name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls.0.MeasureTheory.volume_sum_rpow_le._simp_1_1 | Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls | [
"WithLp",
"NegZeroClass.toNeg",
"WithLp.instAddCommGroup",
"WithLp.toLp",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"WithLp.toLp_neg",
"ENNReal",
"AddCommGroup.toDivisionAddCommMonoid",
"Eq.symm",
"... | false |
Std.TreeMap.Raw.keys_filter_key | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.keys",
"Std.TreeMap.Raw.WF.out",
"Ordering",
"Std.TreeMap.Raw.filter",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"List",
"List.filter",
"Bool",
"Eq",
"Std.DTreeMap.Raw.keys_filter_key"
] | true |
OrderEmbedding.sortedLE_listMap._simp_1 | Mathlib.Data.List.Sort | [
"List.map",
"List.SortedLE",
"Preorder.toLE",
"List",
"propext",
"OrderEmbedding.sortedLE_listMap",
"OrderEmbedding",
"Eq",
"DFunLike.coe",
"instFunLikeOrderEmbedding",
"Preorder"
] | false |
PresheafOfModules.freeYonedaEquiv.eq_1 | Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"Equiv.trans",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"AddCommGroup.toAddGroup",
"AddCommGrpCat.instConcreteCategoryA... | true |
_private.Mathlib.InformationTheory.Coding.KraftMcMillan.0.InformationTheory.kraft_mcmillan_inequality._proof_1_1 | Mathlib.InformationTheory.Coding.KraftMcMillan | [
"Lean.Grind.Semiring.one_mul",
"Lean.Grind.Field.toCommRing",
"False",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"instHDiv",
"Lean.Grind.Field.toDiv",
"HMul.hMul",
"eq_false",
"congrArg",
"Real.instInv",
"Finset",
"Real.instDivInvMonoid",
"Classical.byContradiction",
"PartialOrder.... | false |
Lean.MVarId.congrN | Lean.Meta.Tactic.Congr | [
"Pure.pure",
"Lean.Core.instMonadLiftIOCoreM",
"IO.instMonadLiftSTRealWorldBaseIO",
"Lean.Meta.State",
"instMonadLiftT",
"IO",
"Lean.MVarId",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instOfNatNat",
"ReaderT.instMonadLift",
"Applicative.toPure",
"Array.toList",
"List.toArray",
"Array",
"Bool... | true |
Function.Surjective.semigroup._proof_1 | Mathlib.Algebra.Group.InjSurj | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"congrArg",
"mul_assoc",
"Mul",
"congr",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq.symm",
"Eq",
"Eq.trans",
"instHMul"
] | false |
_private.Mathlib.MeasureTheory.Covering.Besicovitch.0.Besicovitch.TauPackage.lastStep_nonempty._simp_1_3 | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
CochainComplex.instAdditiveHomologicalComplexIntUpShiftFunctor | Mathlib.Algebra.Homology.HomotopyCategory.Shift | [
"Int.instAddCommGroup",
"HomologicalComplex.instCategory",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"_private.Mathlib.Algebra.Homology.HomotopyCategory.Shift.0.CochainComplex.instAdditiveHomologicalComplexIntUpShiftFunctor._proof_1",
"Int.instLinearOrder",
"CategoryTheory.Functor.Additive",
"PartialO... | true |
WithZero.instAddMonoid | Mathlib.Algebra.Group.WithOne.Defs | [
"AddMonoid.mk",
"AddZeroClass.toAddZero",
"AddSemigroup.mk",
"AddSemigroup",
"nsmulRecAuto",
"AddZero.toZero",
"WithZero.instAddZeroClass",
"AddSemigroup.toAdd",
"AddZeroClass",
"WithZero",
"AddMonoid",
"WithZero.instAddMonoid._proof_1",
"WithZero.instAddMonoid._proof_7",
"WithZero.instAdd... | true |
Option.map₂_coe_right | Mathlib.Data.Option.NAry | [
"Option.some",
"_private.Mathlib.Data.Option.NAry.0.Option.map₂_coe_right._proof_1_1",
"Option.map",
"Eq",
"Option.map₂",
"Option"
] | true |
CategoryTheory.Cat.opEquivalence_counitIso | Mathlib.CategoryTheory.Category.Cat.Op | [
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.Cat.opEquivalence._proof_4",
"CategoryTheory.Cat.opEquivalence",
"Opposite",
"CategoryTheory.opOp",
"CategoryTheory.Bundled.str",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.toCatHom",
