name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
IsApproximateAddSubgroup.addSubgroup | Mathlib.Combinatorics.Additive.ApproximateSubgroup | [
"SetLike",
"AddGroup.toSubtractionMonoid",
"SubtractionMonoid.toInvolutiveNeg",
"False",
"Real.instLE",
"Real",
"instHSMul",
"Finset.coe_singleton",
"eq_false",
"AddMonoid.toAddSemigroup",
"OfNat.ofNat_ne_zero",
"instReflLe",
"congrArg",
"and_self",
"Set.image_id'",
"Finset",
"Std.le... | true |
CommBialgCat.isoMk | Mathlib.Algebra.Category.CommBialgCat | [
"CommRing",
"Coalgebra.toCoalgebraStruct",
"CommBialgCat.ofHom",
"CommBialgCat.isoMk._proof_5",
"Bialgebra.toCoalgebra",
"CommSemiring.toSemiring",
"BialgEquiv",
"CommBialgCat.isoMk._proof_1",
"CommBialgCat.of",
"Algebra.toModule",
"CategoryTheory.Iso",
"CategoryTheory.Iso.mk",
"BialgEquiv.i... | true |
RestrictedProduct.continuous_eval | Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace | [
"Continuous",
"RestrictedProduct.continuous_coe",
"Pi.topologicalSpace",
"Continuous.comp",
"RestrictedProduct.topologicalSpace",
"RestrictedProduct.instDFunLike",
"RestrictedProduct",
"TopologicalSpace",
"continuous_apply",
"DFunLike.coe",
"Filter",
"Set"
] | true |
Std.DTreeMap.Raw.size_le_size_insertIfNew | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.size",
"Std.DTreeMap.Internal.Impl.size_le_size_insertIfNew!",
"Ord.mk",
"Ordering",
"LE.le",
"Std.TransCmp",
"instLENat",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Nat",
"Std.DTreeMap.Raw.insertIfNew",
"Std.DTreeMap.Raw.WF",
"Std.DTreeMap.Raw"
] | true |
Std.HashMap.values | Std.Data.HashMap.Basic | [
"Std.HashMap",
"List",
"Std.DHashMap.values",
"Hashable",
"Std.HashMap.inner",
"BEq"
] | true |
_private.Mathlib.Analysis.Convex.MetricSpace.0.continuous_convexComboPair_of_isBounded._simp_1_4 | Mathlib.Analysis.Convex.MetricSpace | [
"And",
"not_and_or",
"propext",
"Or",
"Eq",
"Not"
] | false |
Std.HashMap.Raw.getKey?_filter_key | Std.Data.HashMap.RawLemmas | [
"Std.HashMap.Raw.getKey?",
"Std.HashMap.Raw.WF.out",
"Std.HashMap.Raw.WF",
"LawfulHashable",
"Std.HashMap.Raw",
"Option.filter",
"EquivBEq",
"Std.DHashMap.Raw.getKey?_filter_key",
"Std.HashMap.Raw.filter",
"Bool",
"Std.HashMap.Raw.inner",
"Hashable",
"BEq",
"Eq",
"Option"
] | true |
instAddCommMonoidWeakDual._proof_11 | Mathlib.Topology.Algebra.Module.WeakDual | [
"Semiring.toModule",
"instAddCommMonoidWeakDual._aux_1",
"CommSemiring.toSemiring",
"Add.mk",
"Algebra.toSMul",
"Algebra.id",
"Distrib.toAdd",
"ContinuousLinearMap.addCommMonoid._proof_5",
"instOfNatNat",
"ContinuousConstSMul",
"AddSemigroup.mk",
"autoParam",
"AddCommMonoid",
"ContinuousLi... | false |
VSub.casesOn | Mathlib.Algebra.Notation.Defs | [
"VSub.mk",
"VSub.rec",
"VSub"
] | false |
Module.Basis.ofSplitExact._proof_3 | Mathlib.LinearAlgebra.Basis.Exact | [
"Function.Exact",
"LinearMap.id",
"AddCommGroup.toAddCommMonoid",
"Module.Basis.ofSplitExact._proof_2",
"LinearMap.instFunLike",
"Function.comp",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"Module.Basis.instFunLike",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtra... | false |
Std.IterM.mk.injEq | Init.Data.Iterators.Basic | [
"Eq.propIntro",
"Std.IterM.mk.inj",
"Std.IterM.mk",
"Eq.ndrec",
"Eq.refl",
"Std.IterM",
"Eq"
] | true |
AddAut.conj._proof_6 | Mathlib.Algebra.Group.End | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"Function.LeftInverse",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"Monoid.toMulOneClass",
"congrArg",
"Additive",
"AddAut.conj._proof_4",
"AddMonoid.toAddZeroClass",
"AddAut.instGroup",
"AddEquiv.ext",
"Additive.toMul... | false |
CategoryTheory.WithInitial.mapId | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.WithInitial.mapId._proof_2",
"CategoryTheory.WithInitial.of",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"CategoryTheory.Iso.refl",
"CategoryTheory.Iso",
"CategoryTheory.WithInitial.map",
"CategoryTheory.WithInitial",
