name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.NumberTheory.Modular.0.ModularGroup.cases_c_one_d_zero._proof_1_4 | Mathlib.NumberTheory.Modular | [
"instIsCharPOfIsLeftCancelAddOfCharP",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Lean.Grind.CommRing.Mon.mult",
"Lean.Grind.CommRing.diseq_to_eq",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"AddLeftCancelSemigroup.toIsLeftC... | false |
Classical.not_imp._simp_1 | Init.Classical | [
"And",
"Classical.not_imp",
"propext",
"Eq",
"Not"
] | false |
CategoryTheory.ShortComplex.LeftHomologyData.leftHomologyIso_hom_naturality_assoc | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.leftHomologyMap'",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.H... | true |
CategoryTheory.Endofunctor.algebraPreadditive._proof_23 | Mathlib.CategoryTheory.Preadditive.EndoFunctor | [
"NegZeroClass.toNeg",
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Functor.Additive",
"Add.mk",
"CategoryTheory.Endofunctor.Algebra.Hom",
"CategoryTheory.Endofunctor.algebraPr... | false |
_private.Lean.Server.Completion.CompletionCollectors.0.Lean.Server.Completion.State.items._default | Lean.Server.Completion.CompletionCollectors | [
"id",
"List.toArray",
"Array",
"Lean.Lsp.ResolvableCompletionItem",
"List.nil"
] | false |
MeasureTheory.Measure.ofMeasurable_zero | Mathlib.MeasureTheory.Measure.MeasureSpace | [
"MeasureTheory.Measure",
"ChainCompletePartialOrder.instOfCompleteLattice",
"MeasurableSet",
"MeasureTheory.OuterMeasure.instZero",
"Function.onFun",
"ENNReal.instAddCommMonoid",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"MeasurableSet.empty",
"congrArg",
"Set.univ",
"PartialOrder.toPre... | true |
Finset.union_smul | Mathlib.Algebra.Group.Pointwise.Finset.Scalar | [
"instHSMul",
"Finset.smul",
"Finset.instUnion",
"Finset",
"SMul",
"Finset.image₂_union_left",
"HSMul.hSMul",
"Union.union",
"Eq",
"DecidableEq"
] | true |
DomMulAct.instDivisionMonoidOfMulOpposite | Mathlib.GroupTheory.GroupAction.DomAct.Basic | [
"DomMulAct",
"MulOpposite",
"DivisionMonoid"
] | true |
LinearMap.BilinForm.flip._proof_2 | Mathlib.LinearAlgebra.BilinearForm.Basic | [
"LinearMap.BilinForm.coeFnAddMonoidHom._proof_1",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LinearMap.instSMulCommClass",
"Algebra.id",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
... | false |
Matrix.piEquiv._proof_2 | Mathlib.Data.Matrix.Basic | [
"Equiv.instEquivLike",
"Matrix",
"Matrix.of",
"Equiv",
"Matrix.map",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | false |
Std.DTreeMap.Raw.ofList_eq_insertMany_empty | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Internal.Impl.ofList_eq_insertMany!",
"Std.DTreeMap.Raw.ofList",
"instForInOfForIn'",
"Ord.mk",
"Ordering",
"inferInstance",
"Id",
"Membership",
"_private.Std.Data.DTreeMap.Raw.Lemmas.0.Std.DTreeMap.Raw.ext",
"List",
"Std.DTreeMap.Raw.insertMany",
"List.instMembership",
"Std.DT... | true |
HasFPowerSeriesAt.const_smul | Mathlib.Analysis.Analytic.Constructions | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"HasFPowerSeriesOnBall.const_smul",
"FormalMultilinearSeries.instAddCommGroup",
"FormalMultilin... | true |
CategoryTheory.LiftLeftAdjoint.otherMap.eq_1 | Mathlib.CategoryTheory.Adjunction.Lifting.Left | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.Functor.id",
"CategoryTheory.Functor.map",
"CategoryTheory.Adjunction.counit",
"CategoryTheory.LiftLeftAdjoint.otherMap",
"CategoryTheo... | true |
SheafOfModules.pushforwardId | Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.isContinuous_id",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso.refl",
"CategoryTheory.Iso",
"RingCat",
"CategoryTheory.GrothendieckTopology",
