name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ODE.FunSpace.instMetricSpace | Mathlib.Analysis.ODE.PicardLindelof | [
"ODE.FunSpace.toContinuousMap",
"Real",
"ODE.FunSpace",
"NormedAddCommGroup.toMetricSpace",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"ODE.FunSpace.instMetricSpace._proof_2",
"Membership.mem",
"inferInstance",
"Set.Elem",
"NNReal",
"ODE.FunSpace.instMetricSpace._proof_1",
"Functio... | true |
_private.Mathlib.CategoryTheory.Sites.SheafCohomology.MayerVietoris.0.CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_δ._proof_1_1 | Mathlib.CategoryTheory.Sites.SheafCohomology.MayerVietoris | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.sub_nonne... | false |
AEMeasurable.map_map_of_aemeasurable | Mathlib.MeasureTheory.Measure.AEMeasurable | [
"Eq.mpr",
"MeasureTheory.Measure",
"AEMeasurable.nullMeasurable",
"MeasurableSet",
"AEMeasurable",
"congrArg",
"Function.comp",
"id",
"Set.preimage_comp",
"MeasurableSpace",
"Set.preimage",
"MeasureTheory.Measure.map_apply_of_aemeasurable",
"MeasureTheory.Measure.map",
"ENNReal",
"Eq.ref... | true |
CategoryTheory.FreeBicategory.Hom₂.associator_inv | Mathlib.CategoryTheory.Bicategory.Free | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.FreeBicategory.categoryStruct",
"CategoryTheory.FreeBicategory",
"CategoryTheory.FreeBicategory.Hom₂.associator_inv",
"CategoryTheory.FreeBicategory.Hom₂",
"CategoryTheory.CategoryStruct.comp",
"Quiver"
] | true |
Std.TreeMap.Raw.getElem?_eq_some_getD_of_contains | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.contains",
"Std.TreeMap.Raw.WF.out",
"Option.some",
"Membership.mem",
"Ordering",
"Std.TreeMap.Raw.instMembership",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Bool.true",
"Std.DTreeMap.Raw.Const.get?_eq_some_getD_of_contains",
"Bool",
... | true |
Lean.Elab.Term.Quotation.precheckAttribute._regBuiltin.Lean.Elab.Term.Quotation.precheckAttribute.declRange_3 | Lean.Elab.Quotation.Precheck | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"Lean.Name.mkStr5",
"IO",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk"
] | false |
Module.DirectLimit.lift_of'._proof_1 | Mathlib.Algebra.Colimit.Module | [
"congrArg",
"Module.DirectLimit.of",
"Module.DirectLimit.module",
"LinearMap.instFunLike",
"Preorder.toLE",
"Module.DirectLimit.of_f",
"LE.le",
"LinearMap",
"AddCommMonoid",
"Module.DirectLimit.addCommMonoid",
"True",
"eq_self",
"of_eq_true",
"Semiring",
"Module.DirectLimit",
"congrFun... | false |
Lean.Firefox.Profile.meta | Lean.Util.Profiler | [
"Lean.Firefox.Profile",
"Lean.Firefox.ProfileMeta"
] | true |
Rack.PreEnvelGroupRel'.trans.elim | Mathlib.Algebra.Quandle | [
"PULift.up",
"Rack.PreEnvelGroupRel'.trans",
"Rack.PreEnvelGroupRel'",
"Rack.PreEnvelGroupRel'.ctorIdx",
"Rack",
"Nat",
"Rack.PreEnvelGroupRel'.ctorElim",
"Eq.symm",
"Eq",
"Rack.PreEnvelGroup"
] | false |
Sublattice.le_prod_iff | Mathlib.Order.Sublattice | [
"Sublattice.prod",
"Sublattice",
"Lattice",
"Sublattice.comap",
"congrArg",
"_private.Mathlib.Order.Sublattice.0.Sublattice.le_prod_iff._simp_1_2",
"PartialOrder.toPreorder",
"Prod.forall._simp_1",
"Preorder.toLE",
"Membership.mem",
"Prod.instLattice",
"Prod.mk",
"LatticeHom",
"LE.le",
"... | true |
CategoryTheory.Functor.IsDenseSubsite.hasWeakSheafify_of_isEquivalence | Mathlib.CategoryTheory.Sites.DenseSubsite.Basic | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.category",
"Nonempty.intro",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.Functor.IsDenseSubsite.instIsContinuous",
"CategoryTheory.HasWeakSheafify",
"Exists.intro",
"Nonempty",
"CategoryTheory.Category.opposite",
"CategoryT... | true |
instPreservesFiniteProductsOppositeYonedaPresheafOfPreservesFiniteCoproductsTopCat | Mathlib.Condensed.TopComparison | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.comp_preservesLimitsOfShape",
"TopCat.instCategory",
"Finite.of_fintype",
