name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ContinuousAlgHom.mk.injEq | Mathlib.Topology.Algebra.Algebra | [
"MulOne.toOne",
"Continuous",
"Eq.propIntro",
"ContinuousAlgHom.mk.inj",
"AlgHom",
"Algebra",
"NonAssocSemiring.toMulZeroOneClass",
"autoParam",
"MulZeroOneClass.toMulOneClass",
"CommSemiring",
"TopologicalSpace",
"MulOneClass.toMulOne",
"OneHom.toFun",
"AlgHom.toRingHom",
"ContinuousAlg... | true |
IsPrimitiveRoot.powerBasis_gen_mem_adjoin_zeta_sub_one | Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots | [
"Subalgebra.instSetLike",
"Eq.mpr",
"IsDomain",
"Polynomial.instOne",
"Nat.instMulZeroClass",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"AlgHom.algHomClass",
"CommRing.toNonUnitalCommRing",
"NonUnitalAlgHomClass.instLinearMapClass",
"AddGroupWithOne.toAd... | true |
Lean.Meta.Simp.preSEval | Lean.Meta.Tactic.Simp.Rewrite | [
"Lean.Meta.Simp.simpMatch",
"HAndThen.hAndThen",
"instHAndThenOfAndThen",
"Lean.Meta.Simp.rewritePre",
"Unit",
"Lean.Meta.Simp.userPreSimprocs",
"Lean.Meta.Simp.SimprocsArray",
"Lean.Meta.Simp.instAndThenSimproc",
"Bool.false",
"Lean.Meta.Simp.Simproc"
] | true |
Set.disjoint_empty._simp_1 | Mathlib.Data.Set.Disjoint | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Set.instDistribLattice",
"Set.instBoundedOrder",
"BoundedOrder.toOrderBot",
"True",
"Set.disjoint_empty",
"eq_true",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollecti... | false |
pow_gcd_card_eq_one_iff | Mathlib.GroupTheory.OrderOfElement | [
"Nat.gcd",
"pow_card_eq_one",
"MulOne.toOne",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"and_true",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Fintype.card",
"DivInvMonoid.toMonoid",
"Monoid.toPow",
"Group.toDiv... | true |
_private.Mathlib.Combinatorics.Additive.FreimanHom.0.isMulFreimanHom_antitone.match_1_4 | Mathlib.Combinatorics.Additive.FreimanHom | [
"Membership.mem",
"Exists",
"Multiset",
"Multiset.instMembership",
"Exists.casesOn",
"Exists.intro"
] | false |
Lean.Meta.DeltaStepResult.eq.sizeOf_spec | Lean.Meta.ExprDefEq | [
"Lean.Meta.DeltaStepResult.eq",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Meta.DeltaStepResult",
"Lean.Meta.DeltaStepResult._sizeOf_inst"
] | true |
CategoryTheory.ShortComplex.exact_iff_iCycles_pOpcycles_zero | Mathlib.Algebra.Homology.ShortComplex.Exact | [
"CategoryTheory.ShortComplex.opcycles",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.leftHomologyData",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"CategoryTheory.ShortComplex.pOpcycles",
... | true |
CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.isInitialIsTerminalIso'_hom_left | Mathlib.CategoryTheory.Monoidal.PushoutProduct | [
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.isInitialIso._proof_2",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.IsPushout.isoPushout",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg... | true |
_private.Mathlib.CategoryTheory.Skeletal.0.CategoryTheory.Functor.instFullSkeletonMapSkeleton._proof_1 | Mathlib.CategoryTheory.Skeletal | [
"CategoryTheory.Functor",
"CategoryTheory.Equivalence.full_functor",
"CategoryTheory.Functor.comp",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.Functor.mapSkeleton",
"CategoryTheory.instCategorySkeleton",
"CategoryTheory.skeletonEquivalence",
"CategoryTheory.Equivalence.full_inverse",
"Cat... | false |
Finset.Ioc_eq_empty | Mathlib.Order.Interval.Finset.Basic | [
"Iff.mpr",
"Preorder.toLT",
"Finset",
"Finset.Ioc_eq_empty_iff",
"Finset.instEmptyCollection",
"LT.lt",
"LocallyFiniteOrder",
"EmptyCollection.emptyCollection",
"Eq",
"Not",
"Preorder",
"Finset.Ioc"
] | true |
exteriorPower.map_id | Mathlib.LinearAlgebra.ExteriorPower.Basic | [
"LinearMap.id",
"AlternatingMap",
"Submodule",
"CommRing",