"CategoryTheory.W... | true |
Lean.Elab.Command.Scope.varUIds._default | Lean.Elab.Command.Scope | [
"id",
"List.toArray",
"Array",
"Lean.Name",
"List.nil"
] | false |
CategoryTheory.ShortComplex.Splitting.ofIso._proof_2 | Mathlib.Algebra.Homology.ShortComplex.Exact | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.Splitting.s_g_assoc",
"CategoryTheory.ShortComplex",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.ShortComplex.instCat... | false |
Lean.Grind.Ring.neg_zsmul | Init.Grind.Ring.Basic | [
"instHSMul",
"Int.instNegInt",
"Int",
"Lean.Grind.Ring.toNeg",
"Lean.Grind.Ring",
"HSMul.hSMul",
"Lean.Grind.Ring.zsmul",
"Eq",
"Neg.neg"
] | true |
Lean.Meta.RefinedDiscrTree.Key.labelledStar.noConfusion | Mathlib.Lean.Meta.RefinedDiscrTree.Basic | [
"Lean.Meta.RefinedDiscrTree.Key.noConfusion",
"id",
"Lean.Meta.RefinedDiscrTree.Key",
"Nat",
"Lean.Meta.RefinedDiscrTree.Key.labelledStar",
"Eq"
] | false |
HasFDerivAt.sub_const | Mathlib.Analysis.Calculus.FDeriv.Add | [
"Iff.mpr",
"HasFDerivAt",
"NormedSpace",
"hasFDerivAt_sub_const_iff",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"NormedAddGroup.toAddGroup",
"Field.toSemifield",
"ContinuousLinearMap",
"SubNegMonoid.toSub",
"instHSub",
"Semifield.toDivi... | true |
Mathlib.Meta.NormNum.isNat_abs_nonneg | Mathlib.Tactic.NormNum.Abs | [
"Eq.mpr",
"Lattice",
"Mathlib.Meta.NormNum.IsNat",
"Nat.abs_cast",
"IsOrderedRing",
"AddGroupWithOne.toAddGroup",
"abs",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"Mathlib.Meta.NormNum.IsNat.mk",
"SemilatticeInf.toPartialOrder",
"id",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"Na... | true |
Pi.single_mul_left_apply | Mathlib.Algebra.GroupWithZero.Pi | [
"HMul.hMul",
"MulZeroClass.toMul",
"MulZeroClass.zero_mul",
"Pi.apply_single",
"MulZeroClass",
"Pi.single",
"Eq.symm",
"Eq",
"MulZeroClass.toZero",
"instHMul",
"DecidableEq"
] | true |
AddCommGroupWithOne.toNatCast | Mathlib.Data.Int.Cast.Defs | [
"AddCommGroupWithOne",
"NatCast"
] | true |
Affine.Simplex.centroid_reindex | Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid | [
"Iff.mpr",
"Eq.mpr",
"Pi.Function.module",
"Affine.Simplex.points",
"Fintype.card_fin",
"Semiring.toModule",
"AffineMap.instFunLike",
"Equiv.instEquivLike",
"Equiv.symm_comp_self",
"Finset.univ",
"outParam",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"Finset",
"Affine.Simp... | true |
ENNReal.div_lt_top | Mathlib.Data.ENNReal.Inv | [
"Iff.mpr",
"Preorder.toLT",
"instHDiv",
"PartialOrder.toPreorder",
"ENNReal.inv_ne_top",
"HDiv.hDiv",
"Ne",
"instZeroENNReal",
"ENNReal.mul_lt_top",
"Inv.inv",
"Ne.lt_top",
"LT.lt",
"ENNReal",
"ENNReal.instDivInvMonoid",
"DivInvMonoid.toDiv",
"ENNReal.instPartialOrder",
"Zero.toOfNat... | true |
List.length_range | Init.Data.List.Range | [
"congrArg",
"List.range'",
"List.length_range'",
"instOfNatNat",
"List.range",
"List",
"Nat",
"List.range_eq_range'",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"OfNat.ofNat",
"Eq",
"List.length",
"Eq.trans"
] | true |
Lean.Elab.Do.mkMonadicType | Lean.Elab.Do.Basic | [
"Pure.pure",
"instMonadReaderOfReaderTOfMonad",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Elab.Do.MonadInfo.m",
"MonadReader.read",
"ReaderT.instMonad",
"Lean.Expr",
"Applicative.toPure",
"instMonadReaderOfMonadReaderOf",
"Lean.Elab.Term.TermElabM",
"Lean.Elab.Do.DoElabM",
"Monad.toBind",
"... | true |
MeasureTheory.integral_union_eq_left_of_forall | Mathlib.MeasureTheory.Integral.Bochner.Set | [
"Real",
"MeasureTheory.Measure",
"MeasurableSet",
"NormedSpace",
"MeasurableSet.nullMeasurableSet",
"Membership.mem",
"Set.instUnion",
"MeasureTheory.Measure.restrict",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Meas... | true |
ModuleCat.linearOverField._proof_2 | Mathlib.Algebra.Category.ModuleCat.Algebra | [
"IsScalarTower.to_smulCommClass'",
"instHSMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"LinearMap.ext",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"ModuleCat.moduleOfAlgebraMod... | false |
ContDiffWithinAt.sinh | Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | [
"Real",
"NormedSpace",
"Real.denselyNormedField",
"Real.sinh",
"Real.normedAddCommGroup",
"ContDiffAt.comp_contDiffWithinAt",
"Real.contDiff_sinh",
"ENat",
"NontriviallyNormedField.toNormedField",
"Real.normedField",
"DenselyNormedField.toNontriviallyNormedField",
"NormedField.toNormedSpace",
... | true |
_private.Init.Data.Vector.Count.0.Vector.count_le_count_map._simp_1_1 | Init.Data.Vector.Count | [
"Array.count_le_count_map",
"LawfulBEq",
"Array.map",
"LE.le",
"instLENat",
"Array",
"Nat",
"True",
"eq_true",
"BEq",
"Eq",
"Array.count"
] | false |
_private.Lean.Meta.Tactic.Grind.Theorems.0.Lean.Meta.Grind.Theorems.mk.noConfusion | Lean.Meta.Tactic.Grind.Theorems | [
"_private.Lean.Meta.Tactic.Grind.Theorems.0.Lean.Meta.Grind.Theorems.mk",
"Lean.Meta.Grind.Theorems.noConfusion",
"Lean.PHashMap",
"id",
"Lean.Meta.Grind.Theorems",
"Lean.PHashSet",
"Lean.Meta.Grind.instBEqOrigin",
"List",
"heq_of_eq",
"Lean.Meta.Grind.Origin",
"Lean.Meta.Grind.instHashableOrigi... | false |
CategoryTheory.RigidCategory.ctorIdx | Mathlib.CategoryTheory.Monoidal.Rigid.Basic | [
"CategoryTheory.MonoidalCategory",
"Nat",
"CategoryTheory.RigidCategory",
"CategoryTheory.Category"
] | false |
Array.all_subtype | Init.Data.Array.Attach | [
"List.unattach",
"Eq.mpr",
"List.all",
"Array.all_congr",
"Array.all",
"congrArg",
"List.unattach_toArray",
"List.length_unattach",
"Array.casesOn",
"Subtype",
"instOfNatNat",
"List.toArray",
"Subtype.mk",
"Array",
"List",
"List.all_toArray'",
"List.size_toArray",
"Nat",
"congr",... | true |
gcd_comm | Mathlib.Algebra.GCDMonoid.Basic | [
"GCDMonoid.toIsCancelMulZero",
"NormalizedGCDMonoid",
"dvd_antisymm_of_normalize_eq",
"GCDMonoid.dvd_gcd",
"normalize_gcd",
"GCDMonoid.gcd",
"NormalizedGCDMonoid.toGCDMonoid",
"CommMonoidWithZero",
"NormalizedGCDMonoid.toNormalizationMonoid",
"GCDMonoid.gcd_dvd_left",
"GCDMonoid.gcd_dvd_right",
... | true |
BoxIntegral.Box.instPartialOrder._proof_3 | Mathlib.Analysis.BoxIntegral.Box.Basic | [
"Real",
"Preorder.toLT",
"BoxIntegral.Box.toSet",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toConditionallyCompleteLattice",
"LE.le",
"And",
"Iff",
"Preorder.lt_iff_le_not_ge",
"LT.lt",
"CompleteBooleanAlgebra.toCompleteLattice",
"ConditionallyCompletePartialOrderSup.toPar... | false |
_private.Std.Data.ExtDHashMap.Lemmas.0.Std.ExtDHashMap.map_eq_empty_iff._simp_1_2 | Std.Data.ExtDHashMap.Lemmas | [
"Bool.coe_iff_coe",
"Bool.true",
"Iff",
"propext",
"Bool",
"Eq"
] | false |
groupHomology.H0π_comp_H0Iso_hom_assoc | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"CategoryTheory.Category.assoc",
"Rep.coinvariantsFunctor",
"Rep.V",
"CommRing",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"groupHomology.H0",
"LinearMap.instFunLike",
"Group",
"R... | true |
Finsupp.support_indicator_subset | Mathlib.Data.Finsupp.Indicator | [
"Finsupp.mem_support_iff",
"Finsupp.instFunLike",
"Finsupp.indicator",
"congrArg",
"Finset",
"Finsupp.indicator_of_notMem",
"Classical.byContradiction",
"Finsupp.support",
"Membership.mem",
"Eq.mp",
"HasSubset.Subset",
"Ne",
"SetLike.coe",
"Finset.instSetLike",
"propext",
"Zero.toOfNat... | true |
AddSubsemigroup.centerToAddOpposite._proof_4 | Mathlib.GroupTheory.Submonoid.Center | [
"Iff.mpr",
"AddSubsemigroup.instSetLike",
"Membership.mem",
"AddOpposite.unop_mem_center_iff",
"AddOpposite",
"AddOpposite.instAdd",
"Subtype",
"AddSubsemigroup.center",
"Set.addCenter",
"AddSubsemigroup",
"AddOpposite.unop",
"Subtype.val",
"Set.instMembership",
"SetLike.instMembership",
... | false |
Substring.Raw.Valid.data_drop | Batteries.Data.String.Lemmas | [
"String.toList_ofList",
"congrArg",
"String",
"Substring.Raw.Valid.validFor",
"_private.Batteries.Data.String.Lemmas.0.Substring.Raw.Valid.data_drop.match_1_1",
