name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Set.image_prod | Mathlib.Data.Set.NAry | [
"Set.instSProd",
"Set.ext",
"SProd.sprod",
"congrArg",
"Set.mem_prod._simp_1",
"Set.mem_image._simp_1",
"_private.Mathlib.Data.Set.NAry.0.Set.image_prod._simp_1_1",
"Prod.exists._simp_1",
"Membership.mem",
"Exists",
"exists_and_left._simp_1",
"Prod.mk",
"Prod.fst",
"Set.mem_image2._simp_1"... | true |
AEMeasurable.sum_measure | Mathlib.MeasureTheory.Measure.AEMeasurable | [
"MeasureTheory.ae",
"Nontrivial",
"Iff.mpr",
"Set.ext",
"Eq.mpr",
"Inhabited.default",
"aemeasurable_of_subsingleton_codomain._simp_1",
"Mathlib.Tactic.Contrapose.contrapose₂",
"MeasureTheory.Measure",
"Set.compl_iInter",
"Set.piecewise_eq_of_notMem",
"MeasurableSet",
"AEMeasurable",
"cong... | true |
Pi.single | Mathlib.Algebra.Notation.Pi.Basic | [
"Function.update",
"Pi.instZero",
"Zero.toOfNat0",
"OfNat.ofNat",
"DecidableEq",
"Zero"
] | true |
CovBySMul.of_subset._simp_2 | Mathlib.Combinatorics.Additive.CovBySMul | [
"Monoid",
"Real",
"HasSubset.Subset",
"Real.instOne",
"CovBySMul",
"MulAction",
"True",
"eq_true",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"CovBySMul.of_subset",
"Set.instHasSubset",
"Set"
] | false |
_private.Mathlib.MeasureTheory.Integral.DivergenceTheorem.0.MeasureTheory._aux_Mathlib_MeasureTheory_Integral_DivergenceTheorem___macroRules__private_Mathlib_MeasureTheory_Integral_DivergenceTheorem_0_MeasureTheory_termFrontFace__1 | Mathlib.MeasureTheory.Integral.DivergenceTheorem | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.... | false |
RingHom.eqLocus | Mathlib.Algebra.Ring.Subring.Basic | [
"RingHom.eqLocus._proof_1",
"RingHom.eqLocus._proof_3",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.eqLocus._proof_6",
"AddMonoidHomClass.toAddMonoidHom",
"AddGroupWithOne.toAddGroup",
"Subsemigroup.mk",
"RingHom.eqLocus._proof_4",
"AddMonoid.toAddZeroClass",
"setOf",
"AddGroupWithOne.to... | true |
IntermediateField.extendScalars._proof_1 | Mathlib.FieldTheory.IntermediateField.Basic | [
"IntermediateField.instPartialOrder",
"IntermediateField",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"Field.toDivisionRing",
"Subfield.instPartialOrder",
"LE.le",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"IntermediateField.toSubfield",
... | false |
Turing.PartrecToTM2.K'.main.sizeOf_spec | Mathlib.Computability.TuringMachine.ToPartrec | [
"instOfNatNat",
"Nat",
"Turing.PartrecToTM2.K'._sizeOf_inst",
"SizeOf.sizeOf",
"Turing.PartrecToTM2.K'.main",
"Eq.refl",
"Turing.PartrecToTM2.K'",
"OfNat.ofNat",
"Eq"
] | true |
connectedComponents_lift_unique' | Mathlib.Topology.Connected.TotallyDisconnected | [
"ConnectedComponents.mk",
"Function.comp",
"ConnectedComponents.surjective_coe",
"Function.Surjective.injective_comp_right",
"TopologicalSpace",
"ConnectedComponents",
"Eq"
] | true |
_private.Mathlib.Order.Filter.Bases.Basic.0.Filter.HasBasis.disjoint_iff_left._simp_1_1 | Mathlib.Order.Filter.Bases.Basic | [
"Filter.instMembership",
"Filter.disjoint_principal_left",
"Compl.compl",
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"Set.instCompl",
"BoundedOrder.toOrderBot",
"propext",
"Filter.principal",... | false |
WeierstrassCurve.a₁_of_isCharNeTwoNF | Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms | [
"CommRing",
"CommSemiring.toSemiring",
"WeierstrassCurve",
"CommRing.toCommSemiring",
"WeierstrassCurve.IsCharNeTwoNF",
"Zero.toOfNat0",
"OfNat.ofNat",
"WeierstrassCurve.IsCharNeTwoNF.a₁",
"Eq",
"MulZeroClass.toZero",