"CategoryTheory.Functor.c... | true |
_private.Lean.Util.ParamMinimizer.0.Lean.Util.ParamMinimizer.Context.mk.noConfusion | Lean.Util.ParamMinimizer | [
"_private.Lean.Util.ParamMinimizer.0.Lean.Util.ParamMinimizer.Context.mk",
"id",
"_private.Lean.Util.ParamMinimizer.0.Lean.Util.ParamMinimizer.Context",
"Array",
"heq_of_eq",
"Nat",
"Bool",
"Eq.refl",
"HEq",
"Eq",
"_private.Lean.Util.ParamMinimizer.0.Lean.Util.ParamMinimizer.Context.noConfusion"... | false |
Turing.ToPartrec.stepNormal | Mathlib.Computability.TuringMachine.Config | [
"Turing.ToPartrec.Code.brecOn",
"Turing.ToPartrec.stepNormal._f",
"Turing.ToPartrec.Cont",
"List",
"Turing.ToPartrec.Cfg",
"Nat",
"Turing.ToPartrec.Code"
] | true |
Int.even_add._simp_1 | Mathlib.Algebra.Group.Int.Even | [
"Int",
"Int.even_add",
"instHAdd",
"Iff",
"HAdd.hAdd",
"Even",
"propext",
"Int.instAdd",
"Eq"
] | false |
tendsto_of_liminf_eq_limsup | Mathlib.Topology.Order.LiminfLimsup | [
"OrderTopology",
"tendsto_of_liminf_eq_limsup._auto_3",
"Filter.liminf",
"Filter.map",
"PartialOrder.toPreorder",
"Preorder.toLE",
"nhds",
"GE.ge",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"tendsto_of_liminf_eq_limsup._auto_1",
"autoParam",
"Filter.limsup",... | true |
AddAction.vadd_zsmul_fixedBy_eq_of_addCommute | Mathlib.GroupTheory.GroupAction.FixedPoints | [
"instHSMul",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"Set.addActionSet",
"AddAction.fixedBy",
"AddZeroClass.toAddZero",
"Set.vaddSet",
"Int",
"AddAction.fixedBy_subset_fixedBy_zsmul",
"AddCommute",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddGroup",
... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.sat_of_insertRup._proof_1_20 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound | [
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.insertUnit",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.assignments",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.InsertUnitInvariant._proof_2",
"Prod.mk",
"List.foldl",
"Fin.val",
"Prod.fst",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultForm... | false |
_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Three.0.IsCyclotomicExtension.Rat.Three.eq_one_or_neg_one_of_unit_of_congruent._simp_1_1 | Mathlib.NumberTheory.NumberField.Cyclotomic.Three | [
"NegZeroClass.toNeg",
"AddMonoid.toAddZeroClass",
"neg_add",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"instHAdd",
"HAdd.hAdd",
"AddZero.toAdd",
"SubNegMo... | false |
UInt16.toUInt32_shiftRight | Init.Data.UInt.Bitwise | [
"instPowNat",
"UInt16.toBitVec",
"UInt32.toBitVec",
"BitVec.setWidth",
"BitVec.instHShiftRight",
"BitVec.instHShiftRightNat",
"Dvd.dvd",
"UInt16.toBitVec_shiftRight",
"instModUInt32",
"of_decide_eq_true",
"BitVec.instOfNat",
"congrArg",
"Nat.decidable_dvd",
"BitVec",
"UInt32.toBitVec_ofN... | true |
_private.Lean.Meta.Tactic.Simp.Main.0.Lean.Meta.Simp.lambdaTelescopeDSimp.go._sparseCasesOn_1 | Lean.Meta.Tactic.Simp.Main | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
Aesop.Index.recOn | Aesop.Index | [
"Aesop.Index.mk",
"Aesop.Rule.instHashable",
"Lean.PHashSet",
"Aesop.Rule",
"Aesop.Rule.instBEq",
"Aesop.Index",
"Lean.Meta.DiscrTree",
"Aesop.Index.rec"
] | false |
Path.Homotopy.symm₂._proof_5 | Mathlib.Topology.Homotopy.Path | [
"Real.instIsOrderedRing",
"Eq.mpr",
"Path.Homotopy",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"Path.symm",
"Path.Homotopy.target",
"congrArg",
"ContinuousMap.mk",
"ContinuousMap",
"Continuous.comp",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"Membership.mem",... | false |
Subfield.coe_copy | Mathlib.Algebra.Field.Subfield.Defs | [
"Subfield.instSetLike",
"Subfield.copy",
"SetLike.coe",
"DivisionRing",
"Subfield",
"Eq",
"rfl",
"Set"
] | true |