"Exists",
"Substring.Raw.ValidFor",
"Substring.Raw.drop",
"Substring.Raw",
"Substring.Raw.toString",
"instHAppendOfAppend",
"List",
... | true |
_private.Mathlib.MeasureTheory.Integral.IntervalAverage.0.exists_eq_interval_average_of_noAtoms._proof_1_1 | Mathlib.MeasureTheory.Integral.IntervalAverage | [
"instLawfulOrderLT_mathlib",
"Set.Ioc",
"Lean.Grind.Field.toCommRing",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"eq_false",
"Lean.Grind.Order.le_lt_trans_k",
"Lean.Grind.iff_eq",
"Lean.Grind.Orde... | false |
_private.Mathlib.Algebra.Category.ModuleCat.Semi.0.SemimoduleCat.mk | Mathlib.Algebra.Category.ModuleCat.Semi | [
"SemimoduleCat",
"AddCommMonoid",
"Semiring",
"Module",
"_private.Mathlib.Algebra.Category.ModuleCat.Semi.0.SemimoduleCat.mk"
] | true |
SimplicialObject.Split.rec | Mathlib.AlgebraicTopology.SimplicialObject.Split | [
"SimplicialObject.Split",
"SimplicialObject.Splitting",
"SimplicialObject.Split.mk",
"CategoryTheory.Category",
"CategoryTheory.SimplicialObject"
] | false |
QuasiconcaveOn.dual | Mathlib.Analysis.Convex.Quasiconvex | [
"OrderDual.instLE",
"OrderDual.toDual",
"Equiv.instEquivLike",
"SMul",
"Function.comp",
"PartialOrder",
"id",
"Equiv",
"LE",
"AddCommMonoid",
"Semiring",
"QuasiconcaveOn",
"OrderDual",
"QuasiconvexOn",
"DFunLike.coe",
"EquivLike.toFunLike",
"Set"
] | true |
IsDedekindDomain.HeightOneSpectrum.under._proof_1 | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"CommRing",
"CommSemiring.toSemiring",
"IsDedekindDomain.HeightOneSpectrum",
"Algebra",
"IsDedekindDomain.HeightOneSpectrum.asIdeal",
"CommRing.toCommSemiring",
"Ideal.IsPrime",
"Ideal.IsPrime.under",
"IsDedekindDomain.HeightOneSpectrum.isPrime",
"Ideal.under"
] | false |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order.0.isStrictlyPositive_add._proof_1_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order | [
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"NormedRing.toRing",
"eq_false",
"Lean.Grind.iff_eq",
"Ring.toNonAssocRing",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Lean.Grind.eq_false_of_imp_eq_true",
"Lean.Grind.and_eq_of_eq_true_left",
"IsUnit",
"NonUnitalNonAssocSemiring.to... | false |
Std.ExtDTreeMap.Const.alter_eq_empty_iff | Std.Data.ExtDTreeMap.Lemmas | [
"Std.ExtDTreeMap.erase_eq_empty_iff",
"Eq.mpr",
"Std.ExtDTreeMap.Const.alter",
"congrArg",
"Std.ExtDTreeMap.erase",
"Iff.rfl",
"Membership.mem",
"Ordering",
"id",
"Std.ExtDTreeMap.instEmptyCollection",
"instOfNatNat",
"Std.TransCmp",
"Std.ExtDTreeMap.Const.get?",
"Option.none",
"And",
... | true |
Lean.Server.FileWorker.WorkerState.mk.injEq | Lean.Server.FileWorker | [
"Lean.Server.FileWorker.WorkerState.mk",
"Lean.Server.FileWorker.AvailableImportsCache",
"Eq.propIntro",
"UInt64",
"UInt64.instOrd",
"Lean.injEq_helper",
"Lean.Server.FileWorker.RpcSession",
"Lean.Server.FileWorker.EditableDocument",
"Ord.compare",
"And",
"Lean.Server.ServerTask",
"Lean.Server... | true |
Finset.gcd_congr | Mathlib.Algebra.GCDMonoid.Finset | [
"Finset",
"NormalizedGCDMonoid",
"Membership.mem",
"Finset.fold_congr",
"CommMonoidWithZero.toMonoidWithZero",
"Finset.gcd",
"GCDMonoid.gcd",
"MonoidWithZero.toMulZeroOneClass",
"Finset.instSetLike",
"NormalizedGCDMonoid.toGCDMonoid",
"CommMonoidWithZero",
"instCommutativeGcd",
"Eq.ndrec",
... | true |
Valuation.mem_nhds_iff | Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | [
"Filter.instMembership",
"AddGroup.toSubtractionMonoid",
"Units.val",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"NegZeroClass.toNeg",
"ValuativeRel.instLinearOrderValueGroupWithZero",
"CommRing",
"Preorder.toLT",
"NonUnitalCom... | true |
_private.Mathlib.NumberTheory.ModularForms.QExpansion.0.ModularFormClass.qExpansion_coeff_eq_intervalIntegral._simp_1_7 | Mathlib.NumberTheory.ModularForms.QExpansion | [
"False",
"Real",
"Real.pi",
"eq_false",
"Real.instZero",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Real.pi_ne_zero"