"WeierstrassCurve.a₁",
"instMulZeroClassOfSemiring"
] | true |
pow_succ_nonneg._f | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"_private.Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic.0.pow_succ_nonneg.match_1_1",
"mul_nonneg",
"HMul.hMul",
"MulZeroClass.toMul",
"Monoid.toMulOneClass",
"pow_succ",
"Preorder.toLE",
"Eq.rec",
"MulOne.toMul",
"instOfNatNat",
"LE.le",
"Monoid.toPow",
"Nat.below",
"instHAdd",
"M... | false |
WType.rec | Mathlib.Data.W.Basic | [
"WType",
"WType.mk"
] | false |
_private.Init.Data.Array.InsertIdx.0.Array.getElem?_insertIdx_self._proof_1_1 | Init.Data.Array.InsertIdx | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.s... | false |
ContinuousMul.casesOn | Mathlib.Topology.Algebra.Monoid.Defs | [
"ContinuousMul.rec",
"Continuous",
"HMul.hMul",
"instTopologicalSpaceProd",
"Mul",
"ContinuousMul.mk",
"Prod.fst",
"TopologicalSpace",
"ContinuousMul",
"Prod",
"Prod.snd",
"instHMul"
] | false |
CategoryTheory.Limits.isLimitConeOfHasLimitCurryCompLim._proof_1 | Mathlib.CategoryTheory.Limits.Fubini | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits._proof_1",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.HasLimit",
"CategoryTheory.Functor.curry",
"CategoryTheory.prod'",
"Prod",
"CategoryTheory.Functor.obj",
"Cat... | false |
MvPolynomial.weightedDecomposition | Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous | [
"Submodule",
"DirectSum.Decomposition",
"Nat.instMulZeroClass",
"Submodule.addSubmonoidClass",
"MvPolynomial.weightedHomogeneousSubmodule",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"MvPolynomial.weightedDecomposition._proof_1",
"CommSemiring.toSemiring",
"Membership.mem",
"Subty... | true |
WeierstrassCurve.Projective.addXYZ | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula | [
"CommRing",
"instOfNatNat",
"WeierstrassCurve.Projective.addX",
"WeierstrassCurve.Projective.addZ",
"WeierstrassCurve.Projective",
"Nat",
"Matrix.vecEmpty",
"OfNat.ofNat",
"WeierstrassCurve.Projective.addY",
"Fin",
"Matrix.vecCons"
] | true |
ContinuousMultilinearMap.continuousMapClass | Mathlib.Topology.Algebra.Module.Multilinear.Basic | [
"Pi.topologicalSpace",
"ContinuousMultilinearMap",
"ContinuousMapClass",
"ContinuousMultilinearMap.funLike",
"AddCommMonoid",
"TopologicalSpace",
"ContinuousMultilinearMap.cont",
"ContinuousMapClass.mk",
"Semiring",
"Module"
] | true |
_private.Lean.Elab.Util.0.Lean.Elab.nestedExceptionToMessageData.match_1 | Lean.Elab.Util | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"String.Pos.Raw",
"Option.none",
"Unit",
"Option"
] | false |
_private.Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo.0.Matrix.sub_scalar_sq_eq_discr._simp_1_6 | Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | [
"GroupWithZero.toMonoidWithZero",
"False",
"GroupWithZero.toDivInvMonoid",
"eq_false",
"GroupWithZero",
"DivInvMonoid.toZPow",
"Ne",
"Int",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Zero.toOfNat0",
"zpow_ne_zero",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq... | false |
Vector.getElem?_extract | Init.Data.Vector.Lemmas | [
"instGetElem?OfGetElemOfDecidable",
"Vector",
"congrArg",
"Vector.instGetElemNatLt",
"HSub.hSub",
"Vector.extract",
"Vector.casesOn",
"Eq.rec",
"instSubNat",
"instOfNatNat",
"Vector.getElem?_mk",
"Array.extract",
"Array",
"Option.none",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Vector.... | true |
_private.Batteries.Data.AssocList.0.cond.match_1.eq_2 | Batteries.Data.AssocList | [
"Unit.unit",