"SheafOfModules",... | true |
RingCon.quotientKerEquivOfRightInverse._proof_2 | Mathlib.RingTheory.Congruence.Hom | [
"Equiv.right_inv",
"RingHom",
"Setoid.ker",
"Equiv.toFun",
"NonAssocSemiring",
"RingHom.instFunLike",
"Quotient",
"Function.RightInverse",
"DFunLike.coe",
"Setoid.quotientKerEquivOfRightInverse",
"Equiv.invFun"
] | false |
List.find?_not_eq_head_dropWhile._proof_1 | Mathlib.Data.List.TakeWhile | [
"Eq.mpr",
"List.dropWhile_eq_nil_iff._simp_1",
"congrArg",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"Ne",
"Bool.true",
"funext",
"List",
"And",
"List.instMembership",
"Bool.not_eq_true",
"Bool",
"Classical.not_forall._simp_1",
"List.dropWhile",
"Bool.false",
"Eq",
"Classical.... | false |
_private.Init.Grind.Ring.CommSemiringAdapter.0.Lean.Grind.CommRing.Expr.toPolyS.match_4.splitter | Init.Grind.Ring.CommSemiringAdapter | [
"Lean.Grind.CommRing.Expr",
"Lean.Grind.CommRing.Expr.mul",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.CommRing.Expr.sub",
"Lean.Grind.CommRing.Expr.natCast",
"Lean.Grind.CommRing.Expr.neg",
"Int",
"Lean.Grind.CommRing.Expr.add",
"Lean.Grind.CommRing.Var",
"Nat",
"Lean.Grind.CommRing.Expr.toPol... | true |
CategoryTheory.Adjunction.Quadruple.mk.noConfusion | Mathlib.CategoryTheory.Adjunction.Quadruple | [
"CategoryTheory.Functor",
"CategoryTheory.Adjunction.Quadruple.noConfusion",
"HEq.refl",
"CategoryTheory.Adjunction.Quadruple",
"id",
"CategoryTheory.Adjunction.Quadruple.mk",
"heq_of_eq",
"Eq.refl",
"HEq",
"CategoryTheory.Adjunction",
"Eq",
"CategoryTheory.Category"
] | false |
SSet.ιNormalizedChainComplex_d_assoc | Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate | [
"CategoryTheory.Category.assoc",
"instHSMul",
"Opposite",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Finset.univ",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"Fin... | true |
LinearEquiv.coe_toAddEquiv_symm | Mathlib.Algebra.Module.Equiv.Defs | [
"LinearEquiv.symm",
"RingHom",
"AddEquivClass.toAddEquiv",
"AddCommMonoid",
"RingHomInvPair",
"LinearEquiv",
"Semiring",
"LinearEquiv.instEquivLike",
"AddEquiv",
"AddCommSemigroup.toAddCommMagma",
"SemilinearEquivClass.toAddEquivClass",
"Module",
"AddCommMonoid.toAddCommSemigroup",
"Semiri... | true |
MeasureTheory.integral_prod | Mathlib.MeasureTheory.Integral.Prod | [
"MeasureTheory.ae",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MeasureTheory.integral_indicator",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"Preorder.toLT",
"CompleteSpace",
"RCLike.toNormedAlgebra",
"ChainCompletePartialOrder.instOfCompleteLattice",
"MeasurableSet",
"NormedSpace"... | true |
AlgEquiv.ofRingEquiv._proof_3 | Mathlib.Algebra.Algebra.Equiv | [
"RingEquiv.toEquiv",
"HMul.hMul",
"Distrib.toAdd",
"RingEquiv.map_mul'",
"Equiv.toFun",
"instDistribOfSemiring",
"Distrib.toMul",
"Semiring",
"RingEquiv",
"Eq",
"instHMul"
] | false |
«term_≃ₗ[_]_» | Mathlib.Algebra.Module.Equiv.Defs | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
SSet.Truncated.sk._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.Basic | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.HasLeftKanExtension",
"CategoryTheory.Functor.comp",
"CategoryTheory.CostructuredArrow",
"UnivLE.small",
"LE.le",
"CategoryTheory.Limits.Types.hasColimit",
"instLENat",
"CategoryTheory.instCategoryCostruct... | false |
QuadraticMap.Isometry | Mathlib.LinearAlgebra.QuadraticForm.Isometry | [
"CommSemiring.toSemiring",
"AddCommMonoid",
"CommSemiring",
"QuadraticMap.Isometry.mk",
"Module",
"QuadraticMap"
] | true |
Int.toArray_roc_eq_singleton_append_iff._simp_1 | Init.Data.Range.Polymorphic.IntLemmas | [
"Array.instAppend",
"Std.PRange.instUpwardEnumerableInt",
"Int.decLe",
