name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Matrix.single_apply_of_col_ne | Mathlib.Data.Matrix.Basis | [
"False",
"Matrix.single_apply_of_ne",
"eq_false",
"congrArg",
"Ne",
"And",
"True",
"eq_self",
"of_eq_true",
"Zero.toOfNat0",
"congrFun'",
"and_false",
"OfNat.ofNat",
"not_false_eq_true",
"Eq",
"Not",
"Eq.trans",
"Matrix.single",
"DecidableEq",
"Zero"
] | true |
isPreirreducible_singleton | Mathlib.Topology.Irreducible | [
"IsPreirreducible",
"Set.instSingletonSet",
"Set.subsingleton_singleton",
"TopologicalSpace",
"Singleton.singleton",
"Set.Subsingleton.isPreirreducible",
"Set"
] | true |
CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore._proof_53 | Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | [
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore._auto_49",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore._auto_47",
"Int",
"LE.le",
"autoParam",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"Int.instAdd",
"_private.Mathlib.Algebra.Homology.SpectralObject.HasSpectralSeque... | false |
continuousOn_stereoToFun | Mathlib.Geometry.Manifold.Instances.Sphere | [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Submodule",
"Real",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"NormedRing.toRing",
"ContinuousLinearMap.topologicalSp... | true |
CategoryTheory.Oplax.OplaxTrans.Modification.noConfusion | Mathlib.CategoryTheory.Bicategory.Modification.Oplax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Oplax.OplaxTrans.Modification.casesOn",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunct... | false |
Lean.Data.Trie.empty | Lean.Data.Trie | [
"Lean.Data.Trie",
"Lean.Data.Trie.leaf",
"Option.none"
] | true |
Lean.Meta.Grind.Arith.CommRing.RingM.Context.rec | Lean.Meta.Tactic.Grind.Arith.CommRing.RingM | [
"Lean.Meta.Grind.Arith.CommRing.RingM.Context",
"Nat",
"Bool",
"Lean.Meta.Grind.Arith.CommRing.RingM.Context.mk"
] | false |
Real.sqrt_inj._simp_1 | Mathlib.Data.Real.Sqrt | [
"Real.instLE",
"Real",
"Real.instZero",
"LE.le",
"propext",
"Real.sqrt",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Real.sqrt_inj"
] | false |
instDecidableEqTree.decEq._f | Mathlib.Data.Tree.Basic | [
"Decidable.isTrue",
"instDecidableEqTree.decEq._proof_4",
"Tree.node",
"instDecidableEqTree.decEq._proof_5",
"instDecidableEqTree.decEq._proof_3",
"instDecidableEqTree.decEq._proof_6",
"Decidable",
"Tree.nil",
"instDecidableEqTree.decEq.match_1",
"dite",
"Tree.below",
"Tree",
"Unit",
"inst... | false |
Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.performRatAdd | Std.Tactic.BVDecide.LRAT.Internal.Formula.Implementation | [
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.performRupAdd.match_3",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.insert.match_1",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.performRupCheck",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.insert",
"Bool.not",
"Std.Tactic.BVDecide.LRAT.... | true |
Aesop.RuleTacDescr.cases.noConfusion | Aesop.RuleTac.Descr | [
"Aesop.RuleTacDescr",
"id",
"Lean.Meta.TransparencyMode",
"Array",
"Bool",
"Aesop.RuleTacDescr.cases",
"Aesop.CasesTarget",
"Aesop.RuleTacDescr.noConfusion",
"Eq",
"Aesop.CtorNames"
] | false |
CategoryTheory.ObjectProperty.InheritedFromSource.instMin | Mathlib.CategoryTheory.ObjectProperty.InheritedFromHom | [
"CategoryTheory.ObjectProperty.InheritedFromSource.of_hom_of_source",
"CategoryTheory.MorphismProperty",
"CategoryTheory.ObjectProperty.InheritedFromSource",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ObjectProperty.InheritedFromSource.mk",
"CompleteLattice.toLattice",
"Pi... | true |
Vector.set | Init.Data.Vector.Basic | [
"Vector",
"Array.set",
"autoParam",
"Vector.set._proof_2",
"Vector.mk",
"Vector.set._proof_1",
"Nat",
"LT.lt",
"instLTNat",
"Vector.toArray",
"Vector.set._auto_1"
] | true |