"Semiring.toModule",
"QuadraticMap.instZero",
"Ring.toNonAssocRing",
"ExteriorAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"instAlgebraCliffordAlgebra",
"exteriorPower.... | true |
USize.toFin_ofNatTruncate_of_le._proof_1 | Init.Data.UInt.Lemmas | [
"congrArg",
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"Nat.lt_add_one._simp_1",
"Or.casesOn",
"USize.size_eq",
"instHSub",
"Nat",
"congr",
"LT.lt",
"True",
"of_eq_true",
"Eq.refl",
"congrFun'",
"Or.inl",
"Or",
"USize.size",
"instLTNat",
"OfNat.ofNat",
"Eq",
"Or.inr",
"Eq... | false |
QPF.Wequiv.below.trans | Mathlib.Data.QPF.Univariate.Basic | [
"QPF.Wequiv.trans",
"QPF.Wequiv.below",
"QPF",
"PFunctor.W",
"QPF.Wequiv",
"QPF.Wequiv.below.trans",
"QPF.P"
] | true |
Subalgebra.mopAlgEquivOp_apply_coe | Mathlib.Algebra.Algebra.Subalgebra.MulOpposite | [
"Subalgebra.instSetLike",
"Subsemiring.instSetLike",
"Subalgebra.mopAlgEquivOp",
"MulOpposite.instAlgebra",
"MulOpposite",
"Algebra",
"Membership.mem",
"Subtype",
"Subalgebra.toSubsemiring",
"Subalgebra.op",
"NonAssocSemiring.toMulZeroOneClass",
"Subsemiring.toSubmonoid",
"Subsemiring",
"M... | true |
LinearMap.BilinForm.apply_dualBasis_left | Mathlib.LinearAlgebra.BilinearForm.Properties | [
"Finsupp.instFunLike",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"LinearEquiv.symm",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Finsupp.module",
"Module.Basis.coe_dualBasis",
"Module.Basis.coord",
"LinearMap.BilinForm.dualBasis._proof_3",
"LinearMap.BilinForm.dualBasis._proof_2... | true |
addMonoidHomLequivInt._proof_1 | Mathlib.Algebra.Module.Equiv.Basic | [
"LinearMap.toAddMonoidHom",
"Function.LeftInverse",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Int",
"LinearMap",
"AddGroup.toSubNegMonoid",
"AddCommGroup.toIntModule",
"Eq.refl",
"SubNegMonoid.toAddMonoid... | false |
Module.Basis.linearIndepOn | Mathlib.LinearAlgebra.Basis.Basic | [
"LinearIndependent.linearIndepOn",
"Module.Basis.instFunLike",
"AddCommMonoid",
"Module.Basis",
"Module.Basis.linearIndependent",
"Semiring",
"Module",
"DFunLike.coe",
"LinearIndepOn",
"Set"
] | true |
CategoryTheory.MonoOver.mapIso._proof_7 | Mathlib.CategoryTheory.Subobject.MonoOver | [
"CategoryTheory.Mono",
"CategoryTheory.Iso",
"CategoryTheory.mono_of_strongMono",
"CategoryTheory.Iso.isIso_inv",
"CategoryTheory.Iso.isIso_hom",
"CategoryTheory.mono_comp",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.strongMono_of_isIso",
"Cat... | false |
Std.DTreeMap.Internal.Impl.get!_insertMany_empty_list_of_contains_eq_false | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Inhabited.default",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"congrArg",
"instForInOfForIn'",
"List.map",
"Std.TransOrd",
"List.contains",
"Std.DTreeMap.Internal.Impl.Balanced",
"inferInstance",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inse... | true |
AlgebraicGeometry.Scheme.homOfLE_ι_assoc | Mathlib.AlgebraicGeometry.Restrict | [
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme.homOfLE",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartial... | true |
Lean.Lsp.LeanFileProgressParams._sizeOf_1 | Lean.Data.Lsp.Extra | [
"Lean.Lsp.LeanFileProgressParams.rec",
"instOfNatNat",
"Lean.Lsp.LeanFileProgressProcessingInfo",
"Array._sizeOf_inst",
"Array",
"Lean.Lsp.VersionedTextDocumentIdentifier",
"instHAdd",
"HAdd.hAdd",
"Lean.Lsp.LeanFileProgressProcessingInfo._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
... | false |
_private.Mathlib.GroupTheory.ResiduallyFinite.0.Group.residuallyFinite_iff_exists_finiteIndexNormalSubgroup._simp_1_3 | Mathlib.GroupTheory.ResiduallyFinite | [
"propext",
"Eq",
"Not",
"not_imp_not"
] | false |
List.tailD_cons | Init.Data.List.Basic | [
"List.cons",
"List",
"List.tailD",
"Eq",
"rfl"
] | true |
