name
stringlengths
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stringlengths
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2 classes
CategoryTheory.Limits.CatCospanTransform.«_aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Categorical_CatCospanTransform___macroRules_CategoryTheory_Limits_CatCospanTransform_termλ__1»
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform
[ "Pure.pure", "Lean.MonadRef.mkInfoFromRefPos", "Lean.Syntax.ident", "instMonadExceptOfMonadExceptOf", "String", "Lean.SourceInfo", "MonadExcept.throw", "Lean.Syntax.isOfKind", "EStateM.instMonad", "Lean.Macro.Exception", "Lean.TSyntax.mk", "Lean.Syntax", "ReaderT.instMonad", "Lean.TSyntax....
false
LinearPMap.sSup_apply
Mathlib.LinearAlgebra.LinearPMap
[ "Submodule", "AddCommGroup.toAddCommMonoid", "Submodule.addCommMonoid", "Submodule.completeLattice", "PartialOrder.toPreorder", "Preorder.toLE", "DirectedOn", "RingHom", "Membership.mem", "CompleteLattice.toConditionallyCompleteLattice", "AddCommGroup", "Subtype", "upperBounds", "Submodule...
true
Module.subsingletonEquiv._proof_3
Mathlib.LinearAlgebra.Finsupp.Defs
[ "Finsupp.smulZeroClass", "NonAssocSemiring.toAddCommMonoidWithOne", "instHSMul", "instDistribSMul", "AddMonoid.toAddZeroClass", "smul_zero", "DistribSMul.toSMulZeroClass", "AddCommMonoidWithOne.toAddMonoidWithOne", "NonAssocSemiring.toNonUnitalNonAssocSemiring", "Semiring", "Zero.toOfNat0", "H...
false
AffineBasis.sum_coord_apply_eq_one
Mathlib.LinearAlgebra.AffineSpace.Basis
[ "Finset.mem_univ", "Eq.mpr", "Pi.Function.module", "AffineBasis.tot", "AffineBasis.instFunLike", "Lattice.toSemilatticeSup", "Semiring.toModule", "AffineMap.instFunLike", "Finset.univ", "Ring.toNonAssocRing", "CompleteLattice.toLattice", "AddGroupWithOne.toAddGroup", "congrArg", "AddCommGr...
true
CategoryTheory.ObjectProperty.instPretriangulatedFullSubcategory._proof_7
Mathlib.CategoryTheory.Triangulated.Subcategory
[ "CategoryTheory.ObjectProperty.IsTriangulated.toContainsZero", "CategoryTheory.ObjectProperty.IsTriangulated.toIsStableUnderShift", "CategoryTheory.Functor.fullSubcategoryInclusion_additive", "CategoryTheory.ObjectProperty.ι", "CategoryTheory.Functor.Additive", "CategoryTheory.Pretriangulated.Triangle.obj...
false
Qq.Impl.ExprBackSubstResult.unquoted.injEq
Qq.Macro
[ "Qq.Impl.ExprBackSubstResult.unquoted.inj", "Eq.propIntro", "Lean.Expr", "Qq.Impl.ExprBackSubstResult", "Qq.Impl.ExprBackSubstResult.unquoted", "Eq.ndrec", "Eq.refl", "Eq" ]
true
_private.Lean.Meta.Tactic.Grind.Internalize.0.Lean.Meta.Grind.internalizeImpl.go.match_1
Lean.Meta.Tactic.Grind.Internalize
[ "Lean.Expr.const", "Lean.Expr.letE", "Lean.Expr.mvar", "Lean.MVarId", "Lean.Expr", "Lean.FVarId", "Lean.Expr.sort", "Lean.Expr.bvar", "Lean.Level", "Lean.Literal", "Lean.Expr.mdata", "Lean.Expr.fvar", "Lean.Expr.forallE", "Lean.Expr.casesOn", "List", "Lean.MData", "Lean.Expr.lam", ...
false
Set.smul_mem_smul_set_iff₀._simp_1
Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set
[ "GroupWithZero.toMonoidWithZero", "instHSMul", "GroupWithZero", "Membership.mem", "Set.smul_mem_smul_set_iff₀", "Ne", "MonoidWithZero.toMulZeroOneClass", "MulAction", "propext", "Monoid.toSemigroup", "Zero.toOfNat0", "HSMul.hSMul", "SemigroupAction.toSMul", "MulZeroOneClass.toMulZeroClass"...
false
Subgroup.goursat
Mathlib.GroupTheory.Goursat
[ "MonoidHom.prodMap", "Iff.mpr", "Eq.mpr", "Subgroup.normal_goursatSnd", "MulOne.toOne", "MonoidHom.range", "MonoidHom.instFunLike", "_private.Mathlib.GroupTheory.Goursat.0.Subgroup.goursat._simp_1_17", "MonoidHom", "Iff.of_eq", "Subgroup.map", "Monoid.toMulOneClass", "MonoidHom.prod", "con...
true
Std.DTreeMap.Internal.Impl.insertMin!