"cond.match_1",
"Bool.true",
"Unit",
"Bool",
"Eq.refl",
"Bool.false",
"Eq"
] | true |
_private.Mathlib.CategoryTheory.Sites.Sieves.0.CategoryTheory.Presieve.uncurry_ofArrows._simp_1_1 | Mathlib.CategoryTheory.Sites.Sieves | [
"Set.mem_range",
"Membership.mem",
"Exists",
"propext",
"Set.range",
"Eq",
"Set.instMembership",
"Set"
] | false |
SummableUniformlyOn.exists | Mathlib.Topology.Algebra.InfiniteSum.UniformOn | [
"UniformSpace",
"SummableUniformlyOn",
"HasSumUniformlyOn",
"Exists",
"AddCommMonoid",
"Set"
] | true |
_private.Init.Grind.ToInt.0.Lean.Grind.instBEqIntInterval.beq.eq_4 | Init.Grind.ToInt | [
"Lean.Grind.IntInterval.ii",
"Bool.true",
"Bool",
"Eq.refl",
"Lean.Grind.instBEqIntInterval.beq",
"Eq"
] | true |
_private.Lean.Compiler.LCNF.ElimDeadBranches.0.Lean.Compiler.LCNF.UnreachableBranches.Value.getLiteral.go | Lean.Compiler.LCNF.ElimDeadBranches | [
"Inhabited.default",
"instInhabitedProd",
"instInhabitedOfMonad",
"IO.RealWorld",
"Lean.FVarId",
"Lean.Compiler.LCNF.CompilerM.State",
"Lean.Compiler.LCNF.Purity.pure",
"Array",
"Lean.Core.CoreM",
"StateRefT'",
"Array.instInhabited",
"Lean.instInhabitedFVarId",
"StateRefT'.instMonad",
"Lea... | true |
Equiv.prodShear._proof_2 | Mathlib.Logic.Equiv.Prod | [
"Function.LeftInverse",
"Equiv.instEquivLike",
"Equiv",
"Prod.mk",
"Prod.fst",
"Equiv.symm",
"Prod",
"Prod.snd",
"DFunLike.coe",
"_private.Mathlib.Logic.Equiv.Prod.0.Equiv.prodShear._proof_1",
"EquivLike.toFunLike"
] | false |
CategoryTheory.braiding_rightUnitor_aux₂ | Mathlib.CategoryTheory.Monoidal.Braided.Basic | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Trans.trans",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.id_whiskerLeft",
"congrArg",
"CategoryTheory.MonoidalCategoryStru... | true |
Std.Internal.USquash.rec | Std.Data.Iterators.Lemmas.Equivalence.HetT | [
"Std.Internal.Small",
"Std.Internal.ComputableSmall.choose",
"Std.Internal.USquash.mk'",
"Std.Internal.USquash",
"Std.Internal.ComputableSmall.Target"
] | false |
_private.Mathlib.Order.Filter.Lift.0.Filter.lift'_neBot_iff._simp_1_1 | Mathlib.Order.Filter.Lift | [
"Filter.principal_neBot_iff",
"Filter.NeBot",
"Set.Nonempty",
"propext",
"Filter.principal",
"Eq",
"Set"
] | false |
coe_toIdeal | Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal | [
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HomogeneousSubmodule.setLike",
"Semiring.toModule",
"HomogeneousIdeal._proof_1",
"AddMonoid.toAddSemigroup",
"instVAddOfAdd",
"AddMonoid.toAddZeroClass",
"GradedRing.toDecomposition",
"AddSubmonoidClass",
"AddCommMonoidWithOne.toAddMonoidWit... | true |
Aesop.Script.TacticState.getVisibleGoalIndex? | Aesop.Script.TacticState | [
"Aesop.Script.TacticState.visibleGoals",
"Lean.instBEqMVarId",
"Lean.MVarId",
"Aesop.GoalWithMVars.goal",
"BEq.beq",
"Aesop.GoalWithMVars",
"Nat",
"Aesop.Script.TacticState",
"Array.findIdx?",
"Option"
] | true |
CategoryTheory.Cokleisli.Hom._sizeOf_inst | Mathlib.CategoryTheory.Monad.Kleisli | [
"CategoryTheory.Comonad",
"SizeOf.mk",
"CategoryTheory.Cokleisli.Hom._sizeOf_1",
"SizeOf",
"CategoryTheory.Cokleisli.Hom",
"CategoryTheory.Cokleisli",
"CategoryTheory.Category"
] | false |
_private.Mathlib.Topology.UniformSpace.Equicontinuity.0.Filter.HasBasis.uniformEquicontinuous_iff._simp_1_1 | Mathlib.Topology.UniformSpace.Equicontinuity | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
_private.Init.Data.Array.Find.0.Array.idxOf.eq_1 | Init.Data.Array.Find | [
"Array",
"BEq.beq",
"Nat",
"Eq.refl",
"BEq",
"Eq",
"Array.idxOf",