"CategoryTheory.Limits.instPreservesLimitsOfShapeDiscreteOfFiniteOfPreservesFiniteProducts",
"Fin.fintype",
"CategoryTheory.Limits.prese... | true |
CategoryTheory.Limits.MonoFactorisation.copy_m | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Limits.MonoFactorisation.I",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"autoParam",
"CategoryTheory.Limits.MonoFactorisation",
"CategoryTheory.Limits.MonoFactorisation.copy._auto_1",
"CategoryTheory.Limits.MonoFactorisation.e",
"Eq.refl",
"CategoryTheory.Category.toCate... | true |
Filter.Germ.coeRingHom._proof_3 | Mathlib.Order.Filter.Germ.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"ZeroHom.toFun",
"AddMonoid.toAddZeroClass",
"ZeroHom.map_zero'",
"AddMonoidHom.toZeroHom",
"AddZeroClass.toAddZero",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddZero.toZero",
"Pi.addZeroClass",
"Filter.Germ",
"Semiring",
"Zero.toOfNat0",
"AddMon... | false |
_private.Mathlib.NumberTheory.PythagoreanTriples.0.circleEquivGen._simp_3 | Mathlib.NumberTheory.PythagoreanTriples | [
"False",
"eq_false",
"instOfNatNat",
"two_ne_zero",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
Std.TreeMap.minKeyD_insert | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.minKey?",
"Std.TreeMap.insert",
"Std.TreeMap.inner",
"Ordering",
"instDecidableEqBool",
"Std.TransCmp",
"Bool.true",
"Std.TreeMap.minKeyD",
"Bool",
"Std.DTreeMap.minKeyD_insert",
"Ordering.isLE",
"Option.elim",
"Eq",
"Std.TreeMap",
"ite"
] | true |
ENNReal.limsup_const_mul | Mathlib.Order.Filter.ENNReal | [
"ENNReal.instCanonicallyOrderedAdd",
"Iff.mpr",
"Eq.mpr",
"instDecidableNot",
"False",
"Filter.le_limsup_of_frequently_le",
"ENNReal.limsup_const_mul_of_ne_top",
"Lattice.toSemilatticeSup",
"TopologicalSpace.MetrizableSpace.toPseudoMetrizableSpace",
"HMul.hMul",
"ite_eq_right_iff._simp_1",
"eq... | true |
Encodable.decodeSum._sparseCasesOn_1.else_eq | Mathlib.Logic.Encodable.Basic | [
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Encodable.decodeSum._sparseCasesOn_1",
"Bool.ctorIdx",
"Bool.true",
"Nat.land",
"absurd",
"Bool.casesOn",
"Nat",
"Bool",
"Eq.ndrec",
"Nat.eq_of_beq_eq_true",
"Eq.refl",
"OfNat.ofNat",
"Eq.symm",
"Bool.false",
"Eq"
] | false |
_private.Mathlib.Algebra.Order.SuccPred.PartialSups.0.partialSups_add_one'._simp_1_1 | Mathlib.Algebra.Order.SuccPred.PartialSups | [
"One",
"Order.succ",
"Order.succ_eq_add_one",
"SuccAddOrder",
"instHAdd",
"HAdd.hAdd",
"One.toOfNat1",
"SuccAddOrder.toSuccOrder",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Add",
"Preorder"
] | false |
_private.Mathlib.Computability.EpsilonNFA.0.εNFA.mem_evalFrom_iff_exists_path._simp_1_3 | Mathlib.Computability.EpsilonNFA | [
"List.reduceOption_eq_nil_iff",
"List.replicate",
"Exists",
"Option.none",
"List",
"Nat",
"propext",
"List.reduceOption",
"Eq",
"List.nil",
"Option"
] | false |
IsAtom.of_compl | Mathlib.Order.Atoms | [
"BooleanAlgebra",
"Compl.compl",
"PartialOrder.toPreorder",
"BooleanAlgebra.toCompl",
"SemilatticeInf.toPartialOrder",
"CoheytingAlgebra.toOrderTop",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"IsCoatom",
"BooleanAlgebra.toBiheytingAlgebra",
"Iff.mp",
"IsAtom",... | true |
CategoryTheory.conjugateEquiv_adjunction_id_symm | Mathlib.CategoryTheory.Adjunction.Mates | [
"CategoryTheory.Category.assoc",
"CategoryTheory.mateEquiv._proof_2",
"CategoryTheory.Functor",
"Function.LeftInverse",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Equiv.trans",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.rightUnitor... | true |
Lean.ParametricAttributeExtra.mk._flat_ctor | Batteries.Lean.AttributeExtra | [
"Lean.ParametricAttributeExtra",
"Std.HashMap",
"Lean.ParametricAttribute",
"Lean.Name",
"Lean.ParametricAttributeExtra.mk",
"Lean.Name.instBEq",
"Lean.instHashableName"
] | false |
_private.Mathlib.RingTheory.Etale.Pi.0.Algebra.FormallyEtale.pi_iff._simp_1_1 | Mathlib.RingTheory.Etale.Pi | [
"CommRing",
"CommSemiring.toSemiring",
"Algebra.FormallyEtale",
