidableEqNa... | true |
RCLike.nnnorm_nsmul | Mathlib.Analysis.RCLike.Basic | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"NormedRing.toRing",
"HMul.hMul",
"NormedSpace",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"SeminormedAddGroup.toNNNorm",
... | true |
HomologicalComplex.mapBifunctor₁₂.ι_D₂_assoc | Mathlib.Algebra.Homology.BifunctorAssociator | [
"HomologicalComplex.mapBifunctor₁₂.ι",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"CategoryTheory.func... | true |
LieRinehartAlgebra.Hom.apply_lie | Mathlib.Algebra.LieRinehartAlgebra.Defs | [
"LieHom",
"CommRing",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AlgHom",
"AlgHom.funLike",
"Bracket.bracket",
"Algebra",
"LieRingModule.toBracket",
"LieRinehartAlgebra.Hom.toLieHom",
"LieRing",
"CommRing.toCommSemiring",
"LieRingModule",
"LieRi... | true |
TopologicalSpace.NonemptyCompacts.discreteTopology_iff | Mathlib.Topology.Sets.VietorisTopology | [
"TopologicalSpace.NonemptyCompacts",
"DiscreteTopology",
"TopologicalSpace.NonemptyCompacts.isEmbedding_singleton",
"inferInstance",
"Topology.IsEmbedding.discreteTopology",
"TopologicalSpace",
"TopologicalSpace.NonemptyCompacts.instDiscreteTopology",
"Iff",
"Iff.intro",
"TopologicalSpace.Nonempty... | true |
Batteries.UnionFind.FindAux.mk.congr_simp | Batteries.Data.UnionFind.Basic | [
"Batteries.UnionFind.FindAux.mk",
"Batteries.UFNode",
"Eq.rec",
"Array",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Fin",
"Batteries.UnionFind.FindAux",
"Eq",
"Array.size"
] | true |
UniformOnFun.hasBasis_uniformity_of_basis_aux₁ | Mathlib.Topology.UniformSpace.UniformConvergenceTopology | [
"UniformSpace",
"Eq.mpr",
"UniformOnFun.gen_eq_preimage_restrict",
"Equiv.instEquivLike",
"UniformOnFun.gen",
"congrArg",
"uniformity",
"Function.comp",
"Set.Elem",
"id",
"Equiv",
"UniformFun.uniformSpace",
"UniformFun.gen",
"Prod.map",
"UniformFun.hasBasis_uniformity_of_basis",
"Unifo... | true |
Set.mem_nsmul._simp_1 | Mathlib.Algebra.Group.Pointwise.Set.ListOfFn | [
"instHSMul",
"AddMonoid.toAddZeroClass",
"List.sum",
"List.ofFn",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"Set.Elem",
"AddZero.toZero",
"Set.mem_nsmul",
"Nat",
"AddMonoid",
"propext",
"AddZero.toAdd",
"HSMul.hSMul",
"Set.NSMul",
"Fin",
"Subtype.val",
"Eq",
"Set.in... | false |
_private.Mathlib.Topology.DerivedSet.0.isClosed_derivedSet._simp_1_1 | Mathlib.Topology.DerivedSet | [
"isClosed_iff_derivedSet_subset",
"HasSubset.Subset",
"derivedSet",
"IsClosed",
"TopologicalSpace",
"propext",
"Eq.symm",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
Complement.rec | Init.Prelude | [
"Complement.mk",
"Complement"
] | false |
_private.Std.Data.DHashMap.Internal.WF.0.Std.DHashMap.Raw.fold.eq_1 | Std.Data.DHashMap.Internal.WF | [
"Pure.pure",
"Monad.toApplicative",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.fold",
"Id.run",
"Id",
"Applicative.toPure",
"Eq.refl",
"Std.DHashMap.Raw.foldM",
"Id.instMonad",
"Eq"
] | true |
CategoryTheory.Limits.Sigma.π | Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms | [
"CategoryTheory.Limits.HasZeroMorphisms",
"Function.update",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.HasCoproduct",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"Zero.toOfNat0",
"CategoryTheory.Category.toCategoryStruct",
... | true |
LowerSet.Iic_sup_erase | Mathlib.Order.UpperLower.Closure | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"LowerSet.completeLattice",
"congrArg",
"Preorder.toLE",
"Membership.mem",
"SemilatticeSup.toMax",
"id",
"LowerSet.erase_sup_Iic",
"LE.le",
"LowerSet.instMax",
"sup_comm",
"Max.max",
"LowerSet.erase",