Std.Data.DTreeMap.Internal.Operations
[ "Std.DTreeMap.Internal.Impl.brecOn", "Std.DTreeMap.Internal.Impl", "Std.DTreeMap.Internal.Impl.insertMin!._f" ]
true
NNNorm.recOn
Mathlib.Analysis.Normed.Group.Defs
[ "NNNorm.mk", "NNNorm", "NNReal", "NNNorm.rec" ]
false
LocallyFinite.comp_injOn
Mathlib.Topology.LocallyFinite
[ "Filter.instMembership", "setOf", "Set.Finite", "Function.comp", "Membership.mem", "Exists", "nhds", "Set.instInter", "LocallyFinite", "Inter.inter", "TopologicalSpace", "And", "Set.Nonempty", "Set.preimage", "And.intro", "Exists.intro", "Set.InjOn.mono", "Set.Nonempty.left", "Se...
true
CategoryTheory.AddMon.snd_hom
Mathlib.CategoryTheory.Monoidal.Cartesian.Mon
[ "CategoryTheory.CategoryStruct.toQuiver", "Quiver.Hom", "CategoryTheory.AddMon.instCategory", "CategoryTheory.SemiCartesianMonoidalCategory.snd", "CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory", "CategoryTheory.CartesianMonoidalCategory", "CategoryTheory.BraidedCategory", "CategoryTh...
true
CategoryTheory.HasCardinalFilteredColimits.mk._flat_ctor
Mathlib.CategoryTheory.Presentable.Basic
[ "CategoryTheory.IsCardinalFiltered", "Cardinal.IsRegular", "CategoryTheory.Limits.HasColimitsOfShape", "Cardinal", "Fact", "CategoryTheory.SmallCategory", "autoParam", "CategoryTheory.HasCardinalFilteredColimits.mk", "CategoryTheory.HasCardinalFilteredColimits.hasColimitsOfShape._autoParam", "Cate...
false
WittVector.instAdd
Mathlib.RingTheory.WittVector.Defs
[ "CommRing", "Nat.Prime", "Add.mk", "WittVector.eval", "Fact", "WittVector.wittAdd", "instOfNatNat", "WittVector", "Nat", "Matrix.vecEmpty", "OfNat.ofNat", "Matrix.vecCons", "Add" ]
true
mulLECancellable_mul._simp_2
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
[ "mulLECancellable_mul", "HMul.hMul", "MulLeftMono", "CommMagma.toMul", "LE", "CommSemigroup", "And", "CommSemigroup.toCommMagma", "propext", "MulLECancellable", "Eq", "instHMul" ]
false
OrderDual.instOrderTopOfOrderBot
Mathlib.Order.BoundedOrder.Basic
[ "OrderDual.instLE", "OrderBot.toBot", "OrderBot", "OrderTop.mk", "OrderTop", "LE", "OrderBot.bot_le", "OrderDual", "OrderDual.instTopOfBot" ]
true
Finset.card_le_card_biUnion_add_one
Mathlib.Algebra.Order.BigOperators.Group.Finset
[ "Iff.mpr", "le_refl", "Nat.instIsOrderedAddMonoid", "Finset", "Set.PairwiseDisjoint", "Preorder.toLE", "Membership.mem", "Finset.card_le_one", "instOfNatNat", "add_le_add_right", "Finset.partialOrder", "Finset.decidableEq", "LE.le", "instLENat", "Finset.biUnion", "Finset.instEmptyColle...
true
CategoryTheory.Limits.has_cokernel_pair_of_epi
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono
[ "CategoryTheory.Limits.WalkingSpan", "CategoryTheory.Epi", "CategoryTheory.CategoryStruct.toQuiver", "Quiver.Hom", "CategoryTheory.CategoryStruct.id", "CategoryTheory.Limits.WalkingPair", "Nonempty.intro", "CategoryTheory.Limits.WidePushoutShape.category", "CategoryTheory.Limits.HasColimit.mk'", "...
true
_private.Init.Data.List.Sort.Impl.0.List.MergeSort.Internal.mergeSortTR₂.run'.match_1
Init.Data.List.Sort.Impl
[ "instHDiv", "Subtype", "HDiv.hDiv", "Prod.mk", "instOfNatNat", "List", "instHAdd", "HAdd.hAdd", "Nat", "Nat.instDiv", "instAddNat", "Prod", "Prod.casesOn", "OfNat.ofNat", "Eq", "List.length" ]
false
Mathlib.Tactic.Widget.StringDiagram.mkEqHtml
Mathlib.Tactic.Widget.StringDiagram
[ "Lean.Json.bool", "Lean.Json", "ProofWidgets.Html", "String", "ProofWidgets.Html.element", "Prod.mk", "List.toArray", "List.cons", "Bool.true", "ProofWidgets.Html.text", "Prod", "Lean.Json.str", "List.nil" ]
true
NNReal.agmSequences_zero
Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean
[ "NNReal.agmSequences", "NonAssocSemiring.toAddCommMonoidWithOne", "instHDiv", "HMul.hMul", "PartialOrder.toPreorder", "Nat.instAtLeastTwoHAddOfNat", "Preorder.toLE", "Distrib.toAdd", "HDiv.hDiv", "OrderIso", "Prod.mk", "AddMonoidWithOne.toNatCast", "NNReal", "instOfNatNat", "AddCommMonoi...
true
Language.mem_sub
Mathlib.Computability.Language
[ "Language.instSub", "Iff.rfl", "HSub.hSub", "Membership.mem", "List", "And", "Iff", "instHSub", "Language.instMembershipList", "Language", "Not" ]
true
Std.DHashMap.Raw.getKey?_eq_some
Std.Data.DHashMap.RawLemmas
[ "Std.DHashMap.Raw.WF", "Std.DHashMap.Raw.instMembershipOfBEqOfHashable", "Eq.mpr", "Std.DHashMap.Raw", "Option.some", "LawfulBEq", "Membership.mem", "Std.DHashMap.Raw.contains", "id", "Std.DHashMap.Raw.getKey?_eq_some_of_contains", "Bool.true", "_private.Std.Data.DHashMap.RawLemmas.0.Std.DHash...
true
iInf_prod'
Mathlib.Order.CompleteLattice.Basic
[ "iInf", "Prod.mk", "Prod.fst", "CompleteLattice.toCompleteSemilatticeInf", "iInf_prod", "CompleteSemilatticeInf.toInfSet", "Prod", "Eq.symm", "CompleteLattice", "Eq", "Prod.snd" ]
true
_private.Mathlib.Data.Fin.SuccPred.0.Fin.succAbove_succAbove_succAbove_predAbove._proof_1_8
Mathlib.Data.Fin.SuccPred
[ "Int.Linear.eq_of_core", "Lean.RArray.leaf", "False", "Lean.Grind.not_false", "HMul.hMul", "of_decide_eq_true", "Int.Linear.norm_le", "eq_false", "Int.Linear.Expr.eq_of_norm_eq", "Lean.Grind.ToInt.toInt", "congrArg", "Int.Linear.le_norm_expr", "Lean.Grind.Semiring.mul_one", "Int.Linear.le_...