"Algebra",
"Algebra.FormallyUnramified",
"And",
"CommRing.toCommSemiring",
"Algebra.FormallyEtale.iff_formallyUnramified_and_formallySmooth",
"propext",
"Eq",
"Algebra.FormallySmooth"
] | false |
Lists'.mem_of_subset | Mathlib.SetTheory.Lists | [
"Iff.mpr",
"Lists'.toList",
"Lists'.mem_equiv_left",
"Lists",
"Membership.mem",
"Lists'.instMembershipLists",
"HasSubset.Subset",
"Bool.true",
"List",
"Lists'.instHasSubsetTrue",
"List.instMembership",
"Lists'.mem_of_subset'",
"_private.Mathlib.SetTheory.Lists.0.Lists'.mem_of_subset.match_1_... | true |
_private.Mathlib.Analysis.Complex.Arg.0.Complex.sameRay_iff._simp_1_6 | Mathlib.Analysis.Complex.Arg | [
"False",
"HMul.hMul",
"eq_false",
"Mul",
"Ne",
"NoZeroDivisors",
"Zero.toOfNat0",
"mul_ne_zero",
"OfNat.ofNat",
"Eq",
"instHMul",
"Zero"
] | false |
_private.Mathlib.LinearAlgebra.Matrix.ToLinearEquiv.0.Matrix.det_ne_zero_of_sum_col_pos._simp_1_1 | Mathlib.LinearAlgebra.Matrix.ToLinearEquiv | [
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Finset.lt_sup'_iff",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"And",
"Finset.instSetLike",
"LT.lt",
"propext",
"Finset.Nonempty",
"Finset.su... | false |
LocallyConstant.mapAddMonoidHom.eq_1 | Mathlib.Topology.LocallyConstant.Algebra | [
"AddZeroClass.toAddZero",
"AddMonoidHom.mk",
"LocallyConstant",
"ZeroHom.mk",
"LocallyConstant.mapAddMonoidHom._proof_2",
"TopologicalSpace",
"AddZero.toZero",
"AddZeroClass",
"LocallyConstant.instAddZeroClass",
"LocallyConstant.mapAddMonoidHom",
"LocallyConstant.map",
"Eq.refl",
"AddMonoidH... | true |
Filter.comap_sup | Mathlib.Order.Filter.Map | [
"cond",
"Eq.mpr",
"Filter.instSupSet",
"iSup_bool_eq",
"Bool.cond_true",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"iSup",
"Filter.instCompleteLatticeFilter",
"sup_eq_iSup",
"SemilatticeSup.toMax",
"id",
"Bool.true",
"Max.max",
"Filter.comap_iSup",
"Bool.co... | true |
IsRelUpperSet.mem_of_le | Mathlib.Order.UpperLower.Relative | [
"Membership.mem",
"LE.le",
"IsRelUpperSet",
"LE",
"And.right",
"Set.instMembership",
"Set"
] | true |
Pell.yn_modEq_a_sub_one | Mathlib.NumberTheory.PellMatiyasevic | [
"Pell.yn_modEq_a_sub_one._f",
"HSub.hSub",
"Nat.brecOn",
"instSubNat",
"instOfNatNat",
"Nat.ModEq",
"instHSub",
"Pell.yn",
"Nat",
"LT.lt",
"instLTNat",
"OfNat.ofNat"
] | true |
AddEquiv.prodAssoc.match_1 | Mathlib.Algebra.Group.Prod | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
Ordinal.succ_iSup_eq_lsub_iff | Mathlib.SetTheory.Ordinal.Family | [
"Order.succ",
"Ordinal.partialOrder",
"iSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"Ordinal.instSuccOrder",
"Ordinal.instConditionallyCompleteLinearOrderBot",
"LE.le.ge_iff_eq'",
"Ordinal.lsub",
"Iff... | true |
UInt8.toUInt32_le._simp_1 | Init.Data.UInt.Lemmas | [
"UInt8.toUInt32",
"UInt8.toUInt32_le",
"LE.le",
"propext",
"instLEUInt32",
"UInt32",
"UInt8",
"Eq",
"instLEUInt8"
] | false |
Std.ExtHashMap.getKey!_eq_of_mem | Std.Data.ExtHashMap.Lemmas | [
"instLawfulHashableOfLawfulBEq",
"Std.ExtHashMap.inner",
"LawfulBEq",
"Membership.mem",
"Std.ExtHashMap",
"Std.ExtHashMap.getKey!",
"Inhabited",
"Std.ExtDHashMap.getKey!_eq_of_mem",
"Hashable",
"instEquivBEqOfLawfulBEq",
"Std.ExtHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"BEq",
"Eq"
... | true |
AddMemClass.subtype._proof_1 | Mathlib.Algebra.Group.Subsemigroup.Defs | [
"SetLike",
"Membership.mem",
"Subtype",
"instHAdd",
"AddMemClass.add",
"HAdd.hAdd",
"AddMemClass",
"Subtype.val",
"Eq",
"SetLike.instMembership",
"Add",
"rfl"
] | false |
UInt32.recOn._@.Mathlib.Util.CompileInductive.3197476844._hygCtx._hyg.395 | Mathlib.Util.CompileInductive | [
"BitVec",
"instOfNatNat",
"UInt32.ofBitVec",
"UInt32.rec",
"Nat",
"UInt32",
"OfNat.ofNat"
] | false |
Lean.Elab.Do.Context._sizeOf_inst | Lean.Elab.Do.Basic | [
"SizeOf.mk",
"Lean.Elab.Do.Context._sizeOf_1",
"SizeOf",
"Lean.Elab.Do.Context"
] | false |
bernoulli'_zero | Mathlib.NumberTheory.Bernoulli | [
"Rat.addCommMonoid",