"Eq.refl",
"Lowe... | true |
Mathlib.Tactic.BicategoryCoherence.LiftHom₂.casesOn | Mathlib.Tactic.CategoryTheory.BicategoryCoherence | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.FreeBicategory.of",
"CategoryTheory.FreeBicategory.homCategory",
"Mathlib.Tactic.BicategoryCoherence.LiftHom",
"CategoryTheory.Bicategory.toCategoryStruct",
"Mathlib.Tactic.BicategoryCoherence.LiftHom₂.mk",
"Mathlib.Tactic.Bicateg... | false |
instIsTransOfIsWellOrder | Mathlib.Order.RelClasses | [
"asymm_of",
"instAsymmOfIsWellFounded",
"IsTrans.mk",
"False.elim",
"IsWellOrder",
"IsTrans",
"IsWellFounded.wf",
"Or.casesOn",
"IsWellOrder.toIsWellFounded",
"WellFounded.asymmetric₃",
"Eq.ndrec",
"Or",
"trichotomous_of",
"Eq",
"IsWellOrder.toTrichotomous"
] | true |
Path.add_apply | Mathlib.Topology.Path | [
"Real",
"Set.Elem",
"Path.add",
"TopologicalSpace",
"instHAdd",
"HAdd.hAdd",
"Path.instFunLike",
"Path",
"Eq.refl",
"ContinuousAdd",
"Eq",
"DFunLike.coe",
"unitInterval",
"Add"
] | true |
QuadraticAlgebra.instMul | Mathlib.Algebra.QuadraticAlgebra.Defs | [
"QuadraticAlgebra.re",
"Mul.mk",
"HMul.hMul",
"QuadraticAlgebra",
"Mul",
"instHAdd",
"HAdd.hAdd",
"QuadraticAlgebra.im",
"QuadraticAlgebra.mk",
"Add",
"instHMul"
] | true |
AddConstEquiv._sizeOf_inst | Mathlib.Algebra.AddConstMap.Equiv | [
"AddConstEquiv",
"SizeOf.mk",
"AddConstEquiv._sizeOf_1",
"SizeOf",
"Add"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.Coalgebra.0.InnerProductSpace.ringOfCoalgebra._simp_2 | Mathlib.Analysis.InnerProductSpace.Coalgebra | [
"LinearMap.instFunLike",
"RingHom",
"LinearMap.comp_apply",
"RingHomCompTriple",
"LinearMap",
"AddCommMonoid",
"LinearMap.comp",
"Semiring",
"Module",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe"
] | false |
MeasureTheory.uniformIntegrable_average | Mathlib.MeasureTheory.Function.UniformIntegrable | [
"ENNReal.instCanonicallyOrderedAdd",
"CharP.cast_eq_zero",
"Iff.mpr",
"zero_le",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MeasureTheory.AEStronglyMeasurable.const_smul",
"Nat.instMulZeroClass",
"Real.partialOrder",
... | true |
MonoidHom.mker_inr | Mathlib.Algebra.Group.Submonoid.Operations | [
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom.mker",
"MonoidHom.inr",
"MonoidHom",
"congrArg",
"Submonoid.mem_bot._simp_2",
"Prod.instMulOneClass",
"Membership.mem",
"Prod.mk",
"Bot.bot",
"Submonoid.ext",
"Prod.mk_eq_one._simp_2",
"iff_self",
"MulO... | true |
_private.Init.Data.BitVec.Bitblast.0.BitVec.saddOverflow_eq._simp_1_3 | Init.Data.BitVec.Bitblast | [
"Decidable",
"Bool.decide_and",
"Bool.and",
"And",
"Bool",
"Eq.symm",
"Decidable.decide",
"Eq"
] | false |
PFunctor.Approx.AllAgree | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor",
"PFunctor.Approx.Agree",
"PFunctor.Approx.CofixA",
"Nat",
"Nat.succ"
] | true |
ComplexShape.decidableRelSymm | Mathlib.Algebra.Homology.ComplexShape | [
"decidable_of_iff",
"DecidableRel",
"ComplexShape",
"ComplexShape.symm",
"ComplexShape.Rel",
"ComplexShape.decidableRelSymm._proof_1"
] | true |
_private.Lean.Elab.Tactic.Simp.0.Lean.Elab.Tactic.elabSimpConfig.match_1 | Lean.Elab.Tactic.Simp | [
"Unit.unit",
"Lean.Elab.Tactic.SimpKind.casesOn",
"Unit",
"Lean.Elab.Tactic.SimpKind.simp",
"Lean.Elab.Tactic.SimpKind.dsimp",
"Lean.Elab.Tactic.SimpKind.simpAll",
"Lean.Elab.Tactic.SimpKind"
] | false |
_private.Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage.0.circleAverage_log_norm_sub_const₂._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage | [
"Real.instLE",
"Real",
"Membership.mem",
"LE.le",
"PseudoMetricSpace",
"propext",