_private.Mathlib.Probability.Distributions.Fernique.0.ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure._simp_1_2 | Mathlib.Probability.Distributions.Fernique | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
CategoryTheory.Cat.freeRefl_map | Mathlib.CategoryTheory.Category.ReflQuiv | [
"CategoryTheory.ReflQuiv",
"CategoryTheory.Cat.category",
"CategoryTheory.Cat.FreeRefl.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.toCatHom",
"CategoryTheory.Cat.of",
"CategoryTheory.Cat.instQuiver",
"CategoryTheory.Cat",
"CategoryTheory.Functor.m... | true |
CategoryTheory.MorphismProperty.equivalenceLeftFractionRel | Mathlib.CategoryTheory.Localization.CalculusOfFractions | [
"CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions",
"CategoryTheory.MorphismProperty",
"Equivalence",
"CategoryTheory.MorphismProperty.LeftFraction",
"CategoryTheory.MorphismProperty.LeftFractionRel.symm",
"CategoryTheory.MorphismProperty.LeftFractionRel",
"CategoryTheory.MorphismProperty.Left... | true |
ValuationSubring.instFieldSubtypeMemTop._proof_19 | Mathlib.RingTheory.Valuation.ValuationSubring | [
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"ValuationSubring.instFieldSubtypeMemTop._proof_5",
"AddMonoid.toZero",
"InvMemClass.inv",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Field.toDivisionRing",
"SubfieldClass.toField._proof_7",
"Subtype",
"Subfield.... | false |
instInvInterval | Mathlib.Algebra.Order.Interval.Basic | [
"Inv",
"IsOrderedMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"instInvNonemptyInterval",
"Interval",
"CommGroup",
"Inv.inv",
"Inv.mk",
"WithBot.map",
"CommGroup.toCommMonoid",
"NonemptyInterval"
] | true |
Lean.Lsp.TextDocumentSyncOptions.rec | Lean.Data.Lsp.TextSync | [
"Lean.Lsp.TextDocumentSyncKind",
"Lean.Lsp.TextDocumentSyncOptions",
"Lean.Lsp.SaveOptions",
"Bool",
"Lean.Lsp.TextDocumentSyncOptions.mk",
"Option"
] | false |
Std.Internal.List.containsKey_iff_exists | Std.Data.Internal.List.Associative | [
"Eq.mpr",
"congrArg",
"List.contains",
"Iff.rfl",
"Membership.mem",
"Exists",
"id",
"List.contains_iff_exists_mem_beq",
"Std.Internal.List.containsKey_eq_keys_contains",
"Bool.true",
"List",
"Std.Internal.List.containsKey",
"And",
"BEq.beq",
"Iff",
"List.instMembership",
"PartialEqui... | true |
QuadraticModuleCat.instMonoidalCategory.tensorHom | Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal | [
"CommRing",
"QuadraticMap.Isometry.tmul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"QuadraticModuleCat.toModuleCat",
"QuadraticModuleCat.instMonoidalCategory.tensorObj",
"QuadraticModuleC... | true |
CategoryTheory.Equalizer.Sieve.SecondObj.ext | Mathlib.CategoryTheory.Sites.EqualizerSheafCondition | [
"CategoryTheory.Limits.limit.π",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"Subtype.casesOn",
"TypeCat.instFunLikeFun",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Limits.Pi.π",
"Subtype",
"Catego... | true |
_private.Mathlib.RingTheory.MvPowerSeries.Order.0.MvPowerSeries.coeff_mul_prod_one_sub_of_lt_weightedOrder._simp_1_1 | Mathlib.RingTheory.MvPowerSeries.Order | [
"Finset",
"Membership.mem",
"Insert.insert",
"Finset.mem_insert",
"Finset.instInsert",
"Finset.instSetLike",
"propext",
"Or",
"Eq",
"SetLike.instMembership",
"DecidableEq"
] | false |
NumberField.Units.instFintypeSubtypeUnitsRingOfIntegersMemSubgroupTorsion._proof_1 | Mathlib.NumberTheory.NumberField.Units.Basic | [
"Subalgebra.instSetLike",
"Iff.mpr",
"Norm.norm",
"NumberField.InfinitePlace.instFunLikeReal",
"Units.val",
"Eq.mpr",
"Real.instLE",
"Real",
"RCLike.toNormedAlgebra",
"Algebra.algebraMap",
"NumberField.instCommRingRingOfIntegers",
"congrArg",
"CommSemiring.toSemiring",
"Function.Injective.... | false |
ZFSet.instReflSubset | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet",
"Std.Refl.mk",
"Membership.mem",
"id",
"HasSubset.Subset",
"Std.Refl",
"ZFSet.instHasSubset",
"ZFSet.instSetLike",
"SetLike.instMembership"