"Int",
"List.toArray",
"List.cons",
"Array",
"Int.instLTInt",
"instHAppendOfAppend",
"instHAdd",
"And",
"instOfNat",
"HAdd.hAdd",
"LT.lt",
"propext",
"Int.instAdd",
"Std.Roc.toArray",
"OfNat.ofNat",
"Eq",
"I... | false |
CategoryTheory.WithTerminal.of.noConfusion | Mathlib.CategoryTheory.WithTerminal.Basic | [
"id",
"CategoryTheory.WithTerminal",
"CategoryTheory.WithTerminal.noConfusion",
"CategoryTheory.WithTerminal.of",
"heq_of_eq",
"Eq.refl",
"HEq",
"Eq"
] | false |
Std.Iter.toList_zip_of_finite | Std.Data.Iterators.Lemmas.Combinators.Zip | [
"Std.Iter.Intermediate.zip",
"Std.IterM.IsPlausibleOutput",
"congrArg",
"Option.toList",
"Exists",
"Std.Iterators.Finite",
"Subtype",
"List.zip",
"Std.Iter.zip_eq_intermediateZip",
"Std.Iter.toIterM",
"Std.Iter.zip",
"Id",
"Std.Iterator",
"Std.Iter.toList_intermediateZip_of_finite",
"Opt... | true |
HasStrictFDerivAt.mem_toOpenPartialHomeomorph_source | Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv | [
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"ContinuousLinearEquiv.symm",
"instHDiv",
"CompleteSpace",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"NormedSpace.toModule",
"Nat.instAtLeastTwoHAddOfNat",
"Ap... | true |
_private.Std.Time.Format.Basic.0.Std.Time.parseOffsetO | Std.Time.Format.Basic | [
"_private.Std.Time.Format.Basic.0.Std.Time.parseMod",
"String",
"Std.Time.OffsetO.classify",
"Std.Time.Modifier",
"Std.Time.OffsetO",
"Std.Internal.Parsec.String.Parser"
] | true |
FormalMultilinearSeries.rightInv._proof_20 | Mathlib.Analysis.Analytic.Inverse | [
"AddMonoid.toAddSemigroup",
"ContinuousLinearMap.addCommGroup._proof_6",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"AddSemigroup.toAdd",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"SeminormedAddCommGroup.toAddCommGroup",
"SubNegMonoid.toAddMonoid",
... | false |
Lean.Meta.Grind.Arith.Linear.geAvoiding | Lean.Meta.Tactic.Grind.Arith.Linear.Search | [
"Inhabited.default",
"Rat",
"Array",
"Inhabited",
"Prod",
"Lean.Meta.Grind.Arith.Linear.DiseqCnstr",
"Inhabited.mk"
] | true |
ModularFormClass.modularForm._proof_1 | Mathlib.NumberTheory.ModularForms.Basic | [
"Real",
"outParam",
"Matrix",
"ModularFormClass",
"ModularFormClass.toSlashInvariantFormClass",
"instDecidableEqFin",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"Real.semiring",
"Complex.addGroupWithOne",
"Subgroup",
"instOfNatNat",
"Int",
"Units.instGroup",
"Fin.fintype",
... | false |
CategoryTheory.Localization.SmallHom.mkInv.congr_simp | Mathlib.CategoryTheory.Localization.SmallHom | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Localization.SmallHom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Eq.rec",
"CategoryTheory.Localization.HasSmallLocalizedHom",
"Eq.ndrec",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Localization.SmallHom.... | true |
Finsupp.instCoalgebra._proof_2 | Mathlib.RingTheory.Coalgebra.Basic | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Coalgebra.toCoalgebraStruct",
"Semiring.toModule",
"Finsupp.module",
"Coalgebra",
"LinearMap.rTensor_comp_map",
"congrArg",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.comp_assoc",
"Lin... | false |
PrimeSpectrum.exists_comap_evalRingHom_eq | Mathlib.RingTheory.Spectrum.Prime.RingHom | [
"CommMonoidWithZero.toCommMonoid",
"Finset.mem_univ",
"Eq.mpr",
"PrimeSpectrum.mk",
"Submodule",
"PrimeSpectrum.ext",
"RingHom.instRingHomClass",
"CommRing",
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"Function.update",
"HMul.hMul",
"Finset.univ",
"outParam",
"PrimeSpectrum.isPrime... | true |
Lean.Grind.AC.Seq.renameVars._unsafe_rec | Lean.Meta.Tactic.Grind.AC.VarRename | [
"_private.Lean.Meta.Tactic.Grind.AC.VarRename.0.Lean.Grind.AC.Seq.renameVars.match_1",