false
CFC.sqrt_eq_zero_iff._auto_1
Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
[ "Lean.Syntax.node", "Array.push", "Lean.Syntax", "Array.empty", "Lean.SourceInfo.none", "Lean.Name.mkStr1", "Lean.Name.mkStr4", "Lean.mkAtom" ]
false
SpectrumRestricts.starAlgHom._proof_2
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict
[ "IsTopologicalSemiring", "Algebra", "Algebra.toSMul", "Semifield", "ContinuousConstSMul", "TopologicalSpace", "Semifield.toDivisionSemiring", "NonAssocSemiring.toNonUnitalNonAssocSemiring", "DivisionSemiring.toSemiring", "ContinuousMap.algebra._proof_3", "Semifield.toCommSemiring", "Semiring.t...
false
AdicCompletion.ofValEqZero
Mathlib.RingTheory.AdicCompletion.Completeness
[ "Submodule", "Submodule.Quotient.instZeroQuotient", "Submodule.Quotient.addCommMonoid", "CommRing", "instHSMul", "AdicCompletion.ofPowSMul._proof_1", "Semiring.toModule", "_private.Mathlib.RingTheory.AdicCompletion.Completeness.0.AdicCompletion.ofValEqZero._proof_8", "IsScalarTower.right", "CommSe...
true
AlgebraicGeometry.LocallyRingedSpace.instCategory._proof_3
Mathlib.Geometry.RingedSpace.LocallyRingedSpace
[ "AlgebraicGeometry.LocallyRingedSpace.Hom", "id", "AlgebraicGeometry.LocallyRingedSpace", "Eq.refl", "AlgebraicGeometry.LocallyRingedSpace.comp", "Eq" ]
false
ProbabilityTheory.integrable_exp_mul_of_le_of_le
Mathlib.Probability.Moments.IntegrableExpMul
[ "AEMeasurable.aestronglyMeasurable", "Iff.mpr", "Real.instIsOrderedRing", "Norm.norm", "Eq.mpr", "mul_le_mul_of_nonpos_right", "NormedCommRing.toSeminormedCommRing", "Real.partialOrder", "Real.instLE", "MeasureTheory.AEStronglyMeasurable.aemeasurable", "Real", "Trans.trans", "MeasureTheory.M...
true
Mathlib.Tactic.MkIff.Shape.mk._flat_ctor
Mathlib.Tactic.MkIffOfInductiveProp
[ "List", "Nat", "Bool", "Mathlib.Tactic.MkIff.Shape", "Mathlib.Tactic.MkIff.Shape.mk", "Option" ]
false
_private.Init.Data.String.Lemmas.Pattern.Basic.0.String.Slice.Pattern.Model.matchesAt_iff_matchesAt_ofSliceFrom._simp_1_1
Init.Data.String.Lemmas.Pattern.Basic
[ "String.Slice", "Exists", "String.Slice.Pattern.Model.matchesAt_iff_exists_isLongestMatchAt", "propext", "String.Slice.Pattern.Model.PatternModel", "String.Slice.Pos", "String.Slice.Pattern.Model.IsLongestMatchAt", "String.Slice.Pattern.Model.MatchesAt", "Eq" ]
false
AddChar.FiniteField.primitiveChar._proof_5
Mathlib.NumberTheory.LegendreSymbol.AddCharacter
[ "LinearMap.toAddMonoidHom", "PNat.val", "Iff.mpr", "MulOne.toOne", "IsDomain.to_noZeroDivisors", "Nat.Prime", "Dvd.dvd", "NonUnitalCommRing.toNonUnitalNonAssocCommRing", "NeZero.one", "Semiring.toModule", "HMul.hMul", "CommRing.toNonUnitalCommRing", "ZMod.commRing", "AddChar.IsPrimitive.zm...
false
PMF.bind_const
Mathlib.Probability.ProbabilityMassFunction.Monad
[ "PMF.tsum_coe", "Eq.mpr", "MulOne.toOne", "HMul.hMul", "ENNReal.instAddCommMonoid", "congrArg", "PMF", "CommSemiring.toSemiring", "PMF.bind", "PMF.instFunLike", "id", "MulOne.toMul", "ENNReal.instCommSemiring", "ENNReal.tsum_mul_right", "MulZeroOneClass.toMulOneClass", "instDistribOfSe...
true
PrimeSpectrum.isClosedMap_comap_of_isIntegral
Mathlib.RingTheory.Spectrum.Prime.Topology
[ "Iff.mpr", "PrimeSpectrum.mk", "PrimeSpectrum.ext", "RingHom.instRingHomClass", "CommRing", "Semiring.toModule", "Specializes", "Algebra.algebraMap", "PrimeSpectrum.isPrime", "CommSemiring.toSemiring", "PartialOrder.toPreorder", "Algebra", "Preorder.toLE", "RingHom", "Membership.mem", ...