] | false |
Std.TreeMap.getKeyD_insert_self | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.insert",
"Std.TreeMap.inner",
"Ordering",
"Std.TransCmp",
"Std.TreeMap.getKeyD",
"Std.DTreeMap.getKeyD_insert_self",
"Eq",
"Std.TreeMap"
] | true |
TopCat.ι₁_fst_assoc | Mathlib.Topology.Category.TopCat.Monoidal | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"TopCat.instCategory",
"TopCat.instCartesianMonoidalCategory",
"CategoryTheory.CategoryStruct.id",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.SemiCartesianMonoidalCatego... | true |
List.length_mapFinIdx | Init.Data.List.MapIdx | [
"List.length_mapFinIdx_go",
"congrArg",
"List.mapFinIdx",
"List.toArray",
"List",
"Nat",
"LT.lt",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"instLTNat",
"List.mapFinIdx._proof_5",
"Eq",
"List.length",
"Eq.trans",
"List.nil"
] | true |
Subalgebra.normedCommRing._proof_1 | Mathlib.Analysis.Normed.Ring.Basic | [
"Subalgebra.instSetLike",
"NormedCommRing.toNormedRing",
"NormedCommRing.toCommRing",
"Real",
"CommRing",
"NormedRing.toRing",
"NormedCommRing",
"Real.instZero",
"CommSemiring.toSemiring",
"Algebra",
"Membership.mem",
"Subtype",
"Subalgebra.normedRing",
"MetricSpace.eq_of_dist_eq_zero",
... | false |
RelSeries.head_fromListIsChain | Mathlib.Order.RelSeries | [
"List.head",
"instNeZeroNatHAdd_1",
"SetRel",
"congrArg",
"RelSeries.fromListIsChain._proof_3",
"HSub.hSub",
"Membership.mem",
"id",
"Fin.instOfNat",
"RelSeries.length",
"List.IsChain",
"Prod.mk",
"instSubNat",
"Ne",
"instOfNatNat",
"Fin.val",
"List.getElem_zero_eq_head._proof_2",
... | true |
_private.Mathlib.Tactic.Hint.0.Mathlib.Tactic.Hint._aux_Mathlib_Tactic_Hint___elabRules_Mathlib_Tactic_Hint_registerHintStx_1._sparseCasesOn_1 | Mathlib.Tactic.Hint | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
Graph.IsLoopAt.mono | Mathlib.Combinatorics.Graph.Subgraph | [
"Graph.IsLink.mono",
"Graph.IsLoopAt",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Graph",
"LE.le",
"Graph.instPartialOrder"
] | true |
_private.Mathlib.Data.Seq.Basic.0.Stream'.Seq.take.match_1.splitter | Mathlib.Data.Seq.Basic | [
"Stream'.Seq",
"instOfNatNat",
"Nat",
"Stream'.Seq.take.match_1",
"OfNat.ofNat",
"Nat.succ"
] | true |
ExteriorAlgebra.ι_inj._simp_1 | Mathlib.LinearAlgebra.ExteriorAlgebra.Basic | [
"ExteriorAlgebra.ι_inj",
"CommRing",
"Semiring.toModule",
"QuadraticMap.instZero",
"Ring.toNonAssocRing",
"ExteriorAlgebra",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"QuadraticForm",
"LinearMap.instFunLike",
"AddCommGroup",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",... | false |
CategoryTheory.NatTrans.leftOpWhiskerRight_assoc | Mathlib.CategoryTheory.Opposites | [
"CategoryTheory.Functor.op",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"Eq.mp",
"CategoryTheory.Functor.whiskerLeft",
"id",
"Math... | true |
edist_nndist | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"Eq.mpr",
"NNDist.nndist",
"Real",
"ENNReal.ofNNReal",
"ENNReal.ofReal",
"congrArg",
"PseudoMetricSpace.toNNDist",
"id",
"dist_nndist",
"PseudoMetricSpace",
"edist_dist",
"PseudoMetricSpace.toEDist",
"ENNReal.ofReal_coe_nnreal",
"ENNReal",
"Eq.refl",
"Dist.dist",
"PseudoMetricSpace.t... | true |
linearOrderOfSTO._proof_1 | Mathlib.Order.RelClasses | [
"asymm_of",
"asymm_of_isTrans_of_irrefl",
"irrefl_of",
"IsStrictOrder.toIsTrans",
"Eq.rec",
"id",
"Or.resolve_left",
"IsStrictTotalOrder",
"Iff",
"IsStrictTotalOrder.toIsStrictOrder",
"Iff.intro",
"Or",
"Or.imp",
"Or.elim",
"Eq.symm",
"trichotomous_of",
"Eq",
"IsStrictTotalOrder.to... | false |
Lean.Expr.proj.elim | Lean.Expr | [
"PULift.up",
"Lean.Expr",
"Nat",
"Lean.Expr.ctorElim",
"Lean.Name",
"Lean.Expr.ctorIdx",
"Eq.symm",
"Eq",
"Lean.Expr.proj"
] | false |
CategoryTheory.PreZeroHypercoverFamily._sizeOf_inst | Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily | [
"CategoryTheory.PreZeroHypercoverFamily._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"CategoryTheory.PreZeroHypercoverFamily",
"CategoryTheory.Category"
] | false |
Lean.Lsp.InitializationOptions.ctorIdx | Lean.Data.Lsp.InitShutdown | [
"Lean.Lsp.InitializationOptions",
"Nat"
] | false |
instDecidableIrrationalSqrtOfNatReal | Mathlib.NumberTheory.Real.Irrational | [
"instDecidableNot",
"Real",
"Decidable",
"instMulNat",
"instOfNatNat",
"Nat.instDecidablePredIsSquare",
"Irrational",
"Nat",
"IsSquare",
"decidable_of_iff'",
"Real.sqrt",
"OfNat.ofNat",
"irrational_sqrt_ofNat_iff",
"instOfNatAtLeastTwo",
"Not",
"Nat.AtLeastTwo",
"Real.instNatCast"
] | true |
ZeroAtInftyContinuousMap.rec | Mathlib.Topology.ContinuousMap.ZeroAtInfty | [
"ContinuousMap",
"nhds",
"Filter.cocompact",
"TopologicalSpace",
"Filter.Tendsto",
"ZeroAtInftyContinuousMap.mk",
"Zero.toOfNat0",
"ContinuousMap.toFun",
"ZeroAtInftyContinuousMap",
"OfNat.ofNat",
"Zero"
] | false |
Submonoid.closure_insert_one | Mathlib.Algebra.Group.Submonoid.Basic | [
"Eq.mpr",
"MulOne.toOne",
"Submonoid.closure_singleton_le_iff_mem",
"Lattice.toSemilatticeSup",
"Set.insert_eq",
"CompleteLattice.toLattice",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Set.instUnion",
"SemilatticeSup.toMax",
"Set.instSingletonSet",
"Submonoi... | true |
Std.DHashMap.Const.size_le_size_insertMany_list | Std.Data.DHashMap.Lemmas | [
"instForInOfForIn'",
"Std.DHashMap.Raw",
"Std.DHashMap.size",
"inferInstance",
"Std.DHashMap.Internal.Raw₀.Const.size_le_size_insertMany_list",
"Std.DHashMap.wf",
"instOfNatNat",
"LE.le",
"instLENat",
"Id",
"Membership",
"LawfulHashable",
"Subtype.mk",
"List",
"EquivBEq",
"Std.DHashMap... | true |
AdjoinRoot.instCommRing | Mathlib.RingTheory.AdjoinRoot | [
"Ring.mk",
"Mul.mk",
"CommRing",
"AdjoinRoot.instCommRing._proof_36",
"One.mk",
"AdjoinRoot",
"AdjoinRoot.instCommRing._proof_19",
"CommSemiring.toSemiring",
"AdjoinRoot.instCommRing._aux_13",
"AdjoinRoot.instCommRing._aux_34",
"Add.mk",
"AdjoinRoot.instCommRing._proof_3",
"Neg.mk",
"Adjoi... | true |
Valued.instLinearOrderedCommGroupWithZeroValueGroup₀ValuationV | Mathlib.Topology.Algebra.Valued.ValuedField | [
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"ValuationClass.toMonoidWithZeroHomClass",
"Valued.v",
"MonoidWithZeroHom.ValueGroup₀.instLinearOrderedCommGroupWithZero",
"Field.toDivisionRing",
"DivisionRing.toRing",
"LinearOrderedCommGroupWithZer... | true |
MeasurableSet.image_of_measurable_injOn | Mathlib.MeasureTheory.Constructions.Polish.Basic | [
"StandardBorelSpace",
"Continuous",
"Continuous.continuousOn",
"MeasurableSet",
"Measurable.exists_continuous",
"SecondCountableTopology",
"TopologicalSpace.Subtype.secondCountableTopology",
"PartialOrder.toPreorder",
"upgradeStandardBorel",
"continuous_id_of_le",
"Measurable",
"Preorder.toLE"... | true |
RelEmbedding.recOn | Mathlib.Order.RelIso.Basic | [
"RelEmbedding.mk",
"Function.Embedding",
"RelEmbedding",
"Iff",
"RelEmbedding.rec",
"Function.instFunLikeEmbedding",
"DFunLike.coe"
] | false |
CategoryTheory.Limits.WidePullbackShape.Hom.id.elim | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | [
"PULift.up",
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Limits.WidePullbackShape.Hom",
"CategoryTheory.Limits.WidePullbackShape.Hom.ctorElim",
"Nat",
"CategoryTheory.Limits.WidePullbackShape.Hom.ctorIdx",
"CategoryTheory.Limits.WidePullbackShape.Hom.id",
"Eq.symm",
"Eq"
] | false |
_private.Mathlib.Analysis.Complex.CanonicalDecomposition.0.Complex.canonicalFactor_ne_zero._simp_1_3 | Mathlib.Analysis.Complex.CanonicalDecomposition | [
"Real.instLE",
"Real",
"Membership.mem",
"LE.le",
"PseudoMetricSpace",
"propext",
"Metric.mem_closedBall",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Metric.closedBall",
"Eq",
"Set.instMembership",
"Set"
] | false |
Set.smul_set_univ | Mathlib.Algebra.Group.Action.Pointwise.Set.Basic | [
"instHSMul",
"Set.univ",