CategoryTheory.ObjectProperty.LimitOfShape._sizeOf_1 | Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape | [
"CategoryTheory.Limits.LimitPresentation",
"CategoryTheory.ObjectProperty.LimitOfShape",
"instOfNatNat",
"instHAdd",
"CategoryTheory.ObjectProperty.LimitOfShape.rec",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"CategoryTheory.Category.toCategoryStruct",
"SizeOf",
"CategoryTheory.Limits... | false |
CategoryTheory.Limits.HasCoreflexiveEqualizers | Mathlib.CategoryTheory.Limits.Shapes.Reflexive | [
"CategoryTheory.Limits.HasCoreflexiveEqualizers.mk",
"CategoryTheory.Category"
] | true |
IsLocalMaxOn.eq_1 | Mathlib.Topology.Order.LocalExtr | [
"nhdsWithin",
"IsLocalMaxOn",
"TopologicalSpace",
"Eq.refl",
"Eq",
"Preorder",
"IsMaxFilter",
"Set"
] | true |
Equiv.Perm.eq_top_of_isMultiplyPretransitive | Mathlib.GroupTheory.GroupAction.MultipleTransitivity | [
"Function.instEmbeddingLikeEmbedding",
"Equiv.Perm.applyMulAction",
"Eq.mpr",
"Fin.ext_iff",
"Fintype.card_fin",
"instHSMul",
"Fintype.ofFinite",
"Preorder.toLT",
"lt_irrefl",
"Equiv.instEquivLike",
"lt_or_eq_of_le",
"eq_top_iff",
"SetLike.coe_mem",
"congrArg",
"False.elim",
"Finite",
... | true |
BitVec.sshiftRightRec.eq_2 | Init.Data.BitVec.Bitblast | [
"BitVec.instAndOp",
"BitVec.sshiftRightRec",
"BitVec",
"BitVec.sshiftRight'",
"Nat",
"BitVec.twoPow",
"Eq.refl",
"HAnd.hAnd",
"Nat.succ",
"Eq",
"instHAndOfAndOp"
] | true |
MeasureTheory.Measure.zero_sub | Mathlib.MeasureTheory.Measure.Sub | [
"MeasureTheory.Measure",
"HSub.hSub",
"MeasureTheory.Measure.instSub",
"MeasureTheory.Measure.instZero",
"MeasurableSpace",
"instHSub",
"MeasureTheory.Measure.zero_le",
"MeasureTheory.Measure.sub_eq_zero_of_le",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.Abelian.SpectralObject.d._proof_5 | Mathlib.Algebra.Homology.SpectralObject.Differentials | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"rfl",
"CategoryTheory.Category"
] | false |
NFA.stepSet.eq_1 | Mathlib.Computability.NFA | [
"NFA.step",
"NFA",
"Membership.mem",
"NFA.stepSet",
"Eq.refl",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | true |
_private.Mathlib.MeasureTheory.Function.UniformIntegrable.0.MeasureTheory.MemLp.eLpNormEssSup_indicator_norm_ge_eq_zero._simp_1_1 | Mathlib.MeasureTheory.Function.UniformIntegrable | [
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict_eq_zero",
"MeasureTheory.Measure.restrict",
"MeasureTheory.Measure.instZero",
"MeasurableSpace",
"ENNReal",
"propext",
"Zero.toOfNat0",
"ENNReal.instZero",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"MeasureTheory.Measure.instFunLike",
"Se... | false |
List.range_ne_nil | Init.Data.List.Range | [
"False",
"congrArg",
"False.elim",
"noConfusion_of_Nat",
"not_true_eq_false",
"Ne",
"instOfNatNat",
"List.range",
"Nat.casesAuxOn",
"iff_self",
"List",
"instHAdd",
"Iff",
"List.range_eq_nil._simp_1",
"HAdd.hAdd",
"Nat",
"congr",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
... | true |
AddCon.liftOn₂.eq_1 | Mathlib.GroupTheory.Congruence.Defs | [
"AddCon.instFunLikeForallProp",
"AddCon",
"AddCon.toSetoid",
"Eq.refl",
"AddCon.liftOn₂",
"AddCon.Quotient",
"Eq",
"DFunLike.coe",
"Add",
"Quotient.liftOn₂'"
] | true |
List.kextract_eq_dlookup_kerase._f | Mathlib.Data.List.Sigma | [
"List.eraseP_cons_of_neg",
"Eq.mpr",
"Eq.recOn",
"False",
"dite_congr",
"instDecidableTrue",
"eq_false",
"congrArg",
"Decidable.decide.congr_simp",
"Bool.false_eq_true",
"Option.some",
"Eq.rec",
"dif_pos",
"id",
"List.dlookup_cons_ne",
"_private.Mathlib.Data.List.Sigma.0.List.kextract_... | false |
_private.Mathlib.SetTheory.Ordinal.Notation.0.ONote.ofNat.match_1.eq_2 | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.ofNat.match_1",
"instOfNatNat",
"Unit",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