"Array.findIdx"
] | true |
Std.DTreeMap.size_add_size_eq_size_union_add_size_inter | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap.instUnion",
"Std.DTreeMap.instInter",
"Std.DTreeMap",
"Ord.mk",
"Ordering",
"Std.DTreeMap.Internal.Impl.size_add_size_eq_size_union_add_size_inter",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.size",
"Inter.inter",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Std.DTreeMap.wf",
... | true |
HomologicalComplex.dgoToHomologicalComplex._proof_4 | Mathlib.Algebra.Homology.DifferentialObject | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"dite_congr",
"instHSMul",
"HomologicalComplex.dgoToHomologicalComplex._proof_1",
"instDecidableTrue",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddGroupWithOne.t... | false |
SupBotHom.instSemilatticeSup | Mathlib.Order.Hom.BoundedLattice | [
"Preorder.toLT",
"SupBotHom.instSemilatticeSup._proof_2",
"SupBotHom.instSemilatticeSup._proof_4",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"SupBotHom.instSemilatticeSup._proof_1",
"Preorder.toLE",
"OrderBot",
"SemilatticeSup.toMax",
"Max",
"Function.Injective.semilatticeSup",
"Bot",
"Su... | true |
IsRealClosed.mk._flat_ctor | Mathlib.FieldTheory.IsRealClosed.Basic | [
"NegZeroClass.toNeg",
"Polynomial.IsRoot",
"Odd",
"AddGroupWithOne.toAddMonoidWithOne",
"IsRealClosed",
"Exists",
"Field.toDivisionRing",
"Distrib.toAdd",
"Ne",
"DivisionRing.toRing",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtract... | false |
CategoryTheory.WithTerminal.inclLift._proof_4 | Mathlib.CategoryTheory.WithTerminal.Basic | [
"Eq.mpr",
"CategoryTheory.WithTerminal.lift",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.WithTerminal.id.match_1",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.WithTerminal.incl",
"id",
"Ca... | false |
_private.Mathlib.RingTheory.AdicCompletion.Noetherian.0.IsHausdorff.of_le_jacobson._simp_1_1 | Mathlib.RingTheory.AdicCompletion.Noetherian | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"SModEq.zero",
"Membership.mem",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Submodule.setLike",
"propext",
"Zero.toOfNat0",
"Module",
"AddCommGroup.toDiv... | false |
HasCompactSupport.enorm_le_lintegral_Ici_deriv | Mathlib.MeasureTheory.Integral.IntegralEqImproper | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"WithTop.charZero",
"Real",
"MeasureTheory.Measure",
"instCharZeroENat",
"NormedSpace.toIsBoundedSMul",
"instAddMonoidWithOneENat",
"fderiv_comp_deriv",
"instZeroCompletion",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero",
"Real.instR... | true |
starRingAut._proof_3 | Mathlib.Algebra.Star.Basic | [
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"CommSemiring.toSemiring",
"MulEquiv.map_mul'",
"NonUnitalCommSemiring.toCommSemigroup",
"MulEquiv.toEquiv",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"CommMagma.toMul",
"Equiv.toFun",
"NonUnitalCommSemiring.toNonUnitalSemiring",
"CommS... | false |
RightAddCosetEquivalence | Mathlib.GroupTheory.Coset.Basic | [
"Add.toVAddAddOpposite",
"AddOpposite",
"Set.vaddSet",
"HVAdd.hVAdd",
"instHVAdd",
"Eq",
"AddOpposite.op",
"Add",
"Set"
] | true |
CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_iff_mono_rightTriple_leftToRight | Mathlib.CategoryTheory.Adjunction.Quadruple | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.NatTrans.epi_iff_epi_app",
"CategoryTheory.Epi",
"CategoryTheory.Mono",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Adjunction.Quadruple",
"id",