true
UniformFun.uniformCore.match_5
Mathlib.Topology.UniformSpace.UniformConvergenceTopology
[ "SetRel", "Membership.mem", "UniformFun.gen", "Prod.mk", "Prod.fst", "SetRel.comp", "And.casesOn", "And", "Exists.casesOn", "UniformFun", "And.intro", "Exists.intro", "Prod", "Set.instMembership", "Prod.snd", "Set" ]
false
Filter.Germ.instAddSemigroup.eq_1
Mathlib.Order.Filter.Germ.Basic
[ "Filter.Germ.instAddSemigroup._proof_1", "Filter.Germ.instAdd", "AddSemigroup.mk", "AddSemigroup", "AddSemigroup.toAdd", "Filter.Germ", "Eq.refl", "Eq", "Filter", "Filter.Germ.instAddSemigroup" ]
true
ArithmeticFunction.coe_mk
Mathlib.NumberTheory.ArithmeticFunction.Defs
[ "Nat.instMulZeroClass", "ArithmeticFunction.instFunLikeNat", "ZeroHom.mk", "Nat", "ArithmeticFunction", "Zero.toOfNat0", "OfNat.ofNat", "Eq", "DFunLike.coe", "rfl", "MulZeroClass.toZero", "Zero" ]
true
CategoryTheory.CoreSmallCategoryOfSet.mk.sizeOf_spec
Mathlib.CategoryTheory.SmallRepresentatives
[ "Equiv.instEquivLike", "CategoryTheory.CoreSmallCategoryOfSet._sizeOf_inst", "CategoryTheory.CategoryStruct.toQuiver", "Quiver.Hom", "instSizeOfDefault", "Membership.mem", "Set.Elem", "Equiv", "instOfNatNat", "instHAdd", "CategoryTheory.CoreSmallCategoryOfSet", "CategoryTheory.CoreSmallCategor...
true
univ_eq_singleton_of_card_one
Mathlib.Data.Fintype.Card
[ "Finset.univ", "instReflLe", "congrArg", "Finset", "Std.le_refl._simp_1", "Fintype.card", "instOfNatNat", "LE.le", "instLENat", "Fintype", "Nat.instPreorder", "Nat", "congr", "True", "Finset.card", "of_eq_true", "Finset.eq_of_subset_of_card_le", "Finset.instSingleton", "Singleton...
true
GenContFract.Pair.rec
Mathlib.Algebra.ContinuedFractions.Basic
[ "GenContFract.Pair", "GenContFract.Pair.mk" ]
false
_private.Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality.0.InnerProductGeometry.inner_normalize_ortho
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality
[ "NormedCommRing.toNormedRing", "AddGroup.toSubtractionMonoid", "Norm.norm", "Eq.mpr", "GroupWithZero.toMonoidWithZero", "InnerProductSpace.toNormedSpace", "Real", "GroupWithZero.toDivisionMonoid", "HMul.hMul", "DivInvOneMonoid.toInvOneClass", "Inner.inner", "Real.instZero", "Real.instRCLike"...
true
_private.Mathlib.RingTheory.SimpleModule.WedderburnArtin.0.isSimpleRing_isArtinianRing_iff._simp_1_6
Mathlib.RingTheory.SimpleModule.WedderburnArtin
[ "Semiring.toModule", "Ideal.IsTwoSided", "Ideal", "NonUnitalNonAssocSemiring.toAddCommMonoid", "NonAssocSemiring.toNonUnitalNonAssocSemiring", "propext", "Semiring", "isFullyInvariant_iff_isTwoSided", "Semiring.toNonAssocSemiring", "Eq", "Submodule.IsFullyInvariant" ]
false
Polynomial.ofSubring
Mathlib.RingTheory.Polynomial.Subring
[ "Semiring.toModule", "Subring.instSetLike", "Ring.toNonAssocRing", "LinearMap.instFunLike", "Membership.mem", "Polynomial.monomial", "Subtype", "NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring", "Polynomial.ring", "LinearMap", "NonAssocRing.toNonUnitalNonAssocRing", "Polynomial", "Polynomi...
true
FirstOrder.Language.DirectLimit.exists_quotient_mk'_sigma_mk'_eq
Mathlib.ModelTheory.DirectLimit
[ "FirstOrder.Language.Structure.Sigma.mk", "Eq.mpr", "FirstOrder.Language.DirectLimit.setoid", "le_rfl", "congrArg", "Finite", "FirstOrder.Language.DirectedSystem.map_self", "Preorder.toLE", "Function.comp", "Membership.mem", "Exists", "id", "FirstOrder.Language.DirectLimit.unify.eq_1", "up...
true
_private.Init.Data.String.Lemmas.Order.0.String.Pos.ofSliceFrom_next._simp_1_3
Init.Data.String.Lemmas.Order
[ "String.Pos.sliceFrom", "String.instLEPos_1", "String.sliceFrom", "String", "String.Pos.ofSliceFrom_le_iff", "Exists", "LE.le", "String.Pos.ofSliceFrom", "propext", "String.Pos", "String.instLEPos", "String.Slice.Pos", "Eq" ]
false
_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.CodeDecl.fvarId.match_1
Lean.Compiler.LCNF.Basic
[ "Lean.Compiler.LCNF.CodeDecl.setTag", "Lean.Compiler.LCNF.Arg", "Lean.Compiler.LCNF.CodeDecl.dec", "Lean.Compiler.LCNF.CodeDecl._auto_11", "Lean.Compiler.LCNF.CodeDecl.casesOn", "Lean.Compiler.LCNF.CodeDecl._auto_13", "Lean.Compiler.LCNF.CodeDecl._auto_5", "Lean.Expr", "Lean.Compiler.LCNF.FunDecl", ...
false
MulSemiringAction.noConfusionType
Mathlib.Algebra.Ring.Action.Basic
[ "Monoid", "NonAssocSemiring.toAddCommMonoidWithOne", "instHSMul", "MulSemiringAction.casesOn", "HMul.hMul", "AddCommMonoidWithOne.toAddMonoidWithOne", "instDistribOfSemiring", "AddMonoidWithOne.toOne", "Distrib.toMul", "MulSemiringAction", "Monoid.toSemigroup", "Semiring", "One.toOfNat1", ...