Std.DTreeMap.Internal.Impl.maxKey!._proof_2 | Std.Data.DTreeMap.Internal.Queries | [
"Lean.RArray.leaf",
"invImage",
"Nat.lt_add_left_iff_pos._simp_1",
"instSizeOfDefault",
"Nat.Linear.ExprCnstr.eq_true_of_isValid",
"Lean.RArray.branch",
"namedPattern",
"Std.DTreeMap.Internal.Impl.inner",
"id",
"instOfNatNat",
"LE.le",
"sizeOfWFRel",
"instLENat",
"Nat.Linear.Expr.num",
"... | false |
_private.Mathlib.Algebra.Ring.Defs.0.ite_zero_mul_ite_zero._simp_1_2 | Mathlib.Algebra.Ring.Defs | [
"and_comm",
"And",
"propext",
"Eq"
] | false |
ZMod.subsingleton_ringHom | Mathlib.Data.ZMod.Basic | [
"ZMod.commRing",
"CommSemiring.toSemiring",
"RingHom",
"ZMod",
"RingHom.ext_zmod",
"CommRing.toCommSemiring",
"Subsingleton.intro",
"Nat",
"Semiring",
"Subsingleton",
"Semiring.toNonAssocSemiring"
] | true |
Manifold.IsImmersionAtOfComplement.prodMap | Mathlib.Geometry.Manifold.Immersion | [
"_private.Mathlib.Geometry.Manifold.Immersion.0.Manifold.ImmersionAtProp._proof_1",
"Set.instSProd",
"Eq.mpr",
"Prod.normedSpace",
"SeminormedAddGroup.toAddGroup",
"Prod.normedAddCommGroup",
"NormedSpace",
"Set.eqOn_prod_iff",
"SProd.sprod",
"congrArg",
"PartialEquiv.prod",
"AddCommGroup.toAdd... | true |
MulOpposite.instAddSemigroup | Mathlib.Algebra.Group.Opposite | [
"MulOpposite.instAddSemigroup._proof_1",
"MulOpposite",
"AddSemigroup",
"Function.Injective.addSemigroup",
"AddSemigroup.toAdd",
"MulOpposite.instAdd",
"MulOpposite.unop",
"MulOpposite.unop_injective"
] | true |
CategoryTheory.Functor.mapBifunctorHomologicalComplexObj._proof_10 | Mathlib.Algebra.Homology.Bifunctor | [
"CategoryTheory.Functor.mapBifunctorHomologicalComplexObj._proof_5",
"Eq.mpr",
"HomologicalComplex.hom_ext",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"HomologicalComplex₂.ofGradedObject",
"HomologicalComplex.Hom.f",
"CategoryTheory.Catego... | false |
YoungDiagram.mk_mem_row_iff | Mathlib.Combinatorics.Young.YoungDiagram | [
"Finset.mem_filter._simp_1",
"YoungDiagram",
"and_true",
"congrArg",
"Finset",
"Membership.mem",
"YoungDiagram.cells",
"Prod.mk",
"Prod.fst",
"iff_self",
"And",
"Iff",
"Finset.instSetLike",
"Nat",
"YoungDiagram.row",
"congr",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"ins... | true |
ENNReal.ofNNReal | Mathlib.Data.ENNReal.Basic | [
"NNReal",
"WithTop.some",
"ENNReal"
] | true |
Std.ExtTreeMap.maxKey?_eq_some_maxKeyD | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtTreeMap.maxKey?",
"Option.some",
"Std.ExtTreeMap.mk",
"Ordering",
"mt",
"Ne",
"Std.ExtDTreeMap.instEmptyCollection",
"Std.TransCmp",
"Std.ExtDTreeMap.maxKey?_eq_some_maxKeyD",
"Std.ExtTreeMap",
"_private.Std.Data.ExtTreeMap.Lemmas.0.Std.ExtTreeMap.ext",
"Std.ExtTreeMap.inner",
"Std.E... | true |
addCommutator | Mathlib.GroupTheory.Commutator.Basic | [
"AddSubgroup.addCommutator",
"Bracket.bracket",
"AddSubgroup",
"AddGroup",
"Top.top",
"AddSubgroup.instTop"
] | true |
Lean.Doc.Data.Tactic.mk.injEq | Lean.Elab.DocString.Builtin | [
"Lean.Doc.Data.Tactic",
"Eq.propIntro",
"Lean.Doc.Data.Tactic.mk.inj",
"Eq.ndrec",
"Lean.Doc.Data.Tactic.mk",
"Lean.Name",
"Eq.refl",
"Eq"
] | true |
List.maximum_mem | Mathlib.Data.List.MinMax | [
"List.maximum",
"WithBot.some",
"WithBot",
"Preorder.toLT",
"List.argmax_mem",
"Membership.mem",
"id",
"List",
"List.instMembership",
"Eq",
"DecidableLT",
"Preorder"
] | true |
_private.Mathlib.RingTheory.MvPowerSeries.Substitution.0.MvPowerSeries.rescale._simp_1 | Mathlib.RingTheory.MvPowerSeries.Substitution | [
"Decidable",
"ite_eq_right_iff",
"propext",
"Eq",
"ite"
] | false |
symmDiff._aux_Mathlib_Order_SymmDiff___unexpand_symmDiff_1 | Mathlib.Order.SymmDiff | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
Set.ncard_strictMono | Mathlib.Data.Set.Card | [
"Preorder.toLT",
"ChainCompletePartialOrder.instOfCompleteLattice",