] | true |
Ideal.mulQuot | Mathlib.RingTheory.OrderOfVanishing.Basic | [
"Submodule.pointwiseDistribMulAction",
"Submodule.instAddCommMonoidWithOne",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Ideal.mulQuot._proof_5",
"C... | true |
Filter.comap_lift_eq | Mathlib.Order.Filter.Lift | [
"Filter.instMembership",
"Eq.mpr",
"iInf",
"congrArg",
"Filter.instInfSet",
"Function.comp",
"Membership.mem",
"id",
"Filter.comap_iInf",
"funext",
"Filter.lift",
"Eq.refl",
"congrFun'",
"Eq",
"Filter",
"Eq.trans",
"Filter.comap",
"Set"
] | true |
Filter.Germ.const_lt_iff | Mathlib.Order.Filter.FilterProduct | [
"Filter.Germ.ofFun",
"Preorder.toLT",
"Filter.Germ.coe_lt",
"Ultrafilter.neBot",
"Filter.Eventually",
"Filter.Germ.liftRel_const_iff",
"Filter.Germ.const",
"Iff",
"Filter.Germ",
"LT.lt",
"Iff.trans",
"Ultrafilter",
"Ultrafilter.toFilter",
"Preorder",
"Filter.Germ.instPreorder"
] | true |
FormalMultilinearSeries.rightInv._proof_16 | Mathlib.Analysis.Analytic.Inverse | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"IsBoundedSMul.toUniformContinuousConstSMul"... | false |
CategoryTheory.Comonad.ForgetCreatesLimits'.newCone_pt | Mathlib.CategoryTheory.Monad.Limits | [
"CategoryTheory.Comonad",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Comonad.forget",
"CategoryTheory.Functor.comp",
"CategoryTheory.Comonad.ForgetCreatesLimits'.newCone",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Comonad.toFunctor",
"Eq.refl",
"CategoryTheory.C... | true |
_private.Mathlib.RingTheory.PowerSeries.Schroder.0.PowerSeries.coeff_X_mul_largeSchroderSeries._simp_1_1 | Mathlib.RingTheory.PowerSeries.Schroder | [
"Finset",
"Membership.mem",
"Finset.mem_range",
"Finset.range",
"Finset.instSetLike",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Eq",
"SetLike.instMembership"
] | false |
Lean.Grind.Linarith.Poly.NonnegCoeffs.brecOn | Init.Grind.Module.NatModuleNorm | [
"Lean.Grind.Linarith.Poly.NonnegCoeffs.below",
"Lean.Grind.Linarith.Poly.NonnegCoeffs.rec",
"GE.ge",
"Lean.Grind.Linarith.Poly.NonnegCoeffs.below.nil",
"Int",
"Lean.Grind.Linarith.Var",
"Lean.Grind.Linarith.Poly.NonnegCoeffs.below.add",
"instOfNat",
"Lean.Grind.Linarith.Poly.NonnegCoeffs",
"OfNat.... | true |
MeasureTheory.lintegral_prod_mul | Mathlib.MeasureTheory.Measure.Prod | [
"MeasureTheory.QuasiMeasurePreserving.snd",
"Eq.mpr",
"MeasureTheory.Measure",
"HMul.hMul",
"AEMeasurable",
"congrArg",
"CommSemiring.toSemiring",
"MeasureTheory.QuasiMeasurePreserving.fst",
"AEMeasurable.comp_quasiMeasurePreserving",
"MeasureTheory.lintegral_lintegral_mul",
"ENNReal.measurableS... | true |
Asymptotics.isBigO_const_mul_self | Mathlib.Analysis.Asymptotics.Defs | [
"Norm.norm",
"SeminormedRing.toNorm",
"HMul.hMul",
"Asymptotics.IsBigO",
"SeminormedRing.toRing",
"instDistribOfSemiring",
"Distrib.toMul",
"Asymptotics.IsBigOWith.isBigO",
"Asymptotics.isBigOWith_const_mul_self",
"Ring.toSemiring",
"SeminormedRing",
"Filter",
"instHMul"
] | true |
Batteries.Tactic.Lint.LintVerbosity._sizeOf_1 | Batteries.Tactic.Lint.Frontend | [
"Batteries.Tactic.Lint.LintVerbosity",
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"Batteries.Tactic.Lint.LintVerbosity.rec"
] | false |
CategoryTheory.Lax.LaxTrans.LaxFunctor.bicategory_associator_inv_as_app | Mathlib.CategoryTheory.Bicategory.FunctorBicategory.Lax | [
"CategoryTheory.Lax.LaxTrans.Modification.app",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Lax.LaxTrans.Hom.as",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"CategoryTheory.Lax.LaxTrans.app",
"CategoryTheory.LaxFuncto... | true |
_private.Mathlib.CategoryTheory.Triangulated.Orthogonal.0.CategoryTheory.ObjectProperty.isLocal_trW._simp_1_3 | Mathlib.CategoryTheory.Triangulated.Orthogonal | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
completeBipartiteGraph | Mathlib.Combinatorics.SimpleGraph.Basic | [
"Sum.isRight",