"CharP.cast_eq_zero",
"NormedCommRing.toNormedRing",
"Rat.instOfNat",
"Rat.instSub",
"Eq.mpr",
"Rat.instMul",
"Nat.choose",
"instHDiv",
"NormedRing.toRing",
"HMul.hMul",
"congrArg",
"sub_zero",
"Finset",
"AddMonoid.toAddZeroClass",
"Rat",
"AddGroupWithOne.toAddMo... | true |
lTensor.inverse._proof_1 | Mathlib.LinearAlgebra.TensorProduct.RightExactness | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"AddCommGroup",
"Function.surjInv",
"LinearMap",
"CommRing.toCommSemiring",
"Function.RightInverse",
"Function.rightInverse_surjInv",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"DFun... | false |
Polynomial.trinomial_leading_coeff' | Mathlib.Algebra.Polynomial.UnitTrinomial | [
"Eq.mpr",
"Polynomial.C",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"Polynomial.trinomial",
"congrArg",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"id",
"Distrib.toAdd",
"Polynomial.instAdd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Polynomial.coeff_a... | true |
SemilatSupCat.of.sizeOf_spec | Mathlib.Order.Category.Semilat | [
"SemilatSupCat.of",
"PartialOrder.toPreorder",
"instSizeOfDefault",
"Preorder.toLE",
"OrderBot",
"instOfNatNat",
"SemilatSupCat",
"instHAdd",
"SemilatSupCat._sizeOf_inst",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"SemilatticeSup.toPartialOrder",
"OfNat.ofNat",
"E... | true |
AddGroupFilterBasis.instInhabited._proof_1 | Mathlib.Topology.Algebra.FilterBasis | [
"AddGroup.toSubtractionMonoid",
"Set.singleton_subset_iff",
"and_true",
"congrArg",
"Set.subset_inter_iff",
"forall_eq",
"Membership.mem",
"Exists",
"Set.instSingletonSet",
"exists_eq_left",
"HasSubset.Subset",
"SubtractionMonoid.toSubNegZeroMonoid",
"Set.instInter",
"SubNegZeroMonoid.toNe... | false |
_private.Lean.Elab.Command.0.Lean.Elab.Command.withScope.match_1 | Lean.Elab.Command | [
"Unit.unit",
"List.cons",
"List",
"Unit",
"Lean.Elab.Command.Scope",
"List.casesOn",
"List.nil"
] | false |
CategoryTheory.Sheaf.isIso_of_coversTop | Mathlib.CategoryTheory.Sites.LocalProperties | [
"CategoryTheory.GrothendieckTopology.CoversTop.cover",
"CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.op_comp",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Presheaf.IsSheaf.amalgamate_map",
"CategoryTheory.I... | true |
Bool.not_rightInverse | Mathlib.Logic.Equiv.Bool | [
"Bool.not",
"Bool.not_not",
"Function.RightInverse",
"Bool"
] | true |
Polynomial.coeff_ofNat_mul | Mathlib.Algebra.Polynomial.Coeff | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"Polynomial.coeff_C_mul",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Nat.cast",
"Polynomial",
"Polynomial.coeff",
"instDistribOfSemiring",
"Distrib.toMul",
"Nat",
"Semiring",
"Polynomial.instMul",
"OfNat... | true |
AddMonoidHom.fst.eq_1 | Mathlib.Algebra.Group.Prod | [
"AddMonoidHom.fst",
"AddMonoidHom.fst._proof_2",
"Prod.instAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidHom.mk",
"ZeroHom.mk",
"Prod.fst",
"AddZero.toZero",
"AddZeroClass",
"Eq.refl",
"AddMonoidHom.fst._proof_1",
"AddMonoidHom",
"Prod",
"Eq"
] | true |
Std.DTreeMap.getKey_insertMany_list_of_mem | Std.Data.DTreeMap.Lemmas | [
"List.Pairwise",
"Std.DTreeMap",
"instForInOfForIn'",
"List.map",
"Ord.mk",
"Membership.mem",
"Ordering",
"inferInstance",
"Ordering.eq",
"Std.DTreeMap.inner",
"Sigma.fst",
"Std.TransCmp",
"Id",
"Membership",
"Std.DTreeMap.insertMany",
"Std.DTreeMap.instMembership",
"List",
"List.i... | true |
Lean.SimplePersistentEnvExtensionDescr.addImportedFn | Lean.EnvExtension | [
"Array",
"Lean.SimplePersistentEnvExtensionDescr"
] | true |
Fin.insertNthOrderIso_zero | Mathlib.Order.Fin.Tuple | [
"Fin.succAbove",
"instNeZeroNatHAdd_1",
"Equiv.instEquivLike",
"RelIso.mk",
"Prod.instLE_mathlib",
"Fin.succ",
"congrArg",
"OrderIso.ext",
"Fin.insertNthEquiv_zero",
"Fin.insertNthOrderIso",
"Fin.cons",
"Fin.instOfNat",
"Equiv",
"OrderIso",
"Fin.cons._proof_1",
"instOfNatNat",
"LE.le... | true |