"Option.getD",
"Membership.mem",
"instOfNatNat",
"Lean.Grind.AC.Seq.renameVars._unsafe_rec",
"Std.HashMap",
"instHashableNat",
"instBEqOfDecidableEq",
"Lean.Meta.Grind.VarRename.map",
"Lean.Grind.AC.Seq.cons",
... | false |
SimpleGraph.triangle_removal | Mathlib.Combinatorics.SimpleGraph.Triangle.Removal | [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Iff.mpr",
"Mathlib.Tactic.Push.not_and_eq",
"Real",
"Preorder.toLT",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"SimpleGraph.farFromTriangleFree_iff",
"Finset",
"Nat.instMonoid",
"Real.instSub",
"SimpleGraph.Adj",
"SimpleGraph.FarFromTriangleFree",
... | true |
_private.Lean.Elab.PreDefinition.Eqns.0.Lean.Elab.Eqns.findMatchToSplit? | Lean.Elab.PreDefinition.Eqns | [
"Std.Rco",
"Pure.pure",
"Unit.unit",
"Lean.Meta.Match.MatcherInfo.getFirstAltPos",
"Lean.Expr.FindStep.visit",
"Lean.Expr.findExt?",
"instForInOfForIn'",
"Monad.toApplicative",
"Lean.Expr.instBEq",
"Lean.Expr.isAppOf",
"Lean.Expr.FindStep.done",
"Option.some",
"Std.PRange.instLawfulUpwardEnu... | true |
Metric.isBounded_range_of_cauchy_map_cofinite | Mathlib.Topology.MetricSpace.Bounded | [
"Cauchy",
"PseudoMetricSpace.toBornology",
"SProd.sprod",
"Filter.map",
"Filter.NeBot",
"cauchy_map_iff",
"uniformity",
"PseudoMetricSpace.toUniformSpace",
"Prod.mk",
"Bornology.IsBounded",
"Prod.fst",
"And",
"PseudoMetricSpace",
"And.right",
"Filter.Tendsto",
"Iff.mp",
"Metric.isBou... | true |
_private.Init.Data.List.ToArray.0.List.replace_toArray._proof_1_10 | Init.Data.List.ToArray | [
"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.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.combo_sat'",
"id",
"instDecidableEqBool",
... | false |
_private.Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four.0.CategoryTheory.Abelian.isIso_of_isIso_of_mono._proof_1_1 | Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four | [
"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 |
Std.ExtDHashMap.ofList | Std.Data.ExtDHashMap.Basic | [
"Std.DHashMap.ofList",
"Std.ExtDHashMap.mk",
"List",
"Std.ExtDHashMap",
"Hashable",
"BEq",
"Sigma"
] | true |
_private.Lean.Environment.0.Lean.AsyncConsts.findRecAndParent? | Lean.Environment | [
"_private.Lean.Environment.0.Lean.AsyncConst",
"Option.none",
"_private.Lean.Environment.0.Lean.AsyncConsts",
"Lean.Name",
"Prod",
"_private.Lean.Environment.0.Lean.AsyncConsts.findRecAndParent?.go",
"Option"
] | true |
Nat.cast_lt_ofNat | Mathlib.Data.Nat.Cast.Order.Basic | [
"Preorder.toLT",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddLeftMono",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"ZeroLEOneClass",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"Nat.cast",
"CharZero",
"AddMonoidWithOne.toOne",
... | true |
Finset.infs_eq_empty._simp_1 | Mathlib.Data.Finset.Sups | [
"Finset",
"Finset.infs_eq_empty",
"HasInfs.infs",
"Finset.instEmptyCollection",
"SemilatticeInf",
"propext",
"Or",
"EmptyCollection.emptyCollection",
"Eq",
"Finset.hasInfs",
"DecidableEq"
] | false |
Filter.comk._proof_2 | Mathlib.Order.Filter.Defs | [
"congrArg",
"Compl.compl",
"setOf",
"Membership.mem",
"Set.compl_inter",
"Set.instUnion",
"Set.instInter",
"Set.instCompl",
"Inter.inter",
"True",
"eq_true",
"of_eq_true",
"Union.union",
"Set.instMembership",
"Eq.trans",
"Set"
] | false |
List.toFinsupp._proof_4 | Mathlib.Data.List.ToFinsupp | [
"Eq.mpr",
"Mathlib.Tactic.Contrapose.contrapose₂",
"Preorder.toLT",
"_private.Mathlib.Data.List.ToFinsupp.0.List.toFinsupp._simp_2",
"Iff.of_eq",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"List.getD",
"id",
"Ne",
"LE.le",
"Finset.range",
"not_l... | false |