"StrictMono",
"Subtype.finite",
"Finite",
"PartialOrder.toPreorder",
"Membership.mem",
"ChainCompletePartialOrder.toPartialOrder",
"Set.toFinite",
"Nat.instPreorder",
"Nat",
"LT.lt",
"Set.ncard_lt_ncard",
"CompleteBooleanA... | true |
_private.Init.Data.SInt.Lemmas.0.Int64.toNatClampNeg_ofNat_of_lt._proof_1_2 | Init.Data.SInt.Lemmas | [
"instPowNat",
"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",
"id... | false |
Lean.Elab.ErrorExplanation.elabCheckedNamedError._regBuiltin.Lean.Elab.ErrorExplanation.elabCheckedNamedError_11 | Lean.Elab.ErrorExplanation | [
"Lean.Elab.Term.TermElab",
"IO",
"Lean.Elab.ErrorExplanation.elabCheckedNamedError",
"Lean.Elab.Term.termElabAttribute",
"Unit",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Cayley.0.SimpleGraph.mulCayley_insert_one._simp_1_2 | Mathlib.Combinatorics.SimpleGraph.Cayley | [
"MulOne.toOne",
"Set.instSingletonSet",
"MulOne.toMul",
"SimpleGraph",
"SDiff.sdiff",
"MulOneClass.toMulOne",
"One.toOfNat1",
"MulOneClass",
"SimpleGraph.mulCayley_erase_one",
"Singleton.singleton",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"SimpleGraph.mulCayley",
"Set.instSDiff",
"Set"
] | false |
CategoryTheory.Functor.FullyFaithful.mapGrp._proof_4 | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.Functor.FullyFaithful.preimage_map",
"CategoryTheory.Functor",
"CategoryTheory.Functor.mapGrp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.Grp.instCategory",
"CategoryTheory.Grp.homMk'",
"CategoryTheory.SemiCart... | false |
IsAdjoinRoot.mk.noConfusion | Mathlib.RingTheory.IsAdjoinRoot | [
"IsAdjoinRoot.mk",
"IsAdjoinRoot.noConfusion",
"IsAdjoinRoot",
"AlgHom.algHomClass",
"CommSemiring.toSemiring",
"HEq.refl",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"Algebra",
"Algebra.id",
"Set.instSingletonSet",
"id",
"Ideal",
"Polynomial",
"CommSemiring",
"heq_of... | false |
Std.Http.Header.IsValidHeaderValue | Std.Internal.Http.Data.Headers.Value | [
"List.head?",
"List.all",
"List.getLast?",
"String",
"Option.getD",
"Bool.true",
"List",
"Option.map",
"And",
"String.toList",
"Bool",
"Char",
"Std.Http.Internal.Char.fieldContent",
"Eq",
"Std.Http.Internal.Char.fieldVchar"
] | true |
Lean.Elab.Info.ofTacticInfo | Lean.Elab.InfoTree.Types | [
"Lean.Elab.Info.ofTacticInfo",
"Lean.Elab.Info",
"Lean.Elab.TacticInfo"
] | true |
CategoryTheory.Endofunctor.Algebra.Hom.mk.noConfusion | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Endofunctor.Algebra.Hom.noConfusion",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Endofunctor.Algebra.Hom",
"CategoryTheory.Endofunctor.Algebra.Hom.mk",
"CategoryTheory.Endofunctor... | false |
_private.Mathlib.Combinatorics.Extremal.RuzsaSzemeredi.0.card_edgeFinset | Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | [
"Eq.mpr",
"Semigroup.toMul",
"CommRing",
"instFintypeSum",
"HMul.hMul",
"ThreeAPFree",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"SimpleGraph.TripartiteFromTriangles.graph.instDecidableRelAdj",
"_private.Mathlib.Combinatorics.Extremal.RuzsaSzemeredi.0.locallyLinear",
"instDecidableEqSum... | true |
OpenSubgroup.instLattice._proof_5 | Mathlib.Topology.Algebra.OpenSubgroup | [
"OpenSubgroup.instSemilatticeInfOpenSubgroup",
"OpenSubgroup",
"SemilatticeInf.inf_le_right",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"LE.le",
"SemilatticeInf.inf",
"TopologicalSpace"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Bound.0._aux_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound___delab_app__private_Mathlib_Combinatorics_SimpleGraph_Regularity_Bound_0_termM_1 | Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Mathlib.Notation3.MatchState.empty",
"Mathlib.Notation3.withHeadRefIfTagAppFns",
"Mathlib.Notation3.matchApp",
"Lean.PrettyPrinter.Delaborator.instMonadReaderOfSubExprDelabM",