CategoryTheory.Functor.mapAction_map_hom | Mathlib.CategoryTheory.Action.Basic | [
"Monoid",
"MulOne.toOne",
"CategoryTheory.Functor",
"MonoidHom.instFunLike",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"OneHom.mk",
"CategoryTheory.Functor.mapAction._proof_1",
"MonoidHom.mk",
"CategoryTheory.End.monoid",
"CategoryTheory.Fun... | true |
HomologicalComplex.IsSupported.mk._flat_ctor | Mathlib.Algebra.Homology.Embedding.IsSupported | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.ExactAt",
"HomologicalComplex",
"HomologicalComplex.IsSupported.mk",
"Ne",
"ComplexShape",
"ComplexShape.Embedding.f",
"ComplexShape.Embedding",
"HomologicalComplex.IsSupported",
"CategoryTheory.Category"
] | false |
Prefunctor.symmetrify | Mathlib.Combinatorics.Quiver.Symmetric | [
"Sum.map",
"Quiver.Hom",
"Quiver.symmetrifyQuiver",
"Quiver.Symmetrify",
"Prefunctor.map",
"Prefunctor",
"Quiver",
"Prefunctor.mk",
"Prefunctor.obj"
] | true |
OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge' | Mathlib.Order.OmegaCompletePartialOrder | [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"forall_comm",
"id",
"OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge",
"OmegaCompletePartialOrder.instPartialOrderContinuousHom",
"LE.le",
"OmegaCompletePartialOrder.ContinuousHom",
"OmegaCompletePartialO... | true |
Lean.Server.Test.Runner.Client.InfoPopup.mk | Lean.Server.Test.Runner | [
"String",
"Lean.Server.Test.Runner.Client.SubexprInfo",
"Lean.Widget.TaggedText",
"Lean.Server.Test.Runner.Client.InfoPopup.mk",
"Lean.Server.Test.Runner.Client.InfoPopup",
"Option"
] | true |
FreeAddGroup.lift._proof_2 | Mathlib.GroupTheory.FreeGroup.Basic | [
"congrArg",
"AddMonoid.toAddZeroClass",
"FreeAddGroup.Lift.aux",
"Function.comp",
"AddZeroClass.toAddZero",
"Quot.lift",
"FreeAddGroup.of",
"funext",
"List",
"AddGroup",
"AddGroup.toSubNegMonoid",
"FreeAddGroup.Red.Step",
"AddMonoidHom.mk'",
"True",
"eq_self",
"Bool",
"of_eq_true",
... | false |
_private.Lean.Parser.Basic.0.Lean.Parser.longestMatchFn._sparseCasesOn_1 | Lean.Parser.Basic | [
"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 |
Left.mul_lt_one' | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"MulOne.toOne",
"Preorder.toLT",
"HMul.hMul",
"Preorder.toLE",
"mul_lt_of_lt_of_lt_one'",
"MulLeftMono",
"MulOne.toMul",
"MulOneClass.toMulOne",
"LT.lt",
"One.toOfNat1",
"MulOneClass",
"OfNat.ofNat",
"Preorder",
"instHMul"
] | true |
Lean.Compiler.LCNF.Simp.ConstantFold.Folder.rightAnnihilator | Lean.Compiler.LCNF.Simp.ConstantFold | [
"Pure.pure",
"Lean.Compiler.LCNF.Simp.ConstantFold.Literal",
"Lean.Compiler.LCNF.Arg",
"ReaderT",
"Monad.toApplicative",
"Lean.Compiler.LCNF.Simp.ConstantFold.FolderM",
"instMonadLiftT",
"Lean.Compiler.LCNF.LetValue",
"Option.some",
"_private.Lean.Compiler.LCNF.Simp.ConstantFold.0.Lean.Compiler.LC... | true |
String.Legacy.Iterator.nextn._sunfold | Init.Data.String.Iterator | [
"_private.Init.Data.String.Iterator.0.String.Legacy.Iterator.forward.match_1",
"String.Legacy.Iterator.next",
"Nat",
"String.Legacy.Iterator",
"String.Legacy.Iterator.nextn"
] | false |
MulHom.ofDense.eq_1 | Mathlib.Algebra.Group.Subsemigroup.Basic | [
"Semigroup",
"MulHom",
"Semigroup.toMul",
"HMul.hMul",
"Membership.mem",
"MulHom.mk",
"Subsemigroup.instTop",
"Subsemigroup",
"Eq.refl",
"MulHom.ofDense",
"Top.top",
"Eq",
"Set.instMembership",
"MulHom.ofDense._proof_1",
"instHMul",
"Set",
"Subsemigroup.closure"
] | true |
CategoryTheory.SingleFunctors.instIsIsoFunctorHom | Mathlib.CategoryTheory.Shift.SingleFunctors | [
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"CategoryTheory.SingleFunctors.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.SingleFunctors.functor",
"CategoryTheory.SingleFunctors.Hom.hom",
"AddMonoid",
"CategoryTheory.... | true |
CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesEIso_inv_τ₂ | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.opcycles",