CategoryTheory.Functor.OneHypercoverDenseData.isSheaf_iff.liftAux._proof_1 | Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | [
"CategoryTheory.Functor",
"Membership.mem",
"CategoryTheory.Functor.IsDenseSubsite.instIsCocontinuous",
"CategoryTheory.GrothendieckTopology.pullback_stable",
"CategoryTheory.Sieve",
"CategoryTheory.GrothendieckTopology.Cover",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.Functor.PreOneHyper... | false |
_private.Mathlib.Algebra.BigOperators.Fin.0.List.prod_take_ofFn._proof_1_2 | Mathlib.Algebra.BigOperators.Fin | [
"List.ofFn",
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Fin",
"List.length"
] | false |
maximal_and_iff_right_of_imp | Mathlib.Order.Minimal | [
"Eq.mpr",
"and_iff_left_of_imp",
"congrArg",
"Maximal.prop",
"iff_self_and",
"id",
"LE",
"funext",
"And",
"Iff",
"propext",
"Maximal",
"congrFun'",
"Eq"
] | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.getEntry?.match_1 | Std.Data.Internal.List.Associative | [
"Unit.unit",
"List.cons",
"List",
"Unit",
"List.casesOn",
"Sigma.mk",
"Sigma.casesOn",
"Sigma",
"List.nil"
] | false |
_private.Std.Sat.CNF.RelabelFin.0.Std.Sat.CNF.Clause.of_maxLiteral_eq_none._simp_1_2 | Std.Sat.CNF.RelabelFin | [
"List.max?_eq_none_iff",
"Max",
"List.max?",
"Option.none",
"List",
"propext",
"Eq",
"List.nil",
"Option"
] | false |
Lean.Grind.OrderConfig.ringSteps._inherited_default | Init.Grind.Config | [
"id",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | false |
Std.Do.WPMonad | Std.Do.WP.Monad | [
"outParam",
"Std.Do.PostShape",
"Std.Do.WPMonad.mk",
"Monad"
] | true |
AffineIsometryEquiv.instGroup._proof_2 | Mathlib.Analysis.Normed.Affine.Isometry | [
"Mul.mk",
"SeminormedAddCommGroup",
"One.mk",
"HMul.hMul",
"NormedSpace",
"AffineIsometryEquiv.refl",
"Semigroup.mk",
"AffineIsometryEquiv.trans_assoc",
"npowRecAuto",
"instOfNatNat",
"AffineIsometryEquiv",
"NormedField",
"instHAdd",
"PseudoMetricSpace",
"HAdd.hAdd",
"Nat",
"instAddN... | false |
DirectSum.bracket_apply | Mathlib.Algebra.Lie.DirectSum | [
"DirectSum.lieRing._proof_5",
"LieRing.toAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Bracket.bracket",
"AddZeroClass.toAddZero",
"DFinsupp.instDFunLike",
"LieRingModule.toBracket",
"AddZero.toZero",
"LieRing",
"DFinsupp",
"AddCommMonoid.toAddMonoid",
"DFinsupp... | true |
_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.Cb | Mathlib.Topology.MetricSpace.GromovHausdorffRealized | [
"Real",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"Sum",
"instTopologicalSpaceSum",
"MetricSpace",
"MetricSpace.toPseudoMetricSpace",
"Real.pseudoMetricSpace",
"Prod",
"UniformSpace.toTopologicalSpace",
"BoundedContinuousFunction"
] | true |
OrderIso.lt_iff_lt | Mathlib.Order.Hom.Basic | [
"Preorder.toLT",
"OrderIso.toOrderEmbedding",
"Preorder.toLE",
"OrderIso",
"Iff",
"instFunLikeOrderIso",
"LT.lt",
"OrderEmbedding.lt_iff_lt",
"DFunLike.coe",
"Preorder"
] | true |
_private.Std.Data.ExtDHashMap.Lemmas.0.Std.ExtDHashMap.Const.insertMany_list_eq_empty_iff._simp_1_2 | Std.Data.ExtDHashMap.Lemmas | [
"Bool.true",
"List",
"List.isEmpty",
"List.isEmpty_iff",
"propext",
"Bool",
"Eq.symm",
"Eq",
"List.nil"
] | false |
Sym.equivNatSum | Mathlib.Data.Finsupp.Multiset | [
"Nat.instMulZeroClass",
"AddMonoid.toAddZeroClass",
"Finsupp.sum",
"Nat.instAddMonoid",
"Equiv.subtypeEquiv",
"Multiset",
"id",
"Equiv",
"Subtype",
"Finsupp.instAdd",
"Multiset.toFinsupp",
"Nat",
"Sym",
"Nat.instAddCommMonoid",
"Multiset.card",
"AddEquiv.toEquiv",
"Sym.equivNatSum._p... | true |
_private.Mathlib.Data.Set.Insert.0.Set.insert_subset_insert_iff._proof_1_1 | Mathlib.Data.Set.Insert | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"False",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind.iff_eq",