"completeBipartiteGraph._proof_3",
"SimpleGraph.mk",
"Sum",
"SimpleGraph",
"Bool.true",
"And",
"Bool",
"Or",
"Sum.isLeft",
"Eq",
"completeBipartiteGraph._proof_1"
] | true |
Int.neg_add_le_right_of_le_add | Init.Data.Int.Order | [
"congrArg",
"Eq.mp",
"Int.instNegInt",
"Int",
"LE.le",
"Int.add_comm",
"instHAdd",
"HAdd.hAdd",
"Int.instAdd",
"Int.neg_add_le_left_of_le_add",
"Neg.neg",
"Int.instLEInt"
] | true |
_private.Init.Data.Array.Basic.0.Array.mapM.map._unary._proof_1 | Init.Data.Array.Basic | [
"Array.push",
"InvImage",
"HSub.hSub",
"PSigma.casesOn",
"id",
"instSubNat",
"instOfNatNat",
"Array",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Nat.sub_succ_lt_self",
"PSigma.mk",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"PSigma",
"Array.size"
] | false |
_private.Init.Data.Option.Monadic.0.Option.instForIn'InferInstanceMembershipOfMonad.match_1.splitter | Init.Data.Option.Monadic | [
"ForInStep.done",
"Option.instForIn'InferInstanceMembershipOfMonad.match_1",
"ForInStep",
"ForInStep.yield"
] | true |
Aesop.PostponedSafeRule.ctorIdx | Aesop.Tree.UnsafeQueue | [
"Nat",
"Aesop.PostponedSafeRule"
] | false |
_private.Mathlib.Topology.Order.LeftRightLim.0.tendsto_atTop_of_mapClusterPt._simp_1_1 | Mathlib.Topology.Order.LeftRightLim | [
"Filter.Eventually",
"Preorder.toLE",
"Exists",
"GE.ge",
"Filter.atTop",
"IsDirectedOrder",
"propext",
"Nonempty",
"Filter.eventually_atTop",
"Eq",
"Preorder"
] | false |
Mathlib.Tactic.IntervalCases.Bound.lt.injEq | Mathlib.Tactic.IntervalCases | [
"Eq.propIntro",
"Mathlib.Tactic.IntervalCases.Bound",
"Mathlib.Tactic.IntervalCases.Bound.lt.inj",
"Int",
"Mathlib.Tactic.IntervalCases.Bound.lt",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
CategoryTheory.Grothendieck.Hom.noConfusionType | Mathlib.CategoryTheory.Grothendieck | [
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.Grothendieck.fiber",
"CategoryTheory.Grothendieck.base",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Grothendieck",
"CategoryTheory.Cat.str",
"CategoryTheory.Cat",
"CategoryTheory.Functor.map",
"... | false |
_private.Mathlib.Algebra.Homology.Homotopy.0.Homotopy.toShortComplex._abel_3 | Mathlib.Algebra.Homology.Homotopy | [
"Mathlib.Tactic.Abel.const_add_termg",
"Mathlib.Tactic.Abel.term_atomg",
"NegZeroClass.toNeg",
"HomologicalComplex.instCategory",
"Mathlib.Meta.NormNum.instAddMonoidWithOne",
"Mathlib.Tactic.Abel.zero_termg",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddC... | false |
_private.Mathlib.RingTheory.Filtration.0.Ideal.Filtration.Stable.exists_pow_smul_eq._proof_1_1 | Mathlib.RingTheory.Filtration | [
"Lean.RArray.leaf",
"False",
"Classical.byContradiction",
"Nat.not_le_eq",
"Lean.RArray.branch",
"id",
"False.casesOn",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.Linear.Expr.num",
"Bool.true",
"instHAdd",
"AddSemigroup.toAdd",
"Nat.Linear.ExprCnstr.eq_false_of_isUnsat",
"HAdd.hAdd",
... | false |
_private.Init.Data.Nat.Power2.Basic.0.Nat.nextPowerOfTwo.go._proof_1 | Init.Data.Nat.Power2.Basic | [
"HMul.hMul",
"of_decide_eq_true",
"Nat.mul_pos",
"id",
"instMulNat",
"instOfNatNat",
"Bool.true",
"GT.gt",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
"Decidable.decide",
"Eq",
"instHMul"
] | false |
Lean.Compiler.LCNF.Code.setTag.inj | Lean.Compiler.LCNF.Basic | [
"Lean.Compiler.LCNF.Code.setTag",
"Lean.Compiler.LCNF.Code.setTag.noConfusion",
"Lean.FVarId",
"Lean.Compiler.LCNF.Purity",
"autoParam",
"Lean.Compiler.LCNF.Code",
"And",
"Lean.Compiler.LCNF.Purity.impure",
"Nat",
"And.intro",
"eq_of_heq",
"HEq",
"Lean.Compiler.LCNF.Alt._auto_13",
"Eq"
] | true |
WithZero.instCoeTC.eq_1 | Mathlib.Algebra.Group.WithOne.Defs | [
"CoeTC",
"WithZero.instCoeTC",
"WithZero",
"WithZero.coe",
"Eq.refl",
"Eq",
"CoeTC.mk"
] | true |
MeasureTheory.eLpNorm_le_eLpNorm_mul_eLpNorm_of_nnnorm | Mathlib.MeasureTheory.Function.LpSeminorm.CompareExp | [
"MeasureTheory.ae",