"Lean.SourceInfo",
"Lean.PrettyPrinter.Delaborator.Contex... | false |
Lean.Meta.Grind.EMatch.M | Lean.Meta.Tactic.Grind.EMatch | [
"Lean.Meta.Grind.EMatch.SearchState",
"ReaderT",
"Lean.Meta.Grind.EMatch.Context",
"IO.RealWorld",
"StateRefT'",
"Lean.Meta.Grind.GoalM"
] | true |
Mathlib.Tactic.UnfoldBoundary.UnfoldEntry.unfold.sizeOf_spec | Mathlib.Tactic.Translate.UnfoldBoundary | [
"instOfNatNat",
"instHAdd",
"Mathlib.Tactic.UnfoldBoundary.UnfoldEntry.unfold",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"Mathlib.Tactic.UnfoldBoundary.UnfoldEntry._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Name",
"Mathlib.Tactic.UnfoldBoundary.UnfoldEntry",
"Eq.refl",
"OfNat.ofNa... | true |
List.equivSigmaTuple.match_1 | Mathlib.Data.List.OfFn | [
"Nat",
"Sigma.mk",
"Sigma.casesOn",
"Fin",
"Sigma"
] | false |
SSet.Truncated.spine_map_subinterval._proof_3 | Mathlib.AlgebraicTopology.SimplicialSet.Path | [
"id",
"_private.Mathlib.AlgebraicTopology.SimplicialSet.Path.0.SSet.Truncated.spine_map_subinterval._proof_1",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Nat",
"instAddNat",
"OfNat.ofNat",
"SimplexCategory.len"
] | false |
Lean.CollectLevelMVars.State.rec | Lean.Util.CollectLevelMVars | [
"Lean.ExprSet",
"Array",
"Lean.CollectLevelMVars.State.mk",
"Lean.LevelSet",
"Lean.LMVarId",
"Lean.CollectLevelMVars.State"
] | false |
CategoryTheory.Functor.OplaxMonoidal.whiskeringRight | Mathlib.CategoryTheory.Monoidal.FunctorCategory | [
"CategoryTheory.Functor.OplaxMonoidal.whiskeringRight._proof_6",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.OplaxMonoidal.whiskeringRight._proof_10",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.OplaxMonoidal.δ",
"CategoryTheory.Functor.OplaxMonoid... | true |
Lean.instReprImportArtifacts | Lean.Setup | [
"Repr.mk",
"Lean.instReprImportArtifacts.repr",
"Lean.ImportArtifacts",
"Repr"
] | true |
Equiv.tensorProductComm_def | Mathlib.LinearAlgebra.TensorProduct.Map | [
"LinearEquiv.symm",
"TensorProduct.comm",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"Equiv.linearEquiv",
"RingHom",
"LinearEquiv.ext",
"AddZeroClass.toAddZero",
"map_zero",
"SemilinearE... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_291 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Equiv.instEquivLike",
"Lean.Grind.Nat.lt_eq",
"Equiv",
"instOfNatNat",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"List.cons",
"List.idxOfNth",
"instHAdd",
"HAdd.hAdd",
"Equiv.Perm",
"Nat",
"List.filter",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Deci... | false |
_private.Batteries.Lean.EStateM.0.EStateM.tryCatch.match_1.splitter | Batteries.Lean.EStateM | [
"EStateM.Result.ctorIdx",
"False",
"EStateM.Result",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Bool.true",
"Nat.land",
"absurd",
"Nat",
"Bool",
"Eq.ndrec",
"Nat.eq_of_beq_eq_true",
"Eq.refl",
"EStateM.Result.error",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"_private.Batteries.Le... | true |
Int8.neg_add | Init.Data.SInt.Lemmas | [
"instSubInt8",
"HSub.hSub",
"Int8.instNeg",
"Int8",
"BitVec",
"Int8.toBitVec_inj",
"instOfNatNat",
"instHAdd",
"instAddInt8",
"instHSub",
"HAdd.hAdd",
"Nat",
"Iff.mp",
"Int8.toBitVec",
"BitVec.neg_add",
"OfNat.ofNat",
"Eq",
"Neg.neg"
] | true |
CategoryTheory.Limits.WidePullbackCone.IsLimit.lift | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.WidePullbackCone.mk",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Limits.WidePullbackShape.wideCospan",
"CategoryTheory.Lim... | true |
_private.Mathlib.Topology.Order.LeftRight.0.continuousWithinAt_Ioi_iff_Ici._simp_1_1 | Mathlib.Topology.Order.LeftRight | [
"Set.Ioi",
"Set.Ici",
"PartialOrder.toPreorder",
"PartialOrder",
"Set.instSingletonSet",
"SDiff.sdiff",
"Singleton.singleton",
"Eq.symm",