"Set.subset_def",
"congrArg",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_true",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"Insert.insert",
... | false |
CategoryTheory.ComposableArrows.homMk₁._proof_4 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"instOfNatNat",
"LE.le",
"instLENat",
"_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0.CategoryTheory.ComposableArrows.homMk₁._proof_3",
"Nat",
"Decidable.byContradiction",
"OfNat.ofNat",
"Not",
"Nat.decLe"
] | false |
ContinuousLinearMap.adjointAux._proof_6 | Mathlib.Analysis.InnerProductSpace.Adjoint | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"ContinuousLinearMap.adjointAux._proof_3",
"IsTopologi... | false |
HahnSeries.instAddMonoid._proof_1 | Mathlib.RingTheory.HahnSeries.Addition | [
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"Function.Injective.addSemigroup._proof_2",
"HahnSeries.coeff_injective",
"AddZeroClass.toAddZero",
"PartialOrder",
"HahnSeries.instAdd",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"AddMonoid",
"HahnSeries.coeff",
"Pi.addMonoid",
"Hah... | false |
Mathlib.Meta.Simproc.FactorsHelper.nil | Mathlib.Tactic.Simproc.Factors | [
"Nat.Prime",
"Nat.instOne",
"Membership.mem",
"List.IsChain",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"List.IsChain.singleton",
"List.cons",
"List",
"And",
"List.instMembership",
"Nat",
"And.intro",
"List.prod_nil",
"List.forall_mem_nil",
"OfNat.ofNat",
"Eq",
"List.... | true |
IsClosed.sdiff | Mathlib.Topology.Basic | [
"Iff.mpr",
"False",
"Compl.compl",
"Membership.mem",
"Set.instCompl",
"IsClosed",
"TopologicalSpace",
"SDiff.sdiff",
"IsClosed.inter",
"IsOpen",
"Set.instMembership",
"Set.instSDiff",
"isClosed_compl_iff",
"Set"
] | true |
_private.Mathlib.NumberTheory.ArithmeticFunction.LFunction.0.ArithmeticFunction.ofPowerSeries.match_3 | Mathlib.NumberTheory.ArithmeticFunction.LFunction | [
"Prod.mk",
"Nat",
"Prod",
"Prod.casesOn"
] | false |
Std.Tactic.BVDecide.Frontend.Normalize.BitVec.not_bif_eq_bif' | Std.Tactic.BVDecide.Normalize.Equal | [
"cond",
"BitVec",
"instBEqOfDecidableEq",
"instDecidableEqBitVec",
"Bool.true",
"BEq.beq",
"Bool.casesOn",
"Nat",
"Complement.complement",
"eq_self",
"Bool",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"Eq.symm",
"Bool.false",
"Eq",
"BitVec.instComplement"
] | true |
HomologicalComplex.homologyFunctorIso_inv_app | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | [
"HomologicalComplex.homologyFunctor",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ShortComplex.homologyFunctor",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Short... | true |
Lean.Lsp.InlayHintClientCapabilities.noConfusionType | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.ResolveSupport",
"Lean.Lsp.InlayHintClientCapabilities.casesOn",
"Bool",
"Eq",
"Lean.Lsp.InlayHintClientCapabilities",
"Option"
] | false |
instDecidableAnd._proof_1 | Init.Prelude | [
"False",
"And",
"And.right",
"Not"
] | false |
Lean.Lsp.FileSource.noConfusion | Lean.Server.FileSource | [
"Lean.Lsp.FileSource.noConfusionType",
"HEq.refl",
"Lean.Lsp.DocumentUri",
"Lean.Lsp.FileSource.casesOn",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Lean.Lsp.FileSource",
"Eq"
] | false |
Lean.Meta.Grind.Arith.CommRing.State.semirings | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | [
"Lean.Meta.Grind.Arith.CommRing.State",
"Array",
"Lean.Meta.Grind.Arith.CommRing.CommSemiring"
] | true |
ContinuousAffineMap.coe_continuousMap_mk._simp_1 | Mathlib.Topology.Algebra.ContinuousAffineMap | [
"Continuous",
"AffineMap.instFunLike",
"ContinuousAffineMap.mk",
"AddCommGroup.toAddCommMonoid",
"ContinuousMap.mk",