"CategoryTheory.Limits.HasPullbacks",
"CategoryTheory.NatTrans.mono_iff_mono_app... | true |
HomologicalComplex.natTransHomologyπ_app | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | [
"HomologicalComplex.homologyFunctor",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.homologyπ",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.cyclesFunctor",
"HomologicalComplex.homologyFunctor._proof_1",
"HomologicalCo... | true |
PSigma.Lex.le | Mathlib.Data.PSigma.Order | [
"PSigma.Lex",
"Lex",
"LE.le",
"LE",
"LT.lt",
"LE.mk",
"PSigma",
"LT"
] | true |
CategoryTheory.endofunctorMonoidalCategory_associator_hom_app | Mathlib.CategoryTheory.Monoidal.End | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.endofunctorMonoidalCategory",
"CategoryTheory.MonoidalCategory.toMonoidalCategoryS... | true |
zero_zpow | Mathlib.Algebra.GroupWithZero.Basic | [
"zpow_natCast",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"False",
"DivInvMonoid.toInv",
"GroupWithZero.toDivInvMonoid",
"congrArg",
"zpow_negSucc",
"inv_zero",
"GroupWithZero",
"Nat.add_eq_zero_iff._simp_1",
"Zero.ofOfNat0",
"DivInvMonoid.toZPow",
"Eq.mp",
"id",
"one_ne_zero._simp_1... | true |
ContinuousWithinAt.vsub | Mathlib.Topology.Algebra.Group.AddTorsor | [
"ContinuousWithinAt",
"IsTopologicalAddTorsor",
"nhdsWithin",
"Filter.Tendsto.vsub",
"AddTorsor.toVSub",
"VSub.vsub",
"TopologicalSpace",
"AddGroup",
"AddTorsor",
"Set"
] | true |
_private.Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule.0.trapezoidal_error_le_of_lt._simp_1_8 | Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule | [
"False",
"eq_false",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"CharZero",
"Nat.cast_add_one_ne_zero",
"AddMonoidWithOne.toOne",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat",
"On... | false |
IsLocalization.mk'_self | Mathlib.RingTheory.Localization.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"IsLocalization",
"CommSemiring.toSemiring",
"Submonoid.LocalizationMap.mk'_self",
"Algebra",
"Membership.mem",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"MulZeroOneClass.toMulOneClass",
"Subtype.mk",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
... | true |
CategoryTheory.GlueData.f_hasPullback | Mathlib.CategoryTheory.GlueData | [
"CategoryTheory.GlueData.f",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.GlueData.J",
"Prod.mk",
"CategoryTheory.GlueData",
"CategoryTheory.GlueData.V",
"CategoryTheory.GlueData.U",
"CategoryTheory.Category"
] | true |
lowerCentralSeries_length_eq_nilpotencyClass | Mathlib.GroupTheory.Nilpotent | [
"Group",
"Classical.propDecidable",
"Exists",
"Subgroup.lowerCentralSeries_length_eq_nilpotencyClass",
"Subgroup",
"Bot.bot",
"Group.nilpotencyClass",
"Subgroup.lowerCentralSeries",
"Subgroup.nilpotent_iff_lowerCentralSeries",
"Nat",
"Nat.find",
"Iff.mp",
"Subgroup.instBot",
"Group.IsNilpo... | true |
_private.Mathlib.Topology.MetricSpace.Ultra.Basic.0.IsUltrametricDist.isOpen_closedBall._simp_1_2 | Mathlib.Topology.MetricSpace.Ultra.Basic | [
"Metric.ball_subset_closedBall",
"Real",
"Metric.ball",
"HasSubset.Subset",
"PseudoMetricSpace",
"True",
"eq_true",
"Metric.closedBall",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
_private.Std.Internal.Async.System.0.Std.Internal.IO.Async.System.instDecidableEqSystemUser.decEq.match_1 | Std.Internal.Async.System | [
"Std.Internal.IO.Async.System.GroupId",
"String",
"Std.Internal.IO.Async.System.SystemUser.mk",
"Std.Internal.IO.Async.System.SystemUser.casesOn",