"Set.Ici_diff_left",
"Eq",
"Set.instSDiff",
"Set"
] | false |
_private.Mathlib.Order.Interval.Finset.Gaps.0.Finset.intervalGapsWithin_pairwiseDisjoint_Ioc._proof_1_4 | Mathlib.Order.Interval.Finset.Gaps | [
"instLawfulOrderLT_mathlib",
"Set.ext",
"Set.Ioc",
"instNeZeroNatHAdd_1",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Preorder.toLT",
"Lean.Grind.nestedProof",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Finset",
"Set.mem_inter_iff",
"LinearOrder",
"Classical.byContradiction",
"P... | false |
BoundedLatticeHomClass.toSupBotHomClass | Mathlib.Order.Hom.BoundedLattice | [
"Lattice",
"Lattice.toSemilatticeSup",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"BoundedLatticeHomClass",
"SupBotHomClass",
"BoundedLatticeHomClass.toLatticeHomClass",
"BoundedOrder.toOrderBot",
"LatticeHomClass.toSu... | true |
Lean.Syntax.Range.start | Lean.Syntax | [
"Lean.Syntax.Range",
"String.Pos.Raw"
] | true |
AlgebraNorm._sizeOf_1 | Mathlib.Analysis.Normed.Unbundled.AlgebraNorm | [
"Norm.norm",
"SeminormedRing.toNorm",
"Real",
"instHSMul",
"HMul.hMul",
"SeminormedCommRing",
"Ring.toNonAssocRing",
"SeminormedCommRing.toCommRing",
"NonUnitalNonAssocRing.toAddCommGroup",
"Algebra",
"AddCommGroup.toAddGroup",
"Algebra.toSMul",
"RingNorm._sizeOf_inst",
"RingNorm.toRingSem... | false |
List.lengthTRAux.eq_1 | Init.Data.List.Basic | [
"List.lengthTRAux",
"Nat",
"Eq.refl",
"Eq",
"List.nil"
] | true |
Set.union_diff_cancel' | Mathlib.Order.BooleanAlgebra.Set | [
"Set.instUnion",
"HasSubset.Subset",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
"SDiff.sdiff",
"Set.instBooleanAlgebra",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra",
"sup_sdiff_cancel'",
"Union.union",
"Eq",
"Set.instSDiff",
"Set.instHasSubset",
"Set"
] | true |
induced_iInf | Mathlib.Topology.Order | [
"iInf",
"GaloisConnection.u_iInf",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"TopologicalSpace.coinduced",
"TopologicalSpace",
"TopologicalSpace.induced",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"ConditionallyCompletePartial... | true |
Lean.Elab.Tactic.simpParamsPos | Lean.Elab.Tactic.Simp | [
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | true |
CategoryTheory.InjectiveResolution.Hom.hom'_f_assoc | Mathlib.CategoryTheory.Abelian.Injective.Extend | [
"CategoryTheory.InjectiveResolution.Hom.hom'_f",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.InjectiveResolution.Hom",
"CategoryTheory.InjectiveResolution.cochainComplex",
"CategoryTheory.Category.assoc",
"CategoryTheory.InjectiveResolution.Hom.hom",
"Nat.instOne",
"HomologicalComplex.Hom.... | true |
PeriodPair.weierstrassPExceptSeries.eq_1 | Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Submodule",
"PeriodPair.weierstrassPExceptSeries._proof_1",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"HMul.hMul",
"FormalMultilinearSeries",
"IsSemitopologicalRing.toIsSemitopol... | true |
Mathlib.Meta.NormNum.proveJacobiSymOdd._unsafe_rec | Mathlib.Tactic.NormNum.LegendreSymbol | [
"_private.Mathlib.Tactic.NormNum.LegendreSymbol.0.Mathlib.Meta.NormNum.proveJacobiSymOdd.match_7",
"instHDiv",
"Lean.Expr.natLit!",
"Lean.Expr.const",
"Lean.Name.mkStr5",
"Mathlib.Meta.NormNum.mkRawIntLit",
"HDiv.hDiv",
"Nat.instMod",
"instHMod",
"Int.instNegInt",
"instOfNatNat",
"Lean.Expr.so... | false |
LatticeHom.dual_comp | Mathlib.Order.Hom.Lattice | [
"Lattice",
"Equiv.instEquivLike",
"Equiv",
"LatticeHom",
"OrderDual.instLattice",
"LatticeHom.comp",
"LatticeHom.dual",
"OrderDual",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
SchwartzMap.bilinLeftCLM._proof_3 | Mathlib.Analysis.Distribution.SchwartzSpace.Basic | [
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"SeminormedAddCommGroup.toAddCommGroup",