"CategoryTheory.Abelian.SpectralObject.opcyclesIso",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesEIso._proof_1",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject... | true |
List.Subperm.idxInj._proof_3 | Batteries.Data.List.Perm | [
"List.idxOfNth_lt_length_of_lt_count",
"List.Subperm.idxInj._proof_2",
"Fin.val",
"List.idxOfNth",
"GetElem.getElem",
"List",
"List.count",
"Fin.instGetElemFinVal",
"List.countBefore",
"List.Subperm",
"Nat",
"ReflBEq",
"LT.lt",
"List.Subperm.count_le",
"List.countBefore_lt_count_getElem"... | false |
Lean.SubExpr.GoalsLocation.mk | Lean.SubExpr | [
"Lean.SubExpr.GoalsLocation",
"Lean.MVarId",
"Lean.SubExpr.GoalLocation",
"Lean.SubExpr.GoalsLocation.mk"
] | true |
Nat.eq_sq_add_sq_iff_eq_sq_mul | Mathlib.NumberTheory.SumTwoSquares | [
"Nat.gcd",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Eq.mpr",
"Nat.Coprime",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"Mathlib.Tactic.Ring.Common.mul_congr",
"HMul.hMul",
"Nat.rawCast",
"ZMod.commRing",
"Mathlib.Tactic.Ring.Common.single_pow",
... | true |
Lean.Firefox.SampleUnits.threadCPUDelta._default | Lean.Util.Profiler | [
"String",
"id"
] | false |
ae_lt_of_lt_essInf | Mathlib.MeasureTheory.Function.EssSup | [
"MeasureTheory.ae",
"Filter.eventually_lt_of_lt_liminf",
"MeasureTheory.Measure",
"Preorder.toLT",
"Filter.Eventually",
"PartialOrder.toPreorder",
"Preorder.toLE",
"essInf",
"GE.ge",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"autoParam",
"ae_lt_of_lt_essInf._auto_1",
... | true |
String.contains_iff | Batteries.Data.String.Lemmas | [
"String.Legacy.contains",
"congrArg",
"String",
"instLawfulBEqChar",
"Membership.mem",
"Exists",
"instBEqOfDecidableEq",
"iff_self",
"Bool.true",
"funext",
"List",
"And",
"BEq.beq",
"Iff",
"List.instMembership",
"String.toList",
"True",
"Bool",
"of_eq_true",
"beq_iff_eq._simp_1... | true |
CategoryTheory.Adjunction.CoreHomEquiv.mk.noConfusion | Mathlib.CategoryTheory.Adjunction.Basic | [
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Adjunction.CoreHomEquiv.noConfusion",
"id",
"Equiv",
"CategoryTheory.Adjunction.CoreHomEquiv.mk",
"CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left_sy... | false |
CompleteLat.casesOn | Mathlib.Order.Category.CompleteLat | [
"CompleteLat.rec",
"CompleteLat",
"CompleteLattice",
"CompleteLat.of"
] | false |
_private.Mathlib.RingTheory.MvPowerSeries.LinearTopology.0.MvPowerSeries.LinearTopology.isTopologicallyNilpotent_of_constantCoeff._simp_1_1 | Mathlib.RingTheory.MvPowerSeries.LinearTopology | [
"Nat.instMulZeroClass",
"Semiring.toModule",
"MvPowerSeries.WithPiTopology.instTopologicalSpace",
"LinearMap.instFunLike",
"MvPowerSeries",
"nhds",
"MvPowerSeries.instModule",
"LinearMap",
"MvPowerSeries.instAddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"TopologicalSpace",
"Filt... | false |
Module.annihilator_eq_bot | Mathlib.RingTheory.Ideal.Maps | [
"le_bot_iff",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Module.mem_annihilator",
"Eq.mpr",
"Submodule",
"instHSMul",
"Semiring.toModule",
"Module.annihilator",
"sub_self",
"AddGroupWithOne.toAddGroup",
"congrArg",
"sub_eq_zero",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddComm... | true |
AlgebraicGeometry.LocallyRingedSpace.evaluation_eq_zero_iff_notMem_basicOpen | Mathlib.Geometry.RingedSpace.LocallyRingedSpace.ResidueField | [
"not_iff_not",
"Eq.mpr",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"Classical.not_not",
"TopologicalSpace.Opens.instPartialOrder",
"congrArg",
"CommSemiring.toSemiring",
"CategoryTheory.Con... | true |
ModularForm | Mathlib.NumberTheory.ModularForms.Basic | [
"Real",
"Matrix",
"instDecidableEqFin",
"Real.semiring",
"Subgroup",
"instOfNatNat",
"Int",
"Units.instGroup",
"Fin.fintype",
"ModularForm.mk",
"Nat",
"Semiring.toMonoid",
"Matrix.GeneralLinearGroup",
"Matrix.semiring",
"OfNat.ofNat",
"Fin"
] | true |
Cardinal.lift_iSup | Mathlib.SetTheory.Cardinal.Basic | [
"Set.range_comp",
"Eq.mpr",