CategoryTheory.Abelian.Ext.postcomp_smul_id_mono_iff | Mathlib.Algebra.Category.ModuleCat.Ext.Basic | [
"_private.Mathlib.Algebra.Category.ModuleCat.Ext.Basic.0.CategoryTheory.Abelian.Ext.postcomp_smul_id_mono_iff._simp_1_1",
"Eq.mpr",
"CategoryTheory.Abelian.Ext.instModule",
"CommRing",
"instHSMul",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver... | true |
OrderMonoidIso.Simps.symm_apply | Mathlib.Algebra.Order.Hom.Monoid | [
"Mul",
"OrderMonoidIso.symm",
"OrderMonoidIso",
"OrderMonoidIso.instEquivLike",
"DFunLike.coe",
"Preorder",
"EquivLike.toFunLike"
] | true |
Lean.Grind.CommRing.Poly.brecOn | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.below",
"Lean.Grind.CommRing.Poly.brecOn.go"
] | false |
CommBialgCat.of | Mathlib.Algebra.Category.CommBialgCat | [
"CommRing",
"CommSemiring.toSemiring",
"CommRing.toCommSemiring",
"Bialgebra",
"_private.Mathlib.Algebra.Category.CommBialgCat.0.CommBialgCat.mk",
"CommBialgCat"
] | true |
Subalgebra.lTensorBot_symm_apply | Mathlib.LinearAlgebra.TensorProduct.Subalgebra | [
"Subalgebra.instSetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Lattice.toSemilatticeSup",
"AlgEquiv.symm",
"CompleteLattice.toLattice",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Algebra.instCompleteLatticeSubalgebra",
"Algebra",
"Preorder.toLE",
"Membership.mem",
"OneMemClass.one",
... | true |
Eq.ndrec | Init.Prelude | [
"Eq.rec",
"Eq"
] | false |
CategoryTheory.Over.tensorHom_left_fst | Mathlib.CategoryTheory.Monoidal.Cartesian.Over | [
"CategoryTheory.Limits.pullback",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.BinaryFan",
"CategoryTheory.Functor.category",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Comma.lef... | true |
_private.Mathlib.Analysis.Complex.Basic.0.Complex.subset_slitPlane_iff_of_subset_sphere._simp_1_1 | Mathlib.Analysis.Complex.Basic | [
"PartialOrder.toPreorder",
"Complex.instZero",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"propext",
"Zero.toOfNat0",
"Complex",
"OfNat.ofNat",
"Eq",
"Set.instMembership",
"Not",
"Complex.slitPlane",
"Complex.partialOrder",
"Complex.mem_slitPlane_iff_not_le_zero",
"Set"
] | false |
HasCompactMulSupport.one | Mathlib.Topology.Algebra.Support | [
"One",
"congrArg",
"HasCompactMulSupport",
"Set.Finite",
"TopologicalSpace",
"Pi.instOne",
"True",
"Set.instEmptyCollection",
"of_eq_true",
"One.toOfNat1",
"Set.Finite.isCompact._simp_1",
"EmptyCollection.emptyCollection",
"Set.finite_empty._simp_1",
"OfNat.ofNat",
"mulTSupport",
"mulT... | true |
String.Slice.takeEndWhile_prop_eq_takeEndWhile_decide | Init.Data.String.Lemmas.Pattern.Pred | [
"String.Slice.Pattern.CharPred.Decidable.instBackwardPatternForallCharPropOfDecidablePred",
"String.Slice.takeEndWhile",
"congrArg",
"String.Slice.sliceFrom",
"String.Slice",
"id",
"String.Slice.skipSuffixWhile_prop_eq_skipSuffixWhile_decide",
"String.Slice.Pattern.CharPred.instBackwardPatternForallCh... | true |
Filter.mulActionFilter._proof_2 | Mathlib.Order.Filter.Pointwise | [
"Monoid",
"Semigroup.toMul",
"instHSMul",
"HMul.hMul",
"congrArg",
"Filter.map",
"Function.comp",
"Filter.map_map",
"funext",
"Filter.instSMulFilter",
"MulAction",
"True",
"eq_self",
"Monoid.toSemigroup",
"of_eq_true",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"congrFun'",
"_priva... | false |
CategoryTheory.Limits.pullbackLeftPullbackSndIso | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | [
"CategoryTheory.Limits.hasPullbackVertPaste",
"CategoryTheory.Limits.pullback",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limi... | true |
ModuleCat.instProjectiveObjFree | Mathlib.Algebra.Category.ModuleCat.LeftResolution | [
"Eq.mpr",
"Function.Surjective.hasRightInverse",
"CategoryTheory.Epi",
"ModuleCat.freeMk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"ModuleCat.epi_iff_surject... | true |