"Group",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"Set.image_univ_of_surjective",
"MulAction",
"Monoid.toSemigroup",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Eq",
"Set.smulSet",
"MulAction.surjective",
"Set"
] | true |
UInt16.reduceLT | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | [
"UInt16.decLt",
"UInt16.reduceBinPred._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt.1661162788._hygCtx._hyg.3",
"instOfNatNat",
"UInt16",
"Nat",
"LT.lt",
"Lean.Name.mkStr2",
"instLTUInt16",
"OfNat.ofNat",
"Decidable.decide",
"Lean.Meta.Simp.Simproc"
] | true |
DilationEquiv.symm_bijective | Mathlib.Topology.MetricSpace.DilationEquiv | [
"Iff.mpr",
"Function.LeftInverse",
"Exists",
"PseudoEMetricSpace",
"Function.bijective_iff_has_inverse",
"And",
"And.intro",
"Function.RightInverse",
"Exists.intro",
"Function.Bijective",
"DilationEquiv.symm",
"DilationEquiv",
"DilationEquiv.symm_symm"
] | true |
Valuation.HasExtension.instIsLocalHomValuationInteger | Mathlib.RingTheory.Valuation.Extension | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"RingHom.instRingHomClass",
"MulOne.toOne",
"CommRing",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"IsUnit",
"Algebra",
"Valuation.integer.integers",
"RingHom",
"Membership.mem",
"algebraMap",
... | true |
Vector.instOrientedCmpCompareLex | Init.Data.Ord.Vector | [
"Vector",
"Std.OrientedCmp.mk",
"Ordering",
"Std.OrientedCmp",
"Array",
"Vector.compareLex",
"Array.compareLex",
"Nat",
"Std.OrientedCmp.eq_swap",
"Vector.toArray",
"Array.instOrientedCmpCompareLex"
] | true |
DFinsupp.instDFunLike | Mathlib.Data.DFinsupp.Defs | [
"DFunLike.mk",
"DFunLike",
"DFinsupp.instDFunLike._proof_1",
"DFinsupp",
"DFinsupp.toFun",
"Zero"
] | true |
Mathlib.Meta.FunProp.Mor.Arg.noConfusionType | Mathlib.Tactic.FunProp.Mor | [
"Lean.Expr",
"Mathlib.Meta.FunProp.Mor.Arg",
"Mathlib.Meta.FunProp.Mor.Arg.casesOn",
"Eq",
"Option"
] | false |
SimpleGraph.isMaximalIndepSet_compl._simp_1 | Mathlib.Combinatorics.SimpleGraph.Clique | [
"SimpleGraph.IsIndepSet",
"Compl.compl",
"Finset",
"SimpleGraph.isMaximalIndepSet_compl",
"SimpleGraph",
"SimpleGraph.instCompl",
"SetLike.coe",
"Set.instLE",
"Finset.instSetLike",
"propext",
"Maximal",
"Eq",
"SimpleGraph.IsClique",
"Set"
] | false |
Std.Format.group.injEq | Init.Data.Format.Basic | [
"Eq.propIntro",
"Lean.injEq_helper",
"Std.Format.group",
"And",
"Std.Format",
"Eq.ndrec",
"Eq.refl",
"Std.Format.group.inj",
"Std.Format.FlattenBehavior",
"Eq"
] | true |
RingQuot.instRing._proof_8 | Mathlib.Algebra.RingQuot | [
"Int.cast",
"NonAssocSemiring.toAddCommMonoidWithOne",
"congrArg",
"RingQuot.instRing._proof_6",
"RingQuot.Rel",
"RingQuot",
"AddMonoidWithOne.toNatCast",
"Int",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddGroupWithOne.toIntCast",
"Nat.cast",
"RingQuot.mk",
"Nat",
"instNatCastInt",
"Q... | false |
Sym2.rec.match_1 | Mathlib.Data.Sym.Sym2 | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
AlgebraicGeometry.isSmooth_isStableUnderBaseChange | Mathlib.AlgebraicGeometry.Morphisms.Smooth | [
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.smooth_isStableUnderBaseChange",
"CategoryTheory.MorphismProperty.IsStableUnderBaseChange",
"AlgebraicGeometry.Scheme.instCategory",
"AlgebraicGeometry.Smooth"
] | true |
_private.Mathlib.Algebra.Homology.Localization.0.HomotopyCategory.quotient_map_mem_quasiIso_iff._simp_1_1 | Mathlib.Algebra.Homology.Localization | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.quasiIso",
"HomologicalComplex.mem_quasiIso_iff",
"HomologicalComplex",
"ComplexShape",
"HomologicalComplex.sc",
"CategoryTheory.CategoryWithHomo... | false |
ByteArray.forIn.loop._proof_4 | Init.Data.ByteArray.Basic | [
"LE.le",
"instLENat",
"Nat.le_of_lt",
"Nat",
"LT.lt",
"instLTNat",
"ByteArray",
"ByteArray.size"
] | false |
AddMonoidAlgebra.opRingEquiv_symm_single | Mathlib.Algebra.MonoidAlgebra.Opposite | [