"Real.instIsOrderedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"ENNReal.instAdd",
"ENNReal.toReal_pos_iff",
"MulOne.toOne",
"lt_add_of_pos_right",
"Real.partialOrder",
"Real",
"ENNReal.ofNNReal",
"DivInvMonoid.toInv",
"E... | true |
AffineSubspace.mem_perpBisector_iff_inner_eq_inner | Mathlib.Geometry.Euclidean.PerpBisector | [
"vsub_midpoint",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"inv_eq_zero._simp_1",
"GroupWithZero.toMonoidWithZero",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"False",
"Real",
"instHSMul",
"AffineSubspace.perpBisector",
"GroupWithZero.toDivisionMo... | true |
Part.some_sdiff_some | Mathlib.Data.Part | [
"Part",
"congrArg",
"Part.some",
"Part.bind_some",
"SDiff.sdiff",
"funext",
"Part.map_some",
"True",
"eq_self",
"of_eq_true",
"Part.instSDiff",
"Monad.toBind",
"SDiff",
"Bind.bind",
"congrFun'",
"Eq",
"Eq.trans",
"Part.instMonad",
"Part.map"
] | true |
AlgCat.instMonoidalCategory.tensorHom._proof_1 | Mathlib.Algebra.Category.AlgCat.Monoidal | [
"AlgCat.instAlgebraObjForgetAlgHomCarrier",
"CommRing",
"instSMulOfMul",
"Ring.toNonAssocRing",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"IsScalarTower",
"AlgCat",
"Algebra.toModule",
"MulOne.toMul",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonAssocRing.toNonUnitalNonAss... | false |
_private.Mathlib.Order.CountableDenseLinearOrder.0.Order.exists_orderEmbedding_insert._simp_1_3 | Mathlib.Order.CountableDenseLinearOrder | [
"Finset",
"Finset.mem_attach",
"Membership.mem",
"Subtype",
"Finset.instSetLike",
"True",
"Finset.attach",
"eq_true",
"Eq",
"SetLike.instMembership"
] | false |
Sum.bnot_isRight | Init.Data.Sum.Lemmas | [
"Sum.isRight",
"Bool.not",
"Sum.casesOn",
"Sum",
"Sum.inl",
"Sum.inr",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Sum.isLeft",
"Eq.symm",
"Eq"
] | true |
Valuation.norm._proof_1 | Mathlib.Topology.Algebra.Valued.NormedValued | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"ValuationClass.toMonoidWithZeroHomClass",
"Field.toDivisionRing",
"DivisionRing.toRing",
"CommMonoidWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero",
"LinearOrderedCommMonoidWithZero.toCommMonoidWithZero",
"MonoidWithZero... | false |
Std.DTreeMap.Raw.get!.congr_simp | Std.Data.DTreeMap.Raw.Lemmas | [
"Ordering",
"Eq.rec",
"Std.DTreeMap.Raw.get!",
"Std.LawfulEqCmp",
"Inhabited",
"Eq.refl",
"Eq",
"Std.DTreeMap.Raw"
] | true |
_private.Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral.0._aux_Mathlib_RingTheory_Polynomial_Eisenstein_IsIntegral___macroRules__private_Mathlib_RingTheory_Polynomial_Eisenstein_IsIntegral_0_term𝓟_1_1 | Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.node5",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSy... | false |
_private.Mathlib.Topology.MetricSpace.Pseudo.Constructions.0.sphere_prod._simp_1_5 | Mathlib.Topology.MetricSpace.Pseudo.Constructions | [
"Lattice.toSemilatticeSup",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"LE.le",
"And",
"Max.max",
"propext",
"Or",
"SemilatticeSup.toPartialOrder",
"Eq",
"instDistribLatticeOfLinearOrder",
"max_eq_iff"
] | false |
Batteries.Tactic.TransRelation.implies.elim | Batteries.Tactic.Trans | [
"Batteries.Tactic.TransRelation.implies",
"PULift.up",
"Nat",
"Batteries.Tactic.TransRelation.ctorElim",
"Batteries.Tactic.TransRelation",
"Lean.Name",
"Lean.BinderInfo",
"Batteries.Tactic.TransRelation.ctorIdx",
"Eq.symm",
"Eq"
] | false |
IncidenceAlgebra.lambda_apply | Mathlib.Combinatorics.Enumerative.IncidenceAlgebra | [
"One",
"DecidableRel",
"Preorder.toLE",
"WCovBy",
"IncidenceAlgebra.instFunLike",
"One.toOfNat1",
"Zero.toOfNat0",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"IncidenceAlgebra",
"IncidenceAlgebra.lambda",
"Preorder",
"Zero",
"ite"
] | true |
_private.Lean.ToExpr.0.Lean.Name.toExprAux.isSimple._unsafe_rec | Lean.ToExpr | [
"String",