false
HasSum.hasSum_compl_iff
Mathlib.Topology.Algebra.InfiniteSum.Group
[ "AddGroup.toSubtractionMonoid", "Eq.mpr", "NegZeroClass.toNeg", "Pi.instNeg", "congrArg", "AddCommGroup.toAddCommMonoid", "Set.indicator", "Compl.compl", "AddMonoid.toAddZeroClass", "hasSum_subtype_iff_indicator", "SummationFilter", "sub_eq_add_neg", "HSub.hSub", "AddCommGroup.toAddGroup",...
true
CategoryTheory.Sheaf.instIsRightAdjointΓ
Mathlib.CategoryTheory.Sites.GlobalSections
[ "CategoryTheory.Functor", "Opposite", "CategoryTheory.Functor.category", "CategoryTheory.Functor.IsRightAdjoint", "CategoryTheory.Sheaf.Γ", "CategoryTheory.HasGlobalSectionsFunctor", "CategoryTheory.GrothendieckTopology", "CategoryTheory.HasWeakSheafify", "CategoryTheory.Category.opposite", "Categ...
true
SeparableClosure.hasEnoughRootsOfUnity_pow
Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed
[ "RingHom.instRingHomClass", "SeparableClosure.isSepClosed", "SubsemiringClass.nontrivial", "instSMulOfMul", "IsScalarTower.right", "Algebra.algebraMap", "CommSemiring.toSemiring", "IntermediateField", "AlgebraicClosure.instAlgebra", "Nat.instMonoid", "SubsemiringClass.toAddSubmonoidClass", "Ad...
true
HasFibers.ι
Mathlib.CategoryTheory.FiberedCategory.HasFibers
[ "HasFibers", "CategoryTheory.Functor", "HasFibers.category", "HasFibers.Fib", "CategoryTheory.Category" ]
true
CategoryTheory.Abelian.SpectralObject.instEpiGShortComplexOpcyclesThreeδ₂Toδ₁
Mathlib.Algebra.Homology.SpectralObject.Page
[ "CategoryTheory.Abelian.toPreadditive", "CategoryTheory.Abelian.SpectralObject.E", "CategoryTheory.Epi", "CategoryTheory.CategoryStruct.toQuiver", "Quiver.Hom", "CategoryTheory.Abelian", "CategoryTheory.Abelian.SpectralObject.shortComplexOpcyclesThreeδ₂Toδ₁", "inferInstance", "id", "CategoryTheory...
true
MonoidWithZeroHom.fst.eq_1
Mathlib.Algebra.GroupWithZero.ProdHom
[ "GroupWithZero.toMonoidWithZero", "Units.coeHom", "Equiv.instEquivLike", "MonoidHom", "MonoidWithZeroHom.fst", "Monoid.toMulOneClass", "GroupWithZero", "Prod.instMulOneClass", "Units", "WithZero.instMulZeroOneClass", "Equiv", "MonoidHom.comp", "WithZero.lift'", "MulZeroOneClass.toMulOneCla...
true
ULift.subNegAddMonoid._proof_4
Mathlib.Algebra.Group.ULift
[ "Equiv.instEquivLike", "ULift", "HSub.hSub", "SubNegMonoid", "ULift.sub", "Equiv.ulift", "Equiv", "SubNegMonoid.toSub", "instHSub", "Eq", "DFunLike.coe", "rfl", "EquivLike.toFunLike" ]
false
_private.Mathlib.LinearAlgebra.FreeModule.Norm.0.associated_norm_prod_smith._simp_1_3
Mathlib.LinearAlgebra.FreeModule.Norm
[ "LinearMap.instFunLike", "RingHom", "LinearMap.comp_apply", "RingHomCompTriple", "LinearMap", "AddCommMonoid", "LinearMap.comp", "Semiring", "Module", "Eq.symm", "Semiring.toNonAssocSemiring", "Eq", "DFunLike.coe" ]
false
_private.Mathlib.Combinatorics.Additive.AP.Three.Behrend.0.Behrend.map_succ._simp_1_2
Mathlib.Combinatorics.Additive.AP.Three.Behrend
[ "Semigroup", "Semigroup.toMul", "HMul.hMul", "mul_assoc", "Eq.symm", "Eq", "instHMul" ]
false
Filter.Germ.coe_vadd'._simp_1
Mathlib.Order.Filter.Germ.Basic
[ "Filter.Germ.ofFun", "Filter.Germ.instVAdd'", "Filter.Germ.coe_vadd'", "VAdd", "HVAdd.hVAdd", "Filter.Germ", "instHVAdd", "Eq.symm", "Eq", "Filter", "Pi.vadd'" ]
false
_private.Lean.Parser.Term.Doc.0.Lean.Parser.Term.Doc.getRecommendedSpellingString.bullet._sparseCasesOn_1
Lean.Parser.Term.Doc
[ "Nat.ne_of_beq_eq_false", "Nat.shiftRight", "Nat.hasNotBit", "instOfNatNat", "List.rec", "List.cons", "Nat.land", "List", "Nat", "Bool", "Eq.refl", "OfNat.ofNat", "Bool.false", "List.ctorIdx", "List.nil" ]
false
_private.Mathlib.Tactic.NormNum.Ineq.0.Mathlib.Meta.NormNum.evalLT.core.nnratArm._proof_1
Mathlib.Tactic.NormNum.Ineq
[ "Qq.QuotedDefEq", "Lean.Expr.const", "Lean.Expr.sort", "Lean.Level", "List.cons", "Qq.Quoted", "Lean.Name.mkStr2", "Lean.Expr.app", "Lean.Level.succ", "Lean.Name.mkStr1", "Qq.QuotedDefEq.unsafeIntro", "List.nil" ]
false
Lean.Meta.RefinedDiscrTree.PreDiscrTree.toRefinedDiscrTree
Mathlib.Lean.Meta.RefinedDiscrTree.Initialize
[ "Lean.Meta.RefinedDiscrTree.mk", "Lean.Meta.RefinedDiscrTree.instHashableKey", "Lean.Meta.RefinedDiscrTree", "Lean.Meta.RefinedDiscrTree.Trie.node", "Lean.Meta.RefinedDiscrTree.PreDiscrTree", "Array.map", "Std.HashMap", "instHashableNat", "Lean.Meta.RefinedDiscrTree.Key", "Std.HashMap.instEmptyCol...