"AddMonoidAlgebra.opRingEquiv",
"Finsupp.equivMapDomain_single",
"congrArg",
"AddMonoidAlgebra.opRingEquiv_symm_apply",
"RingEquiv.instEquivLike",
"AddMonoid.toAddZeroClass",
"MulOpposite",
"AddMonoidAlgebra.nonUnitalNonAssocSemiring",
"Finsupp.mapRange.congr_simp",
"MulOpposite.opAddEquiv",
"Ad... | true |
CategoryTheory.Functor.mapHomologicalComplexIdIso._proof_2 | Mathlib.Algebra.Homology.Additive | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.Full.id",
"HomologicalComplex",
"CategoryTheory.Functor.id",
"CategoryTheory.Iso.refl",
"CategoryTheory.Category.comp_id",
"Com... | false |
cfcₙ.congr_simp | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Nontrivial",
"cfcₙ",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsTopologicalSemiring",
"IsScalarTower",
"ContinuousStar",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"PseudoMetricSpace.toUniformSpace",
"NonUnitalNonAssocSemiring.toDistribSMul",
"Add... | true |
Matrix.specialOrthogonalGroup | Mathlib.LinearAlgebra.UnitaryGroup | [
"CommRing",
"CommSemiring.toSemiring",
"Matrix",
"Matrix.specialUnitaryGroup",
"NonAssocSemiring.toMulZeroOneClass",
"Matrix.nonAssocSemiring",
"MulZeroOneClass.toMulOneClass",
"CommRing.toCommSemiring",
"Fintype",
"starRingOfComm",
"Semiring.toNonAssocSemiring",
"Submonoid",
"DecidableEq"
] | true |
Equiv.mulOneClass | Mathlib.Algebra.Group.TransferInstance | [
"Equiv.mulOneClass._proof_2",
"MulOne.toOne",
"One",
"Equiv.instEquivLike",
"Mul",
"Equiv",
"MulOne.toMul",
"Equiv.mulOneClass._proof_1",
"MulOneClass.toMulOne",
"Equiv.mul",
"Function.Injective.mulOneClass",
"Equiv.injective",
"MulOneClass",
"DFunLike.coe",
"Equiv.one",
"EquivLike.toF... | true |
_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding._simp_1 | Mathlib.Combinatorics.Matroid.Map | [
"HasSubset.Subset",
"propext",
"Set.instEmptyCollection",
"Set.subset_empty_iff",
"EmptyCollection.emptyCollection",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
IsCyclotomicExtension.Rat.galEquivZMod.eq_1 | Mathlib.NumberTheory.NumberField.Cyclotomic.Galois | [
"Nat.instMulZeroClass",
"IsCyclotomicExtension.Rat.galEquivZMod._proof_1",
"ZMod.commRing",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Rat",
"IsCyclotomicExtension.Rat.galEquivZMod._proof_2",
"Rat.commSemiring",
"Field.toDivisionRing",
"Units",
"IsCyclotomicExtension.Rat.galEquivZMod",
... | true |
_private.Mathlib.Data.List.Sort.0.List.erase_orderedInsert_of_notMem._proof_1_1 | Mathlib.Data.List.Sort | [
"List.orderedInsert_nil",
"False",
"instDecidableTrue",
"eq_false",
"instLawfulBEq",
"congrArg",
"Decidable.decide.congr_simp",
"Classical.byContradiction",
"DecidableRel",
"Eq.mp",
"List.orderedInsert",
"Lean.Grind.beq_eq_decide_eq",
"id",
"instDecidableEqBool",
"ite_cond_eq_true",
"i... | false |
_private.Mathlib.RingTheory.Ideal.MinimalPrime.Basic.0.Ideal.map_sup_mem_minimalPrimes_of_map_quotientMk_mem_minimalPrimes.match_1_1 | Mathlib.RingTheory.Ideal.MinimalPrime.Basic | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"RingHom",
"algebraMap",
"SemilatticeSup.toMax",
"Algebra.id",
"Ideal.map",
"Submodule.instPartialOrder",
"LE.le",
"Ideal",
"IdemSemiring.toSemilatticeSup",
"And.casesOn",... | false |
Module.Basis.toMatrix_smul | Mathlib.LinearAlgebra.Matrix.Basis | [
"Finsupp.instFunLike",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"Finsupp.module",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"AlgHom",
"Matrix.instHMulOfFintypeOfMulOfAddCommMonoid",
"AlgHom.funLike",
"AddM... | true |
ENNReal.ofReal_essSup | Mathlib.MeasureTheory.Function.EssSup | [
"MeasureTheory.ae",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"ENNReal.ofReal",
"ENNReal.ofReal_limsup",
"Filter.IsCoboundedUnder",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"MeasurableSpace",
"Real.instConditionallyCompleteLinearOrder",
"CompleteLinearO... | true |
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