"Std.Internal.IO.Async.System.SystemUser",
"Std.Internal.IO.Async.System.UserId",
"System.FilePath",
"Option"
] | false |
IsRegularLocalRing.spanFinrank_maximalIdeal | Mathlib.RingTheory.RegularLocalRing.Defs | [
"CommRing",
"WithBot",
"Semiring.toModule",
"ENat.instNatCast",
"CommSemiring.toSemiring",
"IsLocalRing.maximalIdeal",
"IsRegularLocalRing",
"Nat.cast",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.toCommSemiring",
"WithBot.natCast",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
... | true |
Std.Ric.Sliceable.mkSlice | Init.Data.Slice.Notation | [
"outParam",
"Std.Ric",
"Std.Ric.Sliceable"
] | true |
Std.LawfulOrderLeftLeaningMax | Init.Data.Order.Classes | [
"Max",
"LE",
"Std.LawfulOrderLeftLeaningMax.mk"
] | true |
_private.Mathlib.Topology.DiscreteSubset.0.isDiscrete_of_codiscreteWithin._simp_1_1 | Mathlib.Topology.DiscreteSubset | [
"Filter.instMembership",
"Compl.compl",
"Membership.mem",
"Bot.bot",
"Filter.instInf",
"Set.instCompl",
"propext",
"Filter.principal",
"Eq.symm",
"Eq",
"Filter.mem_iff_inf_principal_compl",
"Filter",
"Min.min",
"Filter.instBot",
"Set"
] | false |
Mathlib.Tactic._aux_Mathlib_Tactic_Cases___elabRules_Mathlib_Tactic_induction'_1 | Mathlib.Tactic.Cases | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MessageData",
"Array.instAppend",
"Lean.MonadError.mk",
"Lean.MVarId.withContext",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.ElimInfo.motivePos",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.Elab.Tactic.ElimApp.Result",
"Lean.instMonadMCtxOfM... | false |
CategoryTheory.ComposableArrows.Precomp.map_zero_one' | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"instNeZeroNatHAdd_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ComposableArrows.Precomp.map_zero_one'._proof_2",
"CategoryTheory.ComposableArrows",
"CategoryTheory.ComposableArrows.Precomp.obj",
"Fin.mk",
"Fin.instOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
... | true |
NonUnitalSeminormedCommRing.mk | Mathlib.Analysis.Normed.Ring.Basic | [
"NonUnitalSeminormedRing",
"HMul.hMul",
"NonUnitalNonAssocRing.toMul",
"NonUnitalRing.toNonUnitalNonAssocRing",
"NonUnitalSeminormedCommRing",
"NonUnitalSeminormedRing.toNonUnitalRing",
"Eq",
"instHMul",
"NonUnitalSeminormedCommRing.mk"
] | true |
_private.Mathlib.Control.Fix.0.Part.Fix.approx.match_1.eq_2 | Mathlib.Control.Fix | [
"instOfNatNat",
"Unit",
"Nat",
"Part.Fix.approx.match_1",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
card_vector | Mathlib.Data.Fintype.BigOperators | [
"Fintype.card_pi",
"Eq.mpr",
"Fintype.card_fin",
"Finset.univ",
"Equiv.vectorEquivFin",
"congrArg",
"Nat.instMonoid",
"instDecidableEqFin",
"Pi.instFintype",
"List.Vector",
"Fintype.card",
"id",
"Fintype.ofEquiv",
"Finset.prod_const",
"Fin.fintype",
"Fintype.ofEquiv_card",
"Finset.pr... | true |
String.intercalate_cons_of_ne_nil | Init.Data.String.Lemmas.Intercalate | [
"congrArg",
"String",
"Ne",
"List.cons",
"instAppendString",
"instHAppendOfAppend",
"List",
"True",
"eq_self",
"_private.Init.Data.String.Lemmas.Intercalate.0.String.intercalate_cons_of_ne_nil.match_1_1",
"of_eq_true",
"congrFun'",
"String.intercalate",
"Eq",
"HAppend.hAppend",
"Eq.tra... | true |
intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_ge' | Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus | [
"MeasureTheory.ae",
"Set.Ioc",
"NegZeroClass.toNeg",
"Real.instLE",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"neg_sub",
"CompleteSpace",