true
_private.Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence.0.ContinuousLinearMap.diagonalStrongDualPi._proof_10
Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence
[ "InnerProductSpace.toNormedSpace", "NormedCommRing.toSeminormedCommRing", "Real", "Real.denselyNormedField", "Real.instRCLike", "AddCommGroup.toAddCommMonoid", "NormedSpace.toModule", "NormedField.toField", "Field.toSemifield", "Field.toCommRing", "smulCommClass_self", "Semifield.toDivisionSem...
false
Tactic.ComputeAsymptotics.UnitMonomial.inv
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic
[ "Real", "List.map", "Tactic.ComputeAsymptotics.UnitMonomial", "Real.instNeg", "Neg.neg" ]
true
TopCat.GlueData.ι_fromOpenSubsetsGlue
Mathlib.Topology.Gluing
[ "CategoryTheory.GlueData.diagram", "CategoryTheory.Limits.MultispanShape.prod", "CategoryTheory.Limits.hasColimitOfHasColimitsOfShape", "CategoryTheory.Limits.WalkingMultispan", "CategoryTheory.Limits.MultispanShape.L", "TopCat.GlueData.fromOpenSubsetsGlue", "CategoryTheory.CategoryStruct.toQuiver", "...
true
CategoryTheory.Triangulated.Octahedron.mem
Mathlib.CategoryTheory.Triangulated.Triangulated
[ "CategoryTheory.Triangulated.Octahedron", "CategoryTheory.CategoryStruct.toQuiver", "Quiver.Hom", "CategoryTheory.Triangulated.Octahedron.m₃", "CategoryTheory.Functor.Additive", "CategoryTheory.shiftFunctor", "Membership.mem", "Int", "Int.instAddMonoid", "CategoryTheory.Pretriangulated.Triangle", ...
true
StarAlgHom.fst_apply
Mathlib.Algebra.Star.StarAlgHom
[ "Algebra", "StarAlgHom.instFunLike", "Prod.instSemiring", "StarAlgHom", "Prod.algebra", "Prod.fst", "CommSemiring", "Prod.instStar", "Star", "Semiring", "Eq.refl", "StarAlgHom.fst", "Prod", "Eq", "DFunLike.coe" ]
true
WithVal.congr_trans
Mathlib.Topology.Algebra.Valued.WithVal
[ "LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero", "WithVal.instAdd", "Distrib.toAdd", "LinearOrderedCommGroupWithZero", "WithVal.instMul", "instDistribOfSemiring", "Distrib.toMul", "WithVal", "RingEquiv.trans", "RingEquiv", "Ring.toSemiring", "Eq", "WithVal.congr", "Ring"...
true
ArchimedeanClass.addSubgroup_eq_bot
Mathlib.Algebra.Order.Archimedean.Class
[ "dite_cond_eq_true", "AddSubgroup.instBot", "UpperSet", "LinearOrder.toDecidableEq", "congrArg", "AddCommGroup.toAddCommMonoid", "ArchimedeanClass.addSubgroup._proof_2", "LinearOrder", "ArchimedeanClass.instLinearOrder", "AddMonoid.toAddZeroClass", "PartialOrder.toPreorder", "Preorder.toLE", ...
true
Vector.eraseIdx_set_lt._proof_2
Init.Data.Vector.Erase
[ "HSub.hSub", "instSubNat", "instOfNatNat", "_private.Init.Data.Vector.Erase.0.Vector.eraseIdx_set_lt._proof_1", "instHSub", "Nat", "LT.lt", "Decidable.byContradiction", "Nat.decLt", "instLTNat", "OfNat.ofNat", "Not" ]
false
PowerSeries.invOneSubPow.eq_2
Mathlib.RingTheory.PowerSeries.WellKnown
[ "CommRing", "Nat.choose", "PowerSeries.invOneSubPow", "AddGroupWithOne.toAddGroup", "CommSemiring.toSemiring", "AddGroupWithOne.toAddMonoidWithOne", "HSub.hSub", "Units", "MvPowerSeries.instAddGroup", "AddMonoidWithOne.toNatCast", "instOfNatNat", "PowerSeries.invOneSubPow._proof_3", "PowerSe...
true
NumberField.mixedEmbedding.polarCoordReal
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord
[ "Real", "Pi.topologicalSpace", "NumberField.InfinitePlace.IsComplex", "PseudoMetricSpace.toUniformSpace", "instTopologicalSpaceProd", "Subtype", "OpenPartialHomeomorph.pi", "NumberField.mixedEmbedding.realMixedSpace", "NumberField.InfinitePlace.IsReal", "polarCoord", "NumberField.mixedEmbedding....
true
Homeomorph.toEquiv_piCongr
Mathlib.Topology.Homeomorph.Lemmas
[ "Equiv.instEquivLike", "Pi.topologicalSpace", "Equiv.trans", "Homeomorph.toEquiv", "Homeomorph.piCongr", "Equiv", "Equiv.piCongrLeft", "TopologicalSpace", "Homeomorph", "Equiv.piCongrRight", "Eq.refl", "Eq", "DFunLike.coe", "EquivLike.toFunLike" ]
true
Lean.Grind.instMulBitVecUint
Init.GrindInstances.ToInt
[ "instPowNat", "Int.sub_zero", "HMul.hMul", "Lean.Grind.ToInt.toInt", "congrArg", "Lean.Grind.ToInt.Mul.mk", "HSub.hSub", "Lean.Grind.ToInt.Mul", "Lean.Grind.instToIntBitVecUint", "BitVec", "Lean.Grind.IntInterval.uint", "instHMod", "Int", "BitVec.toNat", "Int.instNatPow", "Lean.Grind.I...