"SeminormedAddCommGroup.toIsTopologicalAddGroup",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"UniformSpace.toTopologicalSpace",
"NormedAddCommGroup"... | false |
_private.Mathlib.Algebra.Polynomial.CoeffList.0.Polynomial.coeffList_eraseLead._proof_1_10 | Mathlib.Algebra.Polynomial.CoeffList | [
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"Lean.RArray.leaf",
"False",
"Preorder.toLT",
"HMul.hMul",
"of_decide_eq_true",
"Int.Linear.norm_le",
"eq_false",
"Int.Linear.Expr.eq_of_norm_eq",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Int.Linear.le_neg",
"W... | false |
iteratedDerivWithin.eq_1 | Mathlib.Analysis.Calculus.IteratedDeriv.Defs | [
"NormedCommRing.toNormedRing",
"NormedRing.toRing",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddGroupWithOne.toAddMonoidWithOne",
"iteratedDerivWithin",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMultilinearMap",
"NormedField.toField",
"iteratedFDerivWithin",
... | true |
QuotientGroup.mk_inv | Mathlib.GroupTheory.QuotientGroup.Defs | [
"DivInvOneMonoid.toInvOneClass",
"QuotientGroup.mk",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"QuotientGroup.instHasQuotientSubgroup",
"Subgroup",
"HasQuotient.Quotient",
"Inv.inv",
"InvOneClass.toInv",
"QuotientGroup.Quotient.group",
"Eq",
"rfl",
"Subgroup.No... | true |
CategoryTheory.Limits.CreatesColimitsOfSize.createsFiniteColimits | Mathlib.CategoryTheory.Limits.Preserves.Creates.Finite | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.CreatesFiniteColimits",
"CategoryTheory.Shrink.instCategoryShrink",
"CategoryTheory.Limits.CreatesLimitsOfSize.createsFiniteLimits._proof_2",
"CategoryTheory.SmallCategory",
"CategoryTheory.CreatesColimitsOfSize.CreatesColimitsOfShape",
"CategoryTheory.Li... | true |
_private.Mathlib.Order.Filter.Prod.0.Filter.eventually_prod_iff._simp_1_1 | Mathlib.Order.Filter.Prod | [
"Set.instSProd",
"SProd.sprod",
"Set.prod_subset_iff",
"Membership.mem",
"Prod.mk",
"HasSubset.Subset",
"propext",
"Prod",
"Eq",
"Set.instMembership",
"Set.instHasSubset",
"Set"
] | false |
StrictMono.mem_upperBounds_image | Mathlib.Order.Bounds.Image | [
"StrictMono",
"congrArg",
"LinearOrder",
"Set.mem_image._simp_1",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"upperBounds",
"LE.le",
"iff_self",
"forall_exists_index._simp_1",
"funext",
... | true |
NonUnitalStarAlgebra.self_mem_adjoin_singleton._simp_1 | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"NonUnitalStarAlgebra.adjoin",
"instSMulOfMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Set.instSingletonSet",
"DistribSMul.toSMulZeroClass",
"NonUnitalSemiring.toNonUnitalNonAssocSemir... | false |
_private.Init.Data.Array.Bootstrap.0.Array.foldlM.loop.match_1.splitter | Init.Data.Array.Bootstrap | [
"instOfNatNat",
"Unit",
"Array.foldlM.loop.match_1",
"Nat",
"OfNat.ofNat",
"Nat.succ"
] | true |
CategoryTheory.Groupoid.invEquivalence._proof_10 | Mathlib.CategoryTheory.Groupoid | [
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Groupoid.invEquivalence._proof_6",
"Quiver.Hom.op",
"CategoryTheory.Functor.mk",
"CategoryTheory.IsIso.inv_inv",
"CategoryTheory.Groupoid.inv",
"CategoryTheory.Functor.comp",
"Qui... | false |
Homeomorph.addRight_symm | Mathlib.Topology.Algebra.Group.Basic | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Homeomorph.ext",
"AddMonoid.toAddZeroClass",
"SeparatelyContinuousAdd",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"AddGroup",
"AddGr... | true |
WithVal.instAlgebra_1._proof_6 | Mathlib.Topology.Algebra.Valued.WithVal | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Equiv.ringEquiv",
"RingEquiv.toEquiv",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"WithVal.instAdd",
"AddMonoid.toAddZeroClass",
"Algebra",
"AddZeroClass.toAddZer... | false |
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