HasCardinalLT.of_injective | Mathlib.SetTheory.Cardinal.HasCardinalLT | [
"Eq.mpr",
"lt_of_le_of_lt",
"Preorder.toLT",
"HasCardinalLT",
"Cardinal",
"Cardinal.lift_lift",
"congrArg",
"PartialOrder.toPreorder",
"ULift",
"Cardinal.lift",
"Cardinal.mk",
"Function.comp",
"Eq.mp",
"id",
"ULift.up_injective",
"Cardinal.lift_lt",
"Cardinal.partialOrder",
"Functi... | true |
CategoryTheory.IsPushout.epi_inr_of_epi._auto_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.CategoryTheory.MorphismProperty.Quotient.0.CategoryTheory.MorphismProperty.quotient_iff.match_1_1 | Mathlib.CategoryTheory.MorphismProperty.Quotient | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Quotient",
"Quiver.Hom",
"CategoryTheory.Quotient.category",
"CategoryTheory.Quotient.functor",
"Exists",
"HomRel",
"CategoryTheory.Functor.map",
"CategoryTheory.MorphismProperty.HasQuotient",
"CategoryT... | false |
Set.bijOn_comp_iff | Mathlib.Data.Set.Function | [
"congrArg",
"Set.SurjOn",
"Function.comp",
"_private.Mathlib.Data.Set.Function.0.Set.bijOn_comp_iff._simp_1_3",
"iff_self",
"And",
"Iff",
"Set.MapsTo",
"_private.Mathlib.Data.Set.Function.0.Set.bijOn_comp_iff._simp_1_2",
"Set.mapsTo_image_iff._simp_1",
"congr",
"True",
"Set.BijOn",
"of_eq_... | true |
Fintype.sum_eq_zero_iff_of_nonpos | Mathlib.Algebra.Order.BigOperators.Group.Finset | [
"Finset.mem_univ",
"Finset.univ",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"instInhabitedTrue",
"AddLeftMono",
"funext_iff",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"PartialOrder",
"Pi.instZero",
"LE.le",
"Pi.hasLe",
"AddCommMo... | true |
Antivary.dual_left | Mathlib.Order.Monotone.Monovary | [
"OrderDual.toDual",
"Equiv.instEquivLike",
"Monovary",
"Antivary",
"Function.comp",
"id",
"Equiv",
"OrderDual",
"OrderDual.instPreorder",
"DFunLike.coe",
"Preorder",
"EquivLike.toFunLike"
] | true |
USize.toUSize_toUInt32 | Init.Data.UInt.Lemmas | [
"instPowNat",
"Eq.mpr",
"Nat.mod_zero",
"UInt32.toNat",
"Nat.mod_self",
"congrArg",
"USize.toNat_lt_size",
"instModUSize",
"Eq.rec",
"id",
"Nat.instMod",
"instHMod",
"USize.toNat_ofNat",
"instOfNatNat",
"Nat.mod_eq_of_lt",
"Or.casesOn",
"instNatPowNat",
"System.Platform.numBits",
... | true |
CategoryTheory.LocallyDiscrete._sizeOf_inst | Mathlib.CategoryTheory.Bicategory.LocallyDiscrete | [
"CategoryTheory.LocallyDiscrete._sizeOf_1",
"CategoryTheory.LocallyDiscrete",
"SizeOf.mk",
"SizeOf"
] | false |
Std.Rcc.size | Init.Data.Range.Polymorphic.Iterators | [
"Std.Rcc.lower",
"Std.Rxc.HasSize",
"Nat",
"Std.Rxc.HasSize.size",
"Std.Rcc",
"Std.Rcc.upper"
] | true |
_private.Lean.Environment.0.Lean.EnvExtension.getStateUnsafe.match_10 | Lean.Environment | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"_private.Lean.Environment.0.Lean.AsyncConst",
"Option.none",
"Unit",
"Option"
] | false |
HahnSeries.instRing._proof_5 | Mathlib.RingTheory.HahnSeries.Multiplication | [
"AddMonoid.toAddSemigroup",
"AddMonoid.toZero",
"AddCommGroup.toAddGroup",
"PartialOrder",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"Ring.toA... | false |
cfcₙ_eq_cfcₙL | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"cfcₙ_def",
"Nontrivial",
"cfcₙ",
"Eq.mpr",
"Semiring.toModule",
"instSMulOfMul",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"quasispectrum.instZero",
"IsTopologicalSemiring",
"IsScalarTower",
"ContinuousMap.mk",
"ContinuousStar",
"SeparatelyContinuousMul.to... | true |
Batteries.Tactic.GeneralizeProofs.MAbs.findProof? | Batteries.Tactic.GeneralizeProofs | [
"Pure.pure",
"Batteries.Tactic.GeneralizeProofs.AState",
"Option.instBEq",
"_private.Batteries.Tactic.GeneralizeProofs.0.Batteries.Tactic.GeneralizeProofs.MAbs.findProof?.match_1",
"instHashableProd",
"Lean.Core.instMonadLiftIOCoreM",
"instMonadReaderOfReaderTOfMonad",