"NormedSpace",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
... | true |
PowerBasis.ofAdjoinEqTop'.congr_simp | Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | [
"PowerBasis",
"IsDomain",
"PowerBasis.ofAdjoinEqTop'",
"CommRing",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Module.IsTorsionFree",
"Algebra.in... | true |
AddSubgroup.one_le_sum_inv_index_of_leftCoset_cover | Mathlib.GroupTheory.CosetCover | [
"Rat.addCommMonoid",
"Rat.instOfNat",
"AddSubgroup.FiniteIndex",
"ChainCompletePartialOrder.instOfCompleteLattice",
"instVAddOfAdd",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"AddSubgroup.index",
"Finset",
"Set.univ",
"Set.PairwiseDisjoint",
"AddMonoid.toAddZeroClass",
"Rat",
"Membe... | true |
CategoryTheory.Comon.tensorObj_comul | Mathlib.CategoryTheory.Monoidal.Comon_ | [
"CategoryTheory.Comon.tensorObj_comul'",
"CategoryTheory.ComonObj.comul",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.BraidedCategory.unop_tensorμ",
"Quiver.Hom.unop",
"CategoryTheory.ComonObj",
"CategoryTheor... | true |
Lean.FromJson.mk.noConfusion | Lean.Data.Json.FromToJson.Basic | [
"Lean.Json",
"String",
"id",
"heq_of_eq",
"Lean.FromJson",
"Lean.FromJson.mk",
"Eq.refl",
"HEq",
"Except",
"Lean.FromJson.noConfusion",
"Eq"
] | false |
_private.Std.Sat.AIG.CachedLemmas.0.Std.Sat.AIG.mkGateCached.go.match_1.splitter | Std.Sat.AIG.CachedLemmas | [
"False",
"Option.some.noConfusion",
"Option.ctorIdx",
"False.elim",
"Nat.shiftRight",
"noConfusion_of_Nat",
"Option.some",
"Nat.hasNotBit",
"instOfNatNat",
"Bool.ctorIdx",
"Bool.true",
"Nat.land",
"absurd",
"Bool.casesOn",
"Nat",
"Bool",
"eq_of_heq",
"Eq.ndrec",
"Nat.eq_of_beq_eq... | true |
SimplexCategory.factorThruImage_eq | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"CategoryTheory.Limits.factorThruImage",
"Eq.mpr",
"CategoryTheory.Limits.HasImages.has_image",
"SimplexCategory.image_ι_eq",
"CategoryTheory.Epi",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.image.ι",
"id",
"CategoryTheory.... | true |
_private.Mathlib.LinearAlgebra.Span.Defs.0.Submodule.mem_span_pair._simp_1_3 | Mathlib.LinearAlgebra.Span.Defs | [
"Exists",
"And",
"exists_exists_eq_and",
"propext",
"Eq"
] | false |
Rat.intCast_div_eq_divInt | Mathlib.Data.Rat.Defs | [
"Int.cast",
"Eq.mpr",
"instHDiv",
"congrArg",
"Rat",
"Rat.divInt",
"Rat.instIntCast",
"id",
"HDiv.hDiv",
"Rat.divInt_eq_div",
"Int",
"Eq.refl",
"Eq",
"Rat.instDiv"
] | true |
Module.End.isSemisimple_iff' | Mathlib.LinearAlgebra.Semisimple | [
"OrderIso.complementedLattice_iff",
"Sublattice",
"Eq.mpr",
"Submodule",
"IsScalarTower.to_smulCommClass'",
"Module.End.IsSemisimple._proof_2",
"CommRing",
"instSMulOfMul",
"Module.AEval.mapSubmodule",
"Module.End.applyModule",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMo... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk.0.SzemerediRegularity.sum_density_div_card_le_density_add_eps._simp_1_4 | Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
CategoryTheory.MonoidalOpposite.mopMopEquivalence.eq_1 | Mathlib.CategoryTheory.Monoidal.Opposite | [
"CategoryTheory.MonoidalOpposite",
"CategoryTheory.Equivalence",
"CategoryTheory.MonoidalOpposite.unmopEquiv",
"Eq.refl",
"CategoryTheory.Equivalence.trans",
"Eq",
"CategoryTheory.MonoidalOpposite.mopMopEquivalence",
"CategoryTheory.Category",
"CategoryTheory.MonoidalOpposite.monoidalOppositeCategor... | true |
TopCat.toSSetObj₁Equiv._proof_3 | Mathlib.Topology.Homotopy.TopCat.ZerothHomotopy | [
"Real.partialOrder",