"Bool.and",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"_private.Lean.ToExpr.0.Lean.Name.toExprAux.isSimple._unsafe_rec",
"instAddNat",
"Lean.Name",
"instLTNat",
"OfNat.ofNat",
"Bool.false",
"_private.Lean... | false |
Valuation.RankOne.toRankLeOne | Mathlib.RingTheory.Valuation.RankOne | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Valuation.RankOne",
"LinearOrderedCommGroupWithZero",
"Valuation.RankLeOne",
"Ring",
"Valuation"
] | true |
Ordinal.lt_add_iff | Mathlib.SetTheory.Ordinal.Arithmetic | [
"add_lt_add_right",
"Preorder.toLT",
"Ordinal.partialOrder",
"Ordinal.instOrderBot",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"Exists",
"Ne",
"LE.le",
"Ordinal.instAddLeftStrictMono",
"And.casesOn",
"instHAdd",
"And",
"Iff",
"instHSub",
"Ordinal.sub",
"Exists.casesO... | true |
FreeMonoid.count_apply | Mathlib.Algebra.FreeMonoid.Count | [
"CancelMonoid.toRightCancelMonoid",
"FreeAddMonoid.toList",
"FreeMonoid",
"MonoidHom.instFunLike",
"Equiv.instEquivLike",
"MonoidHom",
"Monoid.toMulOneClass",
"AddMonoid.toAddZeroClass",
"FreeMonoid.instCancelMonoid",
"Nat.instAddMonoid",
"Multiplicative.mulOneClass",
"Equiv",
"instBEqOfDeci... | true |
AddGroupWithOne.noConfusionType | Mathlib.Data.Int.Cast.Defs | [
"AddMonoid.toAddSemigroup",
"AddMonoid.toZero",
"HSub.hSub",
"IntCast.intCast",
"IntCast",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"Int",
"Nat.cast",
"instHAdd",
"Neg",
"AddSemigroup.toAdd",
"instHSub",
"instOfNat",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Zero.toOfNat0",
"AddGro... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getD_diff_of_contains_eq_false_right._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
Complex.cosh_ofReal_im | Mathlib.Analysis.Complex.Trigonometric | [
"Eq.mpr",
"Real",
"Complex.ofReal_cosh_ofReal_re",
"Real.instZero",
"congrArg",
"Complex.im",
"id",
"Complex.ofReal",
"Complex.re",
"Zero.toOfNat0",
"Eq.refl",
"Complex.ofReal_im",
"Complex",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Complex.cosh"
] | true |
CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory._proof_4 | Mathlib.CategoryTheory.MorphismProperty.Factorization | [
"CategoryTheory.MorphismProperty.FunctorialFactorizationData",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.MorphismProperty.MapFactorizationData.Z",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right"... | false |
Std.HashMap.getKey_eq_getKeyD | Std.Data.HashMap.Lemmas | [
"Std.HashMap.getKey",
"Membership.mem",
"Std.HashMap",
"LawfulHashable",
"EquivBEq",
"Std.HashMap.getKeyD",
"Std.DHashMap.getKey_eq_getKeyD",
"Hashable",
"Std.HashMap.inner",
"BEq",
"Eq",
"Std.HashMap.instMembership"
] | true |
Fin.orderPred_zero | Mathlib.Data.Fin.SuccPredOrder | [
"instNeZeroNatHAdd_1",
"PartialOrder.toPreorder",
"Fin.instPredOrder",
"Fin.instOfNat",
"instOfNatNat",
"instHAdd",
"Fin.instPartialOrder",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"Order.pred",
"instAddNat",
"OfNat.ofNat",
"Fin",
"Eq",
"rfl"
] | true |
CoxeterMatrix.recOn | Mathlib.GroupTheory.Coxeter.Matrix | [
"Matrix",
"CoxeterMatrix.rec",
"Ne",
"instOfNatNat",
"CoxeterMatrix",
"Nat",
"Matrix.IsSymm",
"OfNat.ofNat",
"Eq",
"CoxeterMatrix.mk"
] | false |
CategoryTheory.Mat_.instPreadditive._proof_2 | Mathlib.CategoryTheory.Preadditive.Mat | [
"CategoryTheory.Mat_.instAddCommGroupHom",
"Finset.univ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Mat_.hom_ext",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Finset.sum_add_distrib",
"Finset",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero... | false |
Std.CloseableChannel.Flavors._sizeOf_1 | Std.Sync.Channel | [
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Unbounded",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Bounded._sizeOf_inst",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Unbounded._sizeOf_inst",
"instOfNatNat",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Zero._sizeOf_inst",