"IO.instMonadLiftSTRealWorldBase... | true |
_private.Mathlib.RingTheory.TwoSidedIdeal.Operations.0.TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure_absorbing._simp_1_2 | Mathlib.RingTheory.TwoSidedIdeal.Operations | [
"SetLike",
"Membership.mem",
"SetLike.coe",
"SetLike.mem_coe",
"propext",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
Turing.TM1to1.readAux._sunfold | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Turing.TM1.Stmt.move",
"List.Vector",
"instOfNatNat",
"Turing.TM1to1.readAux.match_1",
"Bool.true",
"instHAdd",
"Turing.TM1to1.Λ'",
"HAdd.hAdd",
"Nat",
"Turing.TM1to1.readAux",
"Bool",
"instAddNat",
"List.Vector.nil",
"OfNat.ofNat",
"Bool.false",
"Turing.Dir.right",
"Turing.TM1.Stmt... | false |
HomogeneousIdeal.irrelevant_eq_span | Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal | [
"SetLike",
"Ideal.span_le",
"Iff.mpr",
"Ideal.subset_span",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"Semiring.toModule",
"HomogeneousIdeal._proof_1",
"Set.iUnion_subset",
"AddMonoid.toAddSemigroup",
"instVAddOfAdd",
"Submodule.toAddSubmonoid",
"HomogeneousIdeal.mem_irrele... | true |
EsakiaHom.mk.injEq | Mathlib.Topology.Order.Hom.Esakia | [
"Eq.propIntro",
"EsakiaHom.mk",
"OrderHom.toFun",
"Preorder.toLE",
"Exists",
"LE.le",
"ContinuousOrderHom",
"TopologicalSpace",
"And",
"ContinuousOrderHom.toOrderHom",
"Eq.ndrec",
"Eq.refl",
"EsakiaHom.mk.inj",
"EsakiaHom",
"Eq",
"Preorder"
] | true |
_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Impl.getEntryGE?ₘ'.match_1.splitter | Std.Data.DTreeMap.Internal.Model | [
"Ordering.gt",
"Ord",
"Std.DTreeMap.Internal.Impl.ExplorationStep.gt",
"Std.DTreeMap.Internal.Impl.ExplorationStep.lt",
"Ordering",
"Std.DTreeMap.Internal.Impl.ExplorationStep.eq",
"Std.DTreeMap.Internal.Impl.ExplorationStep",
"Std.DTreeMap.Internal.Impl.getEntryGE?ₘ'.match_1",
"Ord.compare",
"Std... | true |
CategoryTheory.StrictlyUnitaryLaxFunctor.comp_map₂ | Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.PrelaxFunctorStruct.map₂",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"CategoryTheory.LaxFunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory",
"Prefunctor.map",
"Category... | true |
Std.Internal.UV.System.RUsage.ctorIdx | Std.Internal.UV.System | [
"Std.Internal.UV.System.RUsage",
"Nat"
] | false |
_private.Mathlib.Topology.Connected.PathConnected.0.isPathConnected_iff.match_1_1 | Mathlib.Topology.Connected.PathConnected | [
"IsPathConnected",
"JoinedIn",
"Membership.mem",
"And.casesOn",
"TopologicalSpace",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"Set.instMembership",
"Set"
] | false |
Algebra.IsStandardEtale.mk | Mathlib.RingTheory.Etale.StandardEtale | [
"CommRing",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.IsStandardEtale",
"CommRing.toCommSemiring",
"Algebra.IsStandardEtale.mk",
"Nonempty",
"StandardEtalePresentation"
] | true |
CategoryTheory.Limits.WidePushout.hom_ext_iff | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Limits.widePushout",
"Eq.casesOn",
"CategoryTheory.Limits.WidePushout.head",
"And.casesOn",
"And",
"CategoryTheory.Limits.WidePushout.ι",
"Iff",
"CategoryTheory.Limits.HasWidePushout",
"And.intro",
"Iff.intro... | true |
_private.Std.Data.Iterators.Lemmas.Producers.Monadic.List.0.Std.Types.ListIterator.stepAsHetT_iterM.match_1.eq_2 | Std.Data.Iterators.Lemmas.Producers.Monadic.List | [
"Std.Types.ListIterator.stepAsHetT_iterM.match_1",
"List.cons",
"List",
"Unit",
"Eq.refl",
"Eq",
"List.nil"
] | true |
Exists₂.imp | Mathlib.Logic.Basic | [
"Exists",
"Exists.imp"
] | true |
Multiset.Nodup.filterMap | Mathlib.Data.Multiset.Filter | [
"List.Nodup.filterMap",
"Multiset.filterMap",
"Multiset.Nodup",
"Option.instMembership",
"Membership.mem",
"Multiset",
"Quot.induction_on",
"List",
"List.isSetoid",
"Eq",
"Setoid.r",