"Metric.mem_closedBall",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Metric.closedBall",
"Eq",
"Set.instMembership",
"Set"
] | false |
CategoryTheory.Functor.instIsEquivalenceOppositeOp | Mathlib.CategoryTheory.Opposites | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.IsEquivalence.full",
"CategoryTheory.Functor.instEssSurjOppositeOp",
"CategoryTheory.Functor.instFaithfulOppositeOp",
"inferInstance",
"CategoryTheory.Functor.IsEquivalence.mk",
"CategoryTheory.Functor.IsEquiv... | true |
Std.Sat.AIG.relabel | Std.Sat.AIG.Relabel | [
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.Cache",
"Std.Sat.AIG.relabel._proof_1",
"Std.Sat.AIG.relabel._proof_7",
"Array.map",
"Array",
"Std.Sat.AIG.Decl.relabel",
"Std.Sat.AIG",
"Std.Sat.AIG.Cache.empty",
"Std.Sat.AIG.relabel._proof_2",
"Hashable",
"Std.Sat.AIG.decls",
"Std.Sat.AIG.mk",
"Decidable... | true |
CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.HasFirstPageComputation.recOn | Mathlib.Algebra.Homology.SpectralObject.FirstPage | [
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.i₃",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.i₀",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.HasFirstPageComputation.mk",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.HasFirstPageCom... | false |
CoalgCat.instMonoidalCategoryStruct._proof_1 | Mathlib.Algebra.Category.CoalgCat.Monoidal | [
"CoalgCat.toModuleCat",
"CommRing",
"CoalgCat",
"instSMulOfMul",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"MulOne.toMul",
"IsScalarTower.left",
"MulOneClass.toMulOne",
"CommRing.toCommSemiring",
"ModuleCat.isAddCommGroup",
"ModuleC... | false |
Lean.Server.Watchdog.RequestQueueMap.rec | Lean.Server.Watchdog | [
"Lean.Json",
"Ord.compare",
"Lean.JsonRpc.instOrdRequestID",
"Nat",
"Lean.JsonRpc.Request",
"instOrdNat",
"Prod",
"Lean.JsonRpc.RequestID",
"Lean.Server.Watchdog.RequestQueueMap.mk",
"Std.TreeMap",
"Lean.Server.Watchdog.RequestQueueMap"
] | false |
HomotopicalAlgebra.fibrations_eq_unop | Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | [
"CategoryTheory.MorphismProperty",
"HomotopicalAlgebra.fibrations",
"Opposite",
"CategoryTheory.MorphismProperty.unop",
"HomotopicalAlgebra.instCategoryWithCofibrationsOpposite",
"HomotopicalAlgebra.cofibrations",
"CategoryTheory.Category.opposite",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
... | true |
isEmpty_fintype._simp_1 | Mathlib.Data.Fintype.EquivFin | [
"IsEmpty",
"Fintype",
"propext",
"Infinite",
"Eq",
"isEmpty_fintype"
] | false |
Std.DTreeMap.Internal.Impl.link2._proof_19 | Std.Data.DTreeMap.Internal.Operations | [
"_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.link2._proof_18",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.inner",
"Nat",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | false |
Homotopy.ext | Mathlib.Algebra.Homology.Homotopy | [
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"Homotopy.zero._autoParam",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Homotopy.hom",
"HomologicalComplex",
"AddZeroCl... | true |
ContinuousLinearMap.cont._autoParam | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Lean.Name.mkStr3",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Lean.Data.Json.Printer.0.Lean.Json.needEscape.go._proof_3 | Lean.Data.Json.Printer | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"String",
"InvImage",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.... | false |
Lean.Elab.ComputedFields.Context.compFieldVars | Lean.Elab.ComputedFields | [
"Lean.Expr",
"Array",
"Lean.Elab.ComputedFields.Context"
] | true |
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