"Std.Close... | false |
Matrix._aux_Mathlib_LinearAlgebra_Matrix_GeneralLinearGroup_Defs___unexpand_Matrix_GeneralLinearGroup_1 | Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
_private.Mathlib.Order.OmegaCompletePartialOrder.0.OmegaCompletePartialOrder.isLUB_range_ωSup._simp_1_2 | Mathlib.Order.OmegaCompletePartialOrder | [
"Exists",
"forall_exists_index",
"propext",
"Exists.intro",
"Eq"
] | false |
Array.map_eq_append_iff | Init.Data.Array.Lemmas | [
"Array.instAppend",
"Eq.mpr",
"congrArg",
"Option.some",
"Function.comp",
"Exists",
"Array.map",
"instOfNatNat",
"Array",
"iff_self",
"_private.Init.Data.Array.Lemmas.0.Array.map_eq_append_iff._simp_1_2",
"funext",
"instHAppendOfAppend",
"And",
"Iff",
"Array.filterMap",
"_private.Ini... | true |
MeasureTheory.eLpNormLESNormFDerivOfEqInnerConst.eq_1 | Mathlib.Analysis.FunctionalSpaces.SobolevInequality | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"NNReal.conjExponent",
"Real",
"MeasureTheory.Measure",
"instHDiv",
"HMul.hMul",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"Real.instDivInvMonoid",
"Real.instSub",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"AddC... | true |
CategoryTheory.Limits.ReflectsFilteredColimitsOfSize.casesOn | Mathlib.CategoryTheory.Limits.Preserves.Filtered | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.ReflectsColimitsOfShape",
"CategoryTheory.Limits.ReflectsFilteredColimitsOfSize",
"CategoryTheory.Limits.ReflectsFilteredColimitsOfSize.rec",
"CategoryTheory.Limits.ReflectsFilteredColimitsOfSize.mk",
"CategoryTheory.IsFiltered",
"CategoryTheory.Category"... | false |
instDecidableStrictAntiOnOfForallForallMemSetForallForallForallLt | Mathlib.Order.Monotone.Defs | [
"Preorder.toLT",
"StrictAntiOn",
"Decidable",
"Membership.mem",
"LT.lt",
"Set.instMembership",
"Preorder",
"Set"
] | true |
Std.TreeMap.getElem?_insertMany_list.match_1 | Std.Data.TreeMap.Lemmas | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
MeasureTheory.memLp_congr_norm | Mathlib.MeasureTheory.Function.LpSeminorm.Basic | [
"MeasureTheory.ae",
"Norm.norm",
"Real",
"MeasureTheory.Measure",
"MeasureTheory.MemLp.congr_norm",
"Filter.Eventually",
"PseudoMetricSpace.toUniformSpace",
"SeminormedAddGroup.toContinuousENorm",
"MeasureTheory.MemLp",
"MeasurableSpace",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"Iff",
... | true |
Filter.iSup_inf_principal | Mathlib.Order.Filter.Basic | [
"Filter.instMembership",
"Filter.instSupSet",
"congrArg",
"iSup",
"setOf",
"Membership.mem",
"Filter.ext",
"Filter.instInf",
"iff_self",
"Iff",
"_private.Mathlib.Order.Filter.Basic.0.Filter.iSup_inf_principal._simp_1_1",
"congr",
"True",
"of_eq_true",
"Filter.principal",
"Eq",
"Set.i... | true |
_private.Mathlib.LinearAlgebra.LinearIndependent.Lemmas.0.LinearMap.iSupIndep_map.match_1_3 | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | [
"Submodule",
"RingHomSurjective.ids",
"iSup",
"Submodule.completeLattice",
"LinearMap.instFunLike",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"Ne",
"LinearMap",
"AddCommMonoid",
"And.casesOn",
"And",
"Exists.casesOn",
"SetLike.coe",
"And.intro",
"Submodule.set... | false |
Quiver.Path.rec.eq._@.Mathlib.Combinatorics.Quiver.Path.3963176020._hygCtx._hyg.4 | Mathlib.Combinatorics.Quiver.Path | [
"Quiver.Path.rec.eq._@.Mathlib.Combinatorics.Quiver.Path.3963176020._hygCtx._hyg.4",
"Quiver.Path.rec._@.Mathlib.Combinatorics.Quiver.Path.3963176020._hygCtx._hyg.3",
"Quiver.Hom",
"Quiver.Path.nil",
"Quiver.Path.rec",
"Quiver.Path",
"Quiver.Path.cons",
"Quiver",
"Eq"
] | false |
Units.ctorIdx | Mathlib.Algebra.Group.Units.Defs | [
"Monoid",
"Units",
"Nat"
] | false |
Aesop.UnsafeQueueEntry.unsafeRule.elim | Aesop.Tree.UnsafeQueue | [
"Aesop.UnsafeRule",
"PULift.up",
"Aesop.UnsafeQueueEntry",
"Aesop.IndexMatchResult",
"Aesop.UnsafeQueueEntry.unsafeRule",
"Aesop.UnsafeQueueEntry.ctorElim",