"Cardinal",
"congrArg",
"iSup",
"Cardinal.lift_sSup",
"Cardinal.lift",
"iSup.eq_1",
"Function.comp",
"id",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"BddAbove",
"Cardinal.instLE",
"Cardinal.instConditionallyCompleteLinearOrderBot",
"eq... | true |
_private.Mathlib.Tactic.NormNum.NatFib.0.Mathlib.Meta.NormNum.proveNatFibAux.match_1 | Mathlib.Tactic.NormNum.NatFib | [
"Lean.Expr.const",
"Lean.Level",
"Qq.Quoted",
"Lean.Expr.app",
"Sigma.mk",
"Sigma.casesOn",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Sigma",
"List.nil"
] | false |
ConvexCone.instAddCommSemigroup._proof_1 | Mathlib.Geometry.Convex.Cone.Basic | [
"AddMonoid.toAddSemigroup",
"DistribMulAction.toDistribSMul",
"add_assoc",
"AddMonoid.toAddZeroClass",
"ConvexCone.instSetLike",
"AddZeroClass.toAddZero",
"PartialOrder",
"DistribSMul.toSMulZeroClass",
"SetLike.coe_injective",
"AddCommMonoid",
"AddZero.toZero",
"instHAdd",
"SetLike.coe",
"... | false |
CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight | Mathlib.CategoryTheory.Monoidal.Braided.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight._proof_8",
"CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight._proof_6",
"CategoryTheory.Iso",
"CategoryTheory.Iso.mk",
"CategoryTheory.Monoida... | true |
List.isSome_minOn?_iff | Init.Data.List.MinMaxOn | [
"minOn",
"False",
"List.minOn?",
"congrArg",
"False.elim",
"noConfusion_of_Nat",
"Bool.false_eq_true",
"Option.some",
"not_true_eq_false",
"List.minOn?.fun_cases_unfolding",
"Ne",
"List.foldl",
"LE",
"List.cons",
"iff_self",
"Bool.true",
"Option.none",
"List",
"DecidableLE",
"I... | true |
_private.Lean.Language.Basic.0.Lean.Language.withHeaderExceptions.match_1 | Lean.Language.Basic | [
"Except.ok",
"Except.error",
"IO.Error",
"Except.casesOn",
"Except"
] | false |
CategoryTheory.MorphismProperty.multiplicativeClosure.below | Mathlib.CategoryTheory.MorphismProperty.Composition | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.multiplicativeClosure",
"CategoryTheory.MorphismProperty.multiplicativeClosure.below.comp_of",
"CategoryTheory.MorphismProperty.multiplicativeClosure.below.of",
"CategoryTheory.Cat... | true |
LinearIsometry.isEmbedding | Mathlib.Analysis.Normed.Operator.LinearIsometry | [
"LinearIsometry",
"SeminormedAddCommGroup",
"NormedAddCommGroup.toMetricSpace",
"AddCommGroup.toAddCommMonoid",
"PseudoMetricSpace.toUniformSpace",
"LinearIsometry.instFunLike",
"RingHom",
"Isometry.isEmbedding",
"LinearIsometry.isometry",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Seminorme... | true |
Sublocale.carrier.instCompleteLattice._proof_9 | Mathlib.Order.Sublocale | [
"Lattice.toSemilatticeSup",
"completeLatticeOfInf",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Sublocale.instSetLike",
"CompleteLattice.toConditionallyCompleteLattice",
"Subtype",
"CompleteLattice.toInfSet",
"CompleteLattice.isGLB_sInf",
"Subloc... | false |
Std.ExtTreeSet.get!_inter_of_not_mem_left | Std.Data.ExtTreeSet.Lemmas | [
"Inhabited.default",
"Membership.mem",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Inter.inter",
"Std.ExtTreeSet.get!",
"Std.ExtTreeMap.getKey!_inter_of_not_mem_left",
"Unit",
"Std.ExtTreeSet.instMembershipOfTransCmp",
"Std.ExtTreeSet",
"Inhabited",
"Eq",
"Std.ExtTreeSet.instInter... | true |
AnalyticOnNhd.is_constant_or_isOpen | Mathlib.Analysis.Complex.OpenMapping | [
"Filter.instMembership",
"Iff.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Complex.instNormedAddCommGroup",
"NormedSpace",
"Filter.map",
"Filter.Eventually",
"AnalyticOnNhd",
"PartialOrder.toPreorder",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformS... | true |
Lean.Elab.Tactic.evalApply._regBuiltin.Lean.Elab.Tactic.evalApply_1 | Lean.Elab.Tactic.ElabTerm | [
"Lean.Elab.Tactic.tacticElabAttribute",
"IO",
"Lean.Elab.Tactic.evalApply",
"Unit",
"Lean.Elab.Tactic.Tactic",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