"ContinuousMap",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"ContinuousAffineMap",
"AffineMap",
"ContinuousAffineMap.instContinuousMapClass",
"toContinuousMap",
"TopologicalSp... | false |
MeasureTheory.setToFun_smul_left | Mathlib.MeasureTheory.Integral.SetToL1 | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"CompleteSpace",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpa... | true |
upperClosure_add | Mathlib.Algebra.Order.UpperLower | [
"Eq.mpr",
"UpperSet",
"add_upperClosure",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"UpperSet.instSetLike",
"AddMonoid.toAddZeroClass",
"upperClosure",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"id",
"add_comm",
"instHAdd",
"Set.add",
"Ad... | true |
Real.cos_nat_mul_two_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real",
"Real.pi",
"HMul.hMul",
"Real.cos",
"Nat.instAtLeastTwoHAddOfNat",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Real.semiring",
"Function.Periodic.nat_mul_eq",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWith... | true |
Lean.Elab.InlayHintLabel.toLspInlayHintLabel | Lean.Server.FileWorker.InlayHints | [
"Pure.pure",
"Lean.Lsp.InlayHintLabelPart",
"Monad.toApplicative",
"String",
"Lean.FileMap",
"Lean.Elab.InlayHintLabel",
"IO",
"Lean.Lsp.InlayHintLabel",
"instMonadEIO",
"Applicative.toPure",
"Lean.Lsp.InlayHintLabel.name",
"Array",
"Lean.Elab.InlayHintLabelPart.toLspInlayHintLabelPart",
"... | true |
SelbergSieve.casesOn | Mathlib.NumberTheory.SelbergSieve | [
"Real.instLE",
"Real",
"LE.le",
"SelbergSieve",
"Real.instOne",
"BoundingSieve",
"One.toOfNat1",
"SelbergSieve.rec",
"SelbergSieve.mk",
"OfNat.ofNat"
] | false |
Units.divp_add_divp | Mathlib.Algebra.Ring.Units | [
"add_mul",
"Units.val",
"Eq.mpr",
"MulOne.toOne",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"Monoid.toMulOneClass",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"mul_assoc",
"Units.inv_mul",
"Distrib.rig... | true |
SimpleGraph.Finsubgraph.coe_sup._simp_1 | Mathlib.Combinatorics.SimpleGraph.Finsubgraph | [
"SimpleGraph.Subgraph",
"Set.Finite",
"SimpleGraph.Finsubgraph.instMax",
"SimpleGraph.Subgraph.instMax",
"SimpleGraph",
"Max.max",
"SimpleGraph.Finsubgraph.coe_sup",
"SimpleGraph.Finsubgraph",
"Eq.symm",
"Subtype.val",
"Eq",
"SimpleGraph.Subgraph.verts"
] | false |
Std.DTreeMap.Internal.Cell.property | Std.Data.DTreeMap.Internal.Cell | [
"Ord",
"Std.OrientedOrd",
"Option.some",
"Ordering",
"Ordering.eq",
"Sigma.fst",
"Std.DTreeMap.Internal.Cell",
"Std.DTreeMap.Internal.Cell.inner",
"Eq",
"Sigma",
"Option"
] | true |
Finset.dens_smul_finset | Mathlib.Algebra.Group.Pointwise.Finset.Density | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"instHDiv",
"congrArg",
"NNRat.instSemifield",
"Finset",
"Group",
"Finset.smulFinset",
"Fintype.card",
"HDiv.hDiv",
"NNRat.instDiv",
"DivInvMonoid.toMonoid",
"NNRat",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWi... | true |
ContinuousLinearMap.differentiableAt | Mathlib.Analysis.Calculus.FDeriv.Linear | [
"ContinuousLinearMap.hasFDerivAt",
"AddCommGroup.toAddCommMonoid",
"DifferentiableAt",
"ContinuousLinearMap.funLike",
"NormedField.toField",
"AddCommGroup",
"Field.toSemifield",
"ContinuousLinearMap",
"TopologicalSpace",
"Semifield.toDivisionSemiring",
"HasFDerivAt.differentiableAt",
"Division... | true |
_private.Mathlib.Topology.Algebra.Affine.0.AffineMap.continuous_linear_iff._simp_1_3 | Mathlib.Topology.Algebra.Affine | [
"Continuous",
"Function.comp",
"Homeomorph.comp_continuous_iff'",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"propext",
"Homeomorph",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
CategoryTheory.Core.isoMk_inv_iso | Mathlib.CategoryTheory.Core | [
"CategoryTheory.coreCategory",