"Option"
] | true |
EuclideanGeometry.hasFDerivAt_inversion | Mathlib.Geometry.Euclidean.Inversion.Calculus | [
"neg_add_rev",
"ContinuousLinearMap.comp",
"LinearMap.eqOn_span'",
"LinearIsometryEquiv.instEquivLike",
"HasFDerivAt",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"LinearMap.id",
"LinearMap.ext_on_codisjoint",
"Distrib.leftDistribClass",
"Norm.norm",
"SeminormedAddGroup.toNo... | true |
CommRingCat.Colimits.Relation.mul_zero | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"CommRingCat",
"CommRingCat.Colimits.Relation.mul_zero",
"CommRingCat.instCategory",
"CategoryTheory.SmallCategory",
"CommRingCat.Colimits.Relation",
"CommRingCat.Colimits.Prequotient.mul",
"CommRingCat.Colimits.Prequotient",
"CommRingCat.Colimits.Prequotient.zero"
] | true |
AlgEquiv.sumArrowEquivProdArrow | Mathlib.Algebra.Algebra.Pi | [
"AlgEquiv.sumArrowEquivProdArrow._proof_1",
"Algebra",
"RingEquiv.sumArrowEquivProdArrow",
"Sum",
"Prod.instSemiring",
"Prod.algebra",
"CommSemiring",
"Pi.semiring",
"Function.algebra",
"AlgEquiv",
"Semiring",
"AlgEquiv.ofRingEquiv",
"Prod",
"Semiring.toNonAssocSemiring"
] | true |
EReal.div_nonpos_of_nonneg_of_nonpos | Mathlib.Data.EReal.Inv | [
"EReal.instDivInvMonoid",
"instHDiv",
"EReal.instMulZeroOneClass",
"EReal.instPosMulMono",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"EReal.inv_nonpos_of_nonpos",
"HDiv.hDiv",
"instZeroEReal",
"LE.le",
"Inv.inv",
"Inv.mk",
"DivInvMonoid.toDiv",
"instPartialOrderEReal",
"mul_... | true |
legendreSym_mersenne_three | Mathlib.NumberTheory.LucasLehmer | [
"Int.cast",
"Eq.mpr",
"Nat.Prime",
"Mathlib.Meta.NormNum.isNat_eq_true",
"legendreSym.mod",
"congrArg",
"_private.Mathlib.NumberTheory.LucasLehmer.0.legendreSym_mersenne_three._proof_1_1",
"Int.cast_negSucc._simp_1",
"Odd",
"mersenne_mod_three",
"AddGroupWithOne.toAddMonoidWithOne",
"legendreS... | true |
_private.Mathlib.Logic.IsEmpty.Basic.0.isEmpty_ulift._simp_1_1 | Mathlib.Logic.IsEmpty.Basic | [
"IsEmpty",
"not_nonempty_iff",
"propext",
"Nonempty",
"Eq.symm",
"Eq",
"Not"
] | false |
Finpartition.bind.congr_simp | Mathlib.Combinatorics.SimpleGraph.Regularity.Increment | [
"Lattice",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Eq.rec",
"Finpartition.parts",
"Finset.instSetLike",
"Finpartition.bind",
"Eq.refl",
"IsModularLattice",
"Eq",
"Finpartition",
"SetLike.instMembership",
"L... | true |
List.erase_eq_eraseP._f | Init.Data.List.Erase | [
"List.eraseP_cons_of_neg",
"False",
"BEq.rfl",
"eq_false",
"congrArg",
"Classical.propDecidable",
"List.erase_cons_tail",
"LawfulBEq",
"_private.Init.Data.List.Erase.0.List.erase_eq_eraseP.match_1_1",
"Ne.symm",
"dite",
"List.cons",
"Bool.true",
"funext",
"List",
"EquivBEq.toReflBEq",
... | false |
LSeriesSummable_lt_re_of_abscissaOfAbsConv_lt_re | Mathlib.NumberTheory.LSeries.Convergence | [
"Real",
"Preorder.toLT",
"PartialOrder.toPreorder",
"EReal",
"Real.instLT",
"Exists",
"EReal.coe_lt_coe_iff._simp_1",
"Eq.mp",
"Complex.ofReal",
"And.casesOn",
"Complex.re",
"LSeriesSummable_of_abscissaOfAbsConv_lt_re",
"And",
"Exists.casesOn",
"Nat",
"And.intro",
"LT.lt",
"Exists.... | true |
Mathlib.Tactic.FieldSimp.NF.cons | Mathlib.Tactic.FieldSimp.Lemmas | [
"Int",
"List.cons",
"Prod",
"Mathlib.Tactic.FieldSimp.NF"
] | true |
mfderivWithin_eventually_congr_set' | Mathlib.Geometry.Manifold.MFDeriv.Basic | [
"Iff.mpr",
"eventually_nhds_nhdsWithin",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"Compl.compl",
"instAddCommGroupTangentSpace",
"nhdsWithin",
"Filter.Eventually",
"mfderivWithin",
"NormedField.toField",
"nhds",
"Filter.EventuallyEq",
"Set.instSingletonSet",
"instModuleTangentSpace",... | true |
_private.Mathlib.MeasureTheory.Measure.Hausdorff.0.MeasureTheory.hausdorffMeasure_pi_real._simp_1_5 | Mathlib.MeasureTheory.Measure.Hausdorff | [