true
_private.Mathlib.Combinatorics.Enumerative.DyckWord.0.DyckWord.firstReturn_lt_length._proof_1_2
Mathlib.Combinatorics.Enumerative.DyckWord
[ "Int.Linear.eq_of_core", "Lean.RArray.leaf", "False", "HMul.hMul", "Int.Linear.norm_le", "Int.Linear.Expr.eq_of_norm_eq", "congrArg", "Int.Linear.le_norm_expr", "Lean.Grind.Semiring.mul_one", "Int.Linear.le_unsat", "Int.Linear.le_neg", "Classical.byContradiction", "HSub.hSub", "Lean.Grind....
false
_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_6
Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform
[ "Finset.instUnion", "Finset", "Membership.mem", "Finset.instSetLike", "propext", "Finset.mem_union", "Or", "Union.union", "Eq", "SetLike.instMembership", "DecidableEq" ]
false
Std.ExtDTreeMap.minKey!_insert_le_self
Std.Data.ExtDTreeMap.Lemmas
[ "Std.DTreeMap.minKey!_insert_le_self", "Std.DTreeMap", "Std.ExtDTreeMap.insert", "Ordering", "Std.TransCmp", "Std.ExtDTreeMap.minKey!", "Bool.true", "Std.ExtDTreeMap.inductionOn", "Std.ExtDTreeMap", "Bool", "Inhabited", "Ordering.isLE", "Eq" ]
true
Lean.Lsp.SemanticTokenModifier.declaration.elim
Lean.Data.Lsp.LanguageFeatures
[ "PULift.up", "Lean.Lsp.SemanticTokenModifier", "Lean.Lsp.SemanticTokenModifier.declaration", "Lean.Lsp.SemanticTokenModifier.ctorElim", "Lean.Lsp.SemanticTokenModifier.ctorIdx", "Nat", "Eq.symm", "Eq" ]
false
Algebra.zariskisMainProperty_iff_exists_saturation_eq_top._proof_2
Mathlib.RingTheory.ZariskisMainTheorem
[ "Subalgebra.instSetLike", "Eq.mpr", "CommRing", "Subsemiring.instSetLike", "Monoid.toMulOneClass", "CommSemiring.toSemiring", "PartialOrder.toPreorder", "Subalgebra.mem_toSubsemiring._simp_1", "Algebra", "Preorder.toLE", "Membership.mem", "Subsemiring.mem_toSubmonoid._simp_1", "id", "Subal...
false
Fin.rev_sub
Mathlib.Algebra.Group.Fin.Basic
[ "Eq.mpr", "Fin.instSub", "congrArg", "HSub.hSub", "id", "Fin.rev_add", "instHAdd", "instHSub", "Fin.rev", "HAdd.hAdd", "Nat", "propext", "Eq.refl", "Fin.instAdd", "Fin.rev_rev", "Fin", "Eq", "Fin.rev_eq_iff" ]
true
Finset.sum_eq_zero
Mathlib.Algebra.BigOperators.Group.Finset.Basic
[ "Trans.trans", "Finset", "AddMonoid.toAddZeroClass", "Membership.mem", "AddZeroClass.toAddZero", "Finset.sum_const_zero", "AddCommMonoid", "instTransEq", "AddZero.toZero", "Finset.instSetLike", "Zero.toOfNat0", "AddCommMonoid.toAddMonoid", "OfNat.ofNat", "Eq", "SetLike.instMembership", ...
true
TopModuleCat.withModuleTopologyAdj._proof_1
Mathlib.Algebra.Category.ModuleCat.Topology.Basic
[ "LinearMap.id", "TopModuleCat.instCategory", "TopModuleCat.instHasForget₂ContinuousLinearMapIdCarrierModuleCatLinearMap", "instIsModuleTopology", "CategoryTheory.CategoryStruct.toQuiver", "Quiver.Hom", "ModuleCat", "TopModuleCat.continuousSMul", "DistribMulAction.toDistribSMul", "AddCommGroup.toAd...
false
_private.Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms.0.SimplexCategoryGenRel.IsAdmissible.cons._proof_1_3
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms
[ "Lean.Grind.Nat.lt_eq", "instOfNatNat", "LE.le", "instLENat", "List.cons", "List", "Nat", "LT.lt", "Eq.substr", "instLTNat", "OfNat.ofNat", "List.length" ]
false
isOpen.dynEntourage
Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage
[ "Eq.mpr", "Set.instFintypeIco", "Continuous", "SetRel", "Continuous.prodMap", "congrArg", "Set.iInter", "instTopologicalSpaceProd", "Nat.instLocallyFiniteOrder", "Membership.mem", "Dynamics.dynEntourage", "Set.Elem", "id", "Prod.map", "instOfNatNat", "Finite.of_fintype", "Nat.iterate...
true
_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.ResultingUniverseResult.u
Lean.Elab.MutualInductive
[ "Lean.Level", "_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.ResultingUniverseResult" ]
true
RKHS.ext
Mathlib.Analysis.InnerProductSpace.Reproducing
[ "DFunLike.ext", "RCLike", "RKHS.instFunLike", "RKHS", "NormedAddCommGroup.toSeminormedAddCommGroup", "Eq", "DFunLike.coe", "InnerProductSpace", "NormedAddCommGroup" ]
true
ContinuousLinearMap
Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic
[ "ContinuousLinearMap.mk", "RingHom", "AddCommMonoid", "TopologicalSpace", "Semiring", "Module", "Semiring.toNonAssocSemiring" ]
true
SheafOfModules.instIsLeftAdjointOverOverRingCatPushforwardIdSheafOver
Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous
[ "CategoryTheory.Over", "CategoryTheory.Functor", "CategoryTheory.GrothendieckTopology.instIsContinuousOverStarOver", "Opposite", "CategoryTheory.Functor.category", "SheafOfModules.overPushforwardOverAdj", "CategoryTheory.Sheaf.over", "CategoryTheory.Limits.HasBinaryProducts", "CategoryTheory.Categor...