CochainComplex.HomComplex.Cocycle.isKernel._proof_5 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplex | [
"CochainComplex.HomComplex.Cocycle.isKernel._proof_4",
"CategoryTheory.Limits.KernelFork.ofι",
"CochainComplex.HomComplex.instAddCommGroupCochain",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Concret... | false |
_private.Init.Data.Format.Basic.0.Std.Format.WorkItem.mk._flat_ctor | Init.Data.Format.Basic | [
"Int",
"Nat",
"_private.Init.Data.Format.Basic.0.Std.Format.WorkItem",
"Std.Format",
"_private.Init.Data.Format.Basic.0.Std.Format.WorkItem.mk"
] | false |
CategoryTheory.Localization.Construction.LocQuiver.ctorIdx | Mathlib.CategoryTheory.Localization.Construction | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Localization.Construction.LocQuiver",
"Nat",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | false |
_private.Mathlib.RingTheory.Smooth.AdicCompletion.0.Algebra.FormallySmooth.liftAdicCompletionAux | Mathlib.RingTheory.Smooth.AdicCompletion | [
"CommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"AlgHom",
"Algebra",
"Algebra.id",
"Nat.brecOn",
"Ideal.instAlgebraQuotient",
"Ideal",
"HasQuotient.Quotient",
"CommRing.toCommSemiring",
"HPow.hPow",
"Nat",
"_private.Mathlib.RingTheory.Smooth.AdicComplet... | true |
CommGroupWithZero.instNormalizedGCDMonoid._proof_9 | Mathlib.Algebra.GCDMonoid.Basic | [
"GroupWithZero.toMonoidWithZero",
"InvOneClass.toOne",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"MulZeroClass.toMul",
"congrArg",
"Decidable",
"MonoidWithZeroHom.funLike",
"MonoidHomClass.toOneHomClass",
"DivisionMonoid.toDivInvOneMonoid",
"MonoidWit... | false |
_private.Mathlib.Data.Set.Accumulate.0.Set.exists_accumulate_eq_univ_iff_of_directed._proof_1_3 | Mathlib.Data.Set.Accumulate | [
"Set.univ_subset_iff",
"False",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Set.univ",
"Classical.byContradiction",
"Eq.mp",
"id",
"HasSubset.Subset",
"Ne",
"instLENat",
"Set.accumulate",
"Iff",
"Nat",
"True",
"eq_true",
"Lean.Grind.intro_with_eq",
"Eq.r... | false |
_private.Mathlib.Order.Category.Preord.0.Preord.Hom.mk.injEq | Mathlib.Order.Category.Preord | [
"Eq.propIntro",
"Preord.str",
"Preord",
"Preord.Hom",
"Preord.carrier",
"Eq.ndrec",
"Eq.refl",
"_private.Mathlib.Order.Category.Preord.0.Preord.Hom.mk.inj",
"Eq",
"OrderHom",
"_private.Mathlib.Order.Category.Preord.0.Preord.Hom.mk"
] | true |
LieSubmodule.mk._flat_ctor | Mathlib.Algebra.Lie.Submodule | [
"CommRing",
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Bracket.bracket",
"LieSubmodule",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"LieRingModule.toBra... | false |
MeasureTheory.L1.SimpleFunc.setToL1SCLM._proof_2 | Mathlib.MeasureTheory.Integral.SetToL1 | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedAddCommGroup",
"Real.instLE",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"Preorder.toLT",
"HMul.hMul",
"MeasurableSet",
"NormedSpace",
"MeasureTheory.Lp.simpleFunc.module",
"R... | false |
Int.isCompl_even_odd | Mathlib.Algebra.Order.Ring.Int | [
"congrArg",
"Compl.compl",
"Odd",
"setOf",
"SemilatticeInf.toPartialOrder",
"Int",
"BiheytingAlgebra.toCoheytingAlgebra",
"Set.instCompl",
"BooleanAlgebra.toBiheytingAlgebra",
"funext",
"_private.Mathlib.Algebra.Order.Ring.Int.0.Int.isCompl_even_odd._simp_1_3",
"IsCompl",
"_private.Mathlib.A... | true |
CompHausLike.coproductIsColimit._proof_2 | Mathlib.Topology.Category.CompHausLike.Cartesian | [
"CompHausLike.ofHom",
"CategoryTheory.Limits.BinaryCofan.inr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CompHausLike.coproductCocone._proof_1",
"ContinuousMap.mk",
"ContinuousMap",
"CategoryTheory.Functor.category",
... | false |
_private.Mathlib.Lean.MessageData.ForExprs.0.Lean.MessageData.forExprsIn.go.match_7 | Mathlib.Lean.MessageData.ForExprs | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"ForInStep",
"Option.none",
"Unit",
"Option"
] | false |
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