"DivisionRing.toRatCast",
"LinearOrder",
"Rat",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Rat.cast",
"LE.le",
"Rat.instLE",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
... | false |
Mathlib.Tactic._aux_Mathlib_Tactic_NormNum_Core___elabRules_Mathlib_Tactic_normNum1_1 | Mathlib.Tactic.NormNum.Core | [
"Lean.mkNullNode",
"Lean.TSyntax",
"Lean.instMonadExceptOfExceptionCoreM",
"Mathlib.Meta.NormNum.elabNormNum",
"Lean.Meta.State",
"Lean.Syntax.isOfKind",
"Lean.Elab.Tactic.Context",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr3",
"Lean.TSyntax.raw",
"Lean.Meta.MetaM",
"IO.RealWorld",
... | false |
Mathlib.Tactic.«tacticRename_bvar_→__» | Mathlib.Tactic.RenameBVar | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.Parser.Tactic.location",
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"OfNat.ofNat",
"Bool.false",
... | true |
MeasureTheory.Measure.IsAddHaarMeasure.instHasTemperateGrowth | Mathlib.Analysis.Distribution.TemperateGrowth | [
"Real.instIsOrderedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real.instPow",
"Real.partialOrder",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"lt_add_iff_pos_right._simp_1",
"Real.instAddMonoid",
"Real.instRCLike",
"congrArg",
"AddCommGroup.... | true |
Nat.digitsAux_def | Mathlib.Data.Nat.Digits.Defs | [
"Eq.mpr",
"instHDiv",
"congrArg",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Nat.digitsAux.eq_2",
"Nat.digitsAux",
"id",
"HDiv.hDiv",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.le.step",
"List.cons",
"Nat.casesAuxOn",
"List",
"instHAdd",
"HMod... | true |
ENat.coe_inj._simp_1 | Mathlib.Tactic.ENatToNat | [
"ENat.instNatCast",
"Nat.cast",
"ENat.coe_inj",
"Nat",
"ENat",
"propext",
"Eq"
] | false |
IsClopen.eq_univ | Mathlib.Topology.Connected.Clopen | [
"Set.Nonempty.ne_empty",
"Set.univ",
"PreconnectedSpace",
"Or.resolve_left",
"isClopen_iff",
"TopologicalSpace",
"Set.Nonempty",
"Iff.mp",
"Set.instEmptyCollection",
"Or",
"EmptyCollection.emptyCollection",
"IsClopen",
"Eq",
"Set"
] | true |
Homeomorph.sumPiEquivProdPi._proof_3 | Mathlib.Topology.Homeomorph.Lemmas | [
"Continuous",
"Pi.topologicalSpace",
"Homeomorph.sumPiEquivProdPi._proof_2",
"instTopologicalSpaceProd",
"continuous_pi",
"Sum",
"Sum.inl",
"Equiv.sumPiEquivProdPi",
"TopologicalSpace",
"Sum.inr",
"Prod",
"Equiv.invFun"
] | false |
Rep.FiniteCyclicGroup.groupHomologyIsoEven._proof_5 | Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | [
"CommRing",
"Semiring.toModule",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Nat.instOne",
"ModuleCat",
"CommSemiring.toSemiring",
"Subgroup.zpowers_inv",
"CategoryTheory.ShortComplex.HasHomology",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRight... | false |
tangentConeAt_mono | Mathlib.Analysis.Calculus.TangentCone.Basic | [
"Eq.mpr",
"ClusterPt.mono",
"instHSMul",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"nhdsWithin",
"SMul",
"PartialOrder.toPreorder",
"setOf",
"AddCommGroup",
"id",
"HasSubset.Subset",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSub... | true |
Lean.Elab.instInhabitedComputeKind.default | Lean.Elab.DeclModifiers | [
"Lean.Elab.ComputeKind",
"Lean.Elab.ComputeKind.regular"
] | true |
_private.Mathlib.Analysis.Calculus.FDeriv.Measurable.0.FDerivMeasurableAux.D_subset_differentiable_set._proof_1_5 | Mathlib.Analysis.Calculus.FDeriv.Measurable | [
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"IsUniformAddGroup",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"SeminormedAddCommGroup.toAddCommGroup",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"NormedAddCommGroup",
"SeminormedAddCommGroup.to_isUniformAddGroup"
] | false |
ContDiffAt.comp_contMDiffWithinAt | Mathlib.Geometry.Manifold.ContMDiff.NormedSpace | [