"Aesop.UnsafeQueueEntry.ctorIdx",
"Nat",
"Eq.symm",
"Eq"
] | false |
Function.Embedding.toEmbedding_equivOfFiniteSelfEmbedding | Mathlib.Data.Fintype.EquivFin | [
"Finite",
"Function.Embedding",
"Equiv.toEmbedding",
"Function.Embedding.ext",
"Eq.refl",
"Function.instFunLikeEmbedding",
"Eq",
"DFunLike.coe",
"Function.Embedding.equivOfFiniteSelfEmbedding"
] | true |
Interval.length.match_1 | Mathlib.Algebra.Order.Interval.Basic | [
"Unit.unit",
"PartialOrder.toPreorder",
"Option.casesOn",
"Preorder.toLE",
"Option.some",
"PartialOrder",
"Interval",
"Option.none",
"Unit",
"NonemptyInterval"
] | false |
Std.TreeMap.Raw.foldl | Std.Data.TreeMap.Raw.Basic | [
"Ordering",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Std.DTreeMap.Raw.foldl"
] | true |
CategoryTheory.InjectiveResolution.ι | Mathlib.CategoryTheory.Preadditive.Injective.Resolution | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.single₀",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.instAddCancelCommMonoid",
"AddSemig... | true |
Ordinal.veblen_right_strictMono | Mathlib.SetTheory.Ordinal.Veblen | [
"Ordinal.veblen",
"StrictMono",
"Ordinal.omega0",
"Ordinal.partialOrder",
"Ordinal.veblenWith_right_strictMono",
"PartialOrder.toPreorder",
"Ordinal.isNormal_opow",
"HPow.hPow",
"instHPow",
"Ordinal.instPow",
"Ordinal.one_lt_omega0",
"Ordinal"
] | true |
Lean.hasAssignedLevelMVar._f | Lean.MetavarContext | [
"Pure.pure",
"Monad.toApplicative",
"Lean.Level.mvar",
"Lean.isLevelMVarAssigned",
"Lean.Level.param",
"Lean.Level.imax",
"Lean.Level",
"Applicative.toPure",
"_private.Lean.MetavarContext.0.Lean.hasAssignedLevelMVar.match_1",
"Lean.Level.hasMVar",
"andM",
"instToBoolBool",
"Unit",
"Lean.Le... | false |
ModuleFilterBasis.instInhabitedOfDiscreteTopology | Mathlib.Topology.Algebra.FilterBasis | [
"Inhabited.default",
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"DiscreteTopology",
"ModuleFilterBasis.instInhabitedOfDiscreteTopology._proof_4",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"ModuleFilterBasis.instInhabitedOfDiscreteTopology._proof_2",
"AddGroupFilterBasi... | true |
Function.Injective.coframeMinimalAxioms | Mathlib.Order.CompleteBooleanAlgebra | [
"Function.Injective.coframeMinimalAxioms._proof_1",
"Order.Coframe.MinimalAxioms.toCompleteLattice",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"iInf",
"CompleteLattice.toLattice",
"iSup",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Order.Coframe.MinimalAxioms",
"Membershi... | true |
CategoryTheory.Abelian.SpectralObject.δToCycles_cyclesIso_inv_assoc | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.assoc",
"CategoryTheory.Abelian.SpectralObject.cycles",
"CategoryTheory.Abelian.SpectralObject.δToCycles",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Abelian.SpectralObject.H",
"CategoryTheory.A... | true |
Std.ExtTreeSet.max?_eq_none_iff._simp_1 | Std.Data.ExtTreeSet.Lemmas | [
"Ordering",
"Std.ExtTreeSet.max?_eq_none_iff",
"Std.TransCmp",
"Option.none",
"propext",
"Std.ExtTreeSet",
"Std.ExtTreeSet.max?",
"Std.ExtTreeSet.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Option"
] | false |
_private.Mathlib.CategoryTheory.Monoidal.Limits.Cokernels.0.CategoryTheory.Limits.CokernelCofork.tensor._simp_1 | Mathlib.CategoryTheory.Monoidal.Limits.Cokernels | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.whiskerRight",
"CategoryTheory.MonoidalCategory.comp_whiskerRight_assoc",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.CategoryStruct.comp",
"Category... | false |
CategoryTheory.TwoSquare.structuredArrowRightwardsOpEquivalence.functor._proof_5 | Mathlib.CategoryTheory.GuitartExact.Opposite | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op_inj",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.comp",
"Quiver.Hom.unop",
"CategoryTheory.CostructuredArrow.hom",
"CategoryThe... | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.