true
Relation.ReflGen.mono
Mathlib.Logic.Relation
[ "_private.Mathlib.Logic.Relation.0.Relation.ReflGen.mono.match_1_1", "Relation.ReflGen.single", "Relation.ReflGen", "Relation.ReflGen.refl" ]
true
AddSubgroup.map_injective
Mathlib.Algebra.Group.Subgroup.Ker
[ "AddSubgroup.comap", "Function.LeftInverse.injective", "AddMonoid.toAddZeroClass", "AddZeroClass.toAddZero", "AddSubgroup", "AddGroup", "AddGroup.toSubNegMonoid", "Function.Injective", "SubNegMonoid.toAddMonoid", "AddMonoidHom", "AddMonoidHom.instFunLike", "DFunLike.coe", "AddSubgroup.comap_...
true
MonoidHom.toHomPerm_apply_symm_apply
Mathlib.Algebra.Group.End
[ "Units.val", "MonoidHom.instFunLike", "Function.End", "Equiv.instEquivLike", "MonoidHom", "Monoid.toMulOneClass", "MonoidHom.toHomUnits", "Group", "Units", "Equiv", "DivInvMonoid.toMonoid", "Group.toDivInvMonoid", "Equiv.Perm.permGroup", "MulOneClass.toMulOne", "Inv.inv", "Equiv.Perm",...
true
Lean.Grind.CommRing.Expr.pow.inj
Init.Grind.Ring.CommSolver
[ "Lean.Grind.CommRing.Expr", "And", "Nat", "And.intro", "Lean.Grind.CommRing.Expr.pow.noConfusion", "Eq", "Lean.Grind.CommRing.Expr.pow" ]
true
PresheafOfModules.toPresheaf._proof_3
Mathlib.Algebra.Category.ModuleCat.Presheaf
[ "PresheafOfModules.toPresheaf._proof_1", "CategoryTheory.Functor", "Opposite", "CategoryTheory.CategoryStruct.toQuiver", "AddCommGrpCat.instCategory", "Quiver.Hom", "ModuleCat", "CategoryTheory.ConcreteCategory.hom", "AddCommGroup.toAddCommMonoid", "AddMonoid.toAddZeroClass", "CategoryTheory.Fun...
false
Rat.den_intFract
Mathlib.Data.Rat.Floor
[ "Int.floor", "Int.fract", "Rat", "Rat.instFloorRing", "Rat.linearOrder", "Rat.den", "Rat.instDivisionRing", "DivisionRing.toRing", "Nat", "Eq", "Rat.sub_intCast_den" ]
true
CategoryTheory.ObjectProperty.IsStrongTriangulatedGenerator
Mathlib.CategoryTheory.Triangulated.Generators
[ "CategoryTheory.Functor.Additive", "CategoryTheory.shiftFunctor", "Exists", "Int", "Int.instAddMonoid", "CategoryTheory.Preadditive", "BooleanAlgebra.toTop", "Nat", "CategoryTheory.Limits.HasZeroObject", "CategoryTheory.Pretriangulated", "CategoryTheory.Category.toCategoryStruct", "Prop.instBo...
true
CategoryTheory.MonadHom.app_μ_assoc
Mathlib.CategoryTheory.Monad.Basic
[ "CategoryTheory.Category.assoc", "CategoryTheory.Monad", "CategoryTheory.MonadHom.app_μ", "CategoryTheory.CategoryStruct.toQuiver", "Quiver.Hom", "congrArg", "CategoryTheory.Functor.comp", "Eq.mp", "id", "Mathlib.Tactic.Reassoc.eq_whisker'", "CategoryTheory.Functor.map", "CategoryTheory.Monad....
true
SimpleGraph.isBipartiteWith_bipartiteDoubleCover
Mathlib.Combinatorics.SimpleGraph.Bipartite
[ "Sum.isRight", "SimpleGraph.bipartiteDoubleCover", "False", "Sum.ctorIdx", "and_true", "congrArg", "and_self", "Sum.inr.injEq", "SimpleGraph.Adj", "False.elim", "PartialOrder.toPreorder", "setOf", "instInhabitedTrue", "noConfusion_of_Nat", "Preorder.toLE", "Disjoint", "Bool.false_eq_...
true
_private.Mathlib.MeasureTheory.Measure.Map.0.MeasurableEquiv.map_ae._simp_1_1
Mathlib.MeasureTheory.Measure.Map
[ "Filter.instMembership", "Filter.map", "Membership.mem", "Set.preimage", "propext", "Eq", "Filter.mem_map", "Filter", "Set" ]
false
Lean.Widget.GetWidgetSourceParams.mk.injEq
Lean.Widget.UserWidget
[ "Eq.propIntro", "UInt64", "Lean.injEq_helper", "Lean.Widget.GetWidgetSourceParams.mk.inj", "And", "Eq.ndrec", "Eq.refl", "Lean.Lsp.Position", "Eq", "Lean.Widget.GetWidgetSourceParams", "Lean.Widget.GetWidgetSourceParams.mk" ]
true
MeasurableEmbedding.schroederBernstein._proof_3
Mathlib.MeasureTheory.MeasurableSpace.Embedding
[ "Eq.mpr", "compl_compl", "congrArg", "Compl.compl", "BooleanAlgebra.toCompl", "id", "compl_injective", "Set.instCompl", "Set.instBooleanAlgebra", "True", "eq_self", "of_eq_true", "Set.image", "congrFun'", "Eq.symm", "Eq", "Eq.trans", "Set" ]
false