"ContDiffAt",
"ContDiffAt.contMDiffAt",
"chartedSpaceSelf",
"ContMDiffWithinAt",
"NormedSpace",
"PseudoMetricSpace.toUniformSpace",
"Function.comp",
"TopologicalSpace",
"ModelWithCorners",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedFie... | true |
MeasureTheory.martingale_const | Mathlib.Probability.Martingale.Basic | [
"MeasureTheory.ae",
"Eq.mpr",
"MeasureTheory.stronglyAdapted_const",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"MeasureTheory.Filtration.seq",
"congrArg",
"MeasureTheory.Martingale",
"PseudoMetricSpace.toUniformSpace",
"Preorder.toLE",
"Filter.EventuallyEq",
"MeasureTheory.Filtration",... | true |
Lean.Meta.LazyDiscrTree.PartialMatch.c | Lean.Meta.LazyDiscrTree | [
"Lean.Meta.LazyDiscrTree.PartialMatch",
"Lean.Meta.LazyDiscrTree.TrieIndex"
] | true |
_private.Lean.Expr.0.Lean.natAddFn | Lean.Expr | [
"Lean.mkApp4",
"Lean.Expr",
"Lean.Level",
"Lean.mkConst",
"List.cons",
"Lean.Nat.mkInstHAdd",
"Lean.Name.mkStr2",
"Lean.Nat.mkType",
"Lean.Level.instOfNat",
"OfNat.ofNat",
"List.nil"
] | true |
Lean.Compiler.instHashableInlineAttributeKind | Lean.Compiler.InlineAttrs | [
"Lean.Compiler.instHashableInlineAttributeKind.hash",
"Hashable.mk",
"Hashable",
"Lean.Compiler.InlineAttributeKind"
] | true |
Lean.Lsp.PrepareRenameParams.casesOn | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.PrepareRenameParams",
"Lean.Lsp.PrepareRenameParams.rec",
"Lean.Lsp.TextDocumentPositionParams",
"Lean.Lsp.PrepareRenameParams.mk"
] | false |
Lean.Widget.RpcEncodablePacket.goal.«_@».Lean.Server.FileWorker.WidgetRequests.2377472685._hygCtx._hyg.1.elim | Lean.Server.FileWorker.WidgetRequests | [
"Lean.Json",
"PULift.up",
"Lean.Widget.RpcEncodablePacket._@.Lean.Server.FileWorker.WidgetRequests.2377472685._hygCtx._hyg.1",
"Nat",
"Lean.Widget.RpcEncodablePacket.«_@».Lean.Server.FileWorker.WidgetRequests.2377472685._hygCtx._hyg.1.ctorIdx",
"Eq.symm",
"Eq",
"Lean.Widget.RpcEncodablePacket.goal._@.... | false |
Std.TreeMap.mem_insertMany_list._simp_1 | Std.Data.TreeMap.Lemmas | [
"instForInOfForIn'",
"List.map",
"List.contains",
"Membership.mem",
"Ordering",
"inferInstance",
"Std.TransCmp",
"Id",
"Membership",
"Std.TreeMap.mem_insertMany_list",
"Prod.fst",
"Bool.true",
"List",
"List.instMembership",
"Std.TreeMap.instMembership",
"Std.LawfulBEqCmp",
"propext",... | false |
IsCoinitialFor.of_subset._simp_1 | Mathlib.Order.Bounds.Basic | [
"IsCoinitialFor",
"Preorder.toLE",
"HasSubset.Subset",
"True",
"eq_true",
"IsCoinitialFor.of_subset",
"Eq",
"Preorder",
"Set.instHasSubset",
"Set"
] | false |
«_aux_Mathlib_Data_Rat_Init___macroRules_termℚ≥0_1» | Mathlib.Data.Rat.Init | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad",
"Lean.TSyntax.... | false |
SemiNormedGrp₁.cokernelLift._proof_2 | Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels | [
"NormedAddGroupHom",
"QuotientAddGroup.instSeminormedAddCommGroup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"NormedAddGroupHom.lift",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"CategoryTheory.Limits.CokernelCofork",
"AddMonoid.toAddZeroClass",
"NormedAddGroupHom.lift... | false |
Std.Time.Weekday.sunday | Std.Time.Date.Unit.Weekday | [
"Std.Time.Weekday.sunday",
"Std.Time.Weekday"
] | true |
selfAdjoint.val_qsmul._simp_1 | Mathlib.Algebra.Star.SelfAdjoint | [
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"AddGroupWithOne.toAddGroup",
"Rat.smulDivisionRing",
"Rat",
"Membership.mem",
"Field.toDivisionRing",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"DivisionRing.toRing",
"Field.toC... | false |
_private.Mathlib.Geometry.Manifold.PoincareConjecture.0.term𝕊__ | Mathlib.Geometry.Manifold.PoincareConjecture | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr... | true |
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