"CategoryTheory.Core.isoMk",
"CategoryTheory.CoreHom.iso",
"CategoryTheory.Iso",
"CategoryTheory.Core.of",
"CategoryTheory.Iso.symm",
"Eq.refl",
"CategoryTheory.Groupoid.toCategory",
"CategoryTheory.Core",
"Eq",
"CategoryTheory.Iso.inv",
"CategoryTheory.Category"... | true |
Lean.Grind.Config.revert._default | Init.Grind.Config | [
"id",
"Bool",
"Bool.false"
] | false |
WeierstrassCurve.Projective.addZ | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula | [
"NegZeroClass.toNeg",
"CommRing",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"Fin.instOfNat",
"Distrib.toAdd",
"AddMonoidWithOne.toNatCast",
"SubtractionMonoid.toSubNegZeroMonoid",
"instOfNatNat",
"WeierstrassCurve... | true |
_private.Mathlib.Data.Finset.Powerset.0.Finset.pairwiseDisjoint_pair_insert._simp_1_8 | Mathlib.Data.Finset.Powerset | [
"or_imp",
"And",
"propext",
"Or",
"Eq"
] | false |
List.findFinIdx?.eq_1 | Init.Data.List.Find | [
"instOfNatNat",
"List.findFinIdx?",
"List",
"List.findFinIdx?.go",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Fin",
"Eq",
"List.length",
"List.findFinIdx?._proof_4",
"Option"
] | true |
Lean.IR.instInhabitedCtorInfo | Lean.Compiler.IR.Basic | [
"Lean.IR.CtorInfo",
"Lean.IR.instInhabitedCtorInfo.default",
"Inhabited",
"Inhabited.mk"
] | true |
List.erase_eq_self_iff_forall_bne | Batteries.Data.List.Lemmas | [
"Eq.mpr",
"List.erase_eq_eraseP'",
"congrArg",
"Iff.rfl",
"Membership.mem",
"id",
"Bool.true",
"List",
"BEq.beq",
"Iff",
"List.erase",
"List.instMembership",
"List.eraseP_eq_self_iff",
"propext",
"Bool",
"List.eraseP",
"BEq",
"Eq",
"Not"
] | true |
Std.Do.PredTrans.bind._proof_1 | Std.Do.PredTrans | [
"Std.Do.PredTrans.conjunctive",
"Eq.mpr",
"Std.Do.PredTrans.Conjunctive",
"Std.Do.SPred.bientails.to_eq",
"congrArg",
"Std.Do.PostCond",
"Std.Do.Assertion",
"Eq.rec",
"id",
"Prod.mk",
"Std.Do.PostShape",
"Std.Do.ExceptConds.and",
"funext",
"Std.Do.PostCond.and",
"Std.Do.PredTrans.apply",... | false |
CategoryTheory.Oplax.OplaxTrans.StrongCore.noConfusionType | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.Oplax.OplaxTrans.StrongCore.case... | false |
Rat.den_normalize | Init.Data.Rat.Lemmas | [
"Nat.gcd",
"Int.instDiv",
"instHDiv",
"congrArg",
"Rat",
"Rat.normalize.den_nz",
"Rat.den",
"HDiv.hDiv",
"Ne",
"instOfNatNat",
"Int",
"Nat.cast",
"Rat.normalize",
"Rat.normalize.reduced",
"Nat",
"True",
"Int.natAbs",
"eq_self",
"Nat.instDiv",
"of_eq_true",
"congrFun'",
"Rat... | true |
_private.Mathlib.Tactic.Linter.FlexibleLinter.0.Mathlib.Linter.Flexible.flexibleLinter.match_5 | Mathlib.Tactic.Linter.FlexibleLinter | [
"MProd.casesOn",
"_private.Mathlib.Tactic.Linter.FlexibleLinter.0.Mathlib.Linter.Flexible.StainData",
"Lean.Syntax",
"Lean.MVarId",
"Lean.FVarId",
"MProd.mk",
"Array",
"MProd",
"Prod"
] | false |
Std.CloseableChannel.Error.ctorIdx | Std.Sync.Channel | [
"Std.CloseableChannel.Error",
"Std.CloseableChannel.Error.casesOn",
"Nat"
] | false |
TypeVec.typevecCasesCons₂_appendFun | Mathlib.Data.TypeVec | [
"TypeVec.typevecCasesCons₂",
"TypeVec.append1",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"TypeVec.appendFun",
"instAddNat",
"OfNat.ofNat",
"TypeVec.Arrow",
"Eq",
"rfl",
"TypeVec"
] | true |
_private.Lean.Elab.Tactic.Do.ProofMode.MGoal.0.Lean.Elab.Tactic.Do.ProofMode.parseHyp?._sparseCasesOn_5 | Lean.Elab.Tactic.Do.ProofMode.MGoal | [
"Lean.DataValue.ofInt",
"Nat.ne_of_beq_eq_false",
"Lean.DataValue.rec",
"String",
"Nat.shiftRight",
"Lean.DataValue.ctorIdx",
"Lean.Syntax",
"Nat.hasNotBit",
"instOfNatNat",
"Int",
"Nat.land",
"Nat",
"Lean.DataValue.ofBool",
"Lean.DataValue.ofString",
"Bool",
"Lean.Name",
"Eq.refl",
... | false |
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