"Real",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Pi.topologicalSpace",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"ContinuousMapClass",
"Real.semiring",
"Set.Elem",
"instOfNatNat",
"TopCat.str",
"Homeomorph.instEquivLike",
"TopCat.carrie... | false |
mul_finsum' | Mathlib.Algebra.BigOperators.Finprod | [
"HMul.hMul",
"AddMonoidHom.map_finsum",
"finsum",
"Function.HasFiniteSupport",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"AddMonoidHom.mulLeft",
"NonUnitalNonAssocSemiring",
"Eq",
"MulZeroCla... | true |
Std.Internal.UV.TCP.Socket.getSockName | Std.Internal.UV.TCP | [
"Inhabited.default",
"instInhabitedError",
"IO",
"Std.Net.SocketAddress",
"instInhabitedEIO",
"Std.Internal.UV.TCP.Socket",
"IO.Error"
] | true |
FinBddDistLat.inv_hom_apply | Mathlib.Order.Category.FinBddDistLat | [
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"FinBddDistLat.instBoundedOrderCarrier",
"BoundedLatticeHom.instFunLike",
"FinBddDistLat.instDistribLatticeCarrier",
"DistribLattice.toLattice",
"CategoryTheory.Iso",
"FinBddDistLat.instConcreteCategoryBoundedLatticeHomCarrier",
"CategoryTheory.Iso.... | true |
TrivSqZeroExt.range_inlAlgHom_sup_adjoin_range_inr | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"Subalgebra.instSetLike",
"Set.mem_range_self",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"TrivSqZeroExt.snd",
"TrivSqZeroExt.inr",
"Lattice.toSemilatticeSup",
"AddSubmonoidClass.toAddMemClass",
"TrivSqZeroExt",
"TrivSqZeroExt.inl_fst_add_inr_snd_eq",
"CompleteLattice.toLattice",
"l... | true |
Exists | Init.Core | [
"Exists.intro"
] | true |
Lean.Meta.Grind.AC.EqCnstrProof.below | Lean.Meta.Tactic.Grind.AC.Types | [
"Lean.Meta.Grind.AC.EqCnstr",
"Lean.Grind.AC.Expr",
"Lean.Expr",
"Lean.Meta.Grind.AC.EqCnstrProof",
"Lean.Meta.Grind.AC.EqCnstrProof.rec",
"PProd",
"PUnit",
"Nat",
"Bool",
"Lean.Grind.AC.Var",
"Lean.Grind.AC.Seq"
] | false |
OrthonormalBasis.mkOfOrthogonalEqBot.congr_simp | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"InnerProductSpace.toNormedSpace",
"Submodule",
"Orthonormal",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"Eq.rec",
"OrthonormalBasis.mkOfOrthogonalEqBot",
"Bot.bot",
"Field.toSemifield",
"Submodule.orthogonal",
"RCLike.toDenselyNormedField",
"Submodule.in... | true |
Std.TreeMap.maxKeyD | Std.Data.TreeMap.Basic | [
"Std.DTreeMap.maxKeyD",
"Std.TreeMap.inner",
"Ordering",
"Std.TreeMap"
] | true |
FinTopCat.instCategory._aux_5 | Mathlib.Topology.Category.FinTopCat | [
"FinTopCat.instCategory._aux_1",
"Quiver.mk",
"Quiver.Hom",
"TopCat.instCategory",
"CategoryTheory.InducedCategory.Hom",
"FinTopCat",
"CategoryTheory.InducedCategory",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.InducedCategory.Hom.mk",
"CategoryTheory.Category.toCategoryStruct",
"TopC... | false |
Fin.finsetImage_val_Iic | Mathlib.Order.Interval.Finset.Fin | [
"Fin.image_val_Iic",
"Finset.coe_Iic",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Nat.instLocallyFiniteOrder",
"LocallyFiniteOrder.toLocallyFiniteOrderBot",
"Finset.coe_image",
"Fin.val",
"Fin.instPartialOrder",
"SetLike.coe",
"Finset.instSetLike",
"Nat.instPreorder",
"Nat",
"cong... | true |
LinearEquiv.fixedReduce_mkQ | Mathlib.LinearAlgebra.FixedSubmodule | [
"Submodule",
"Submodule.Quotient.addCommMonoid",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"Submodule.hasQuotient",
"AddCommGroup",
"Submodule.Quotient.module",
"LinearMap",
"HasQuotient.Quotient",
"LinearEquiv.toLinearMap",
"LinearMap.fixedSubmodule",
"RingHomInvPair.ids",
"L... | true |
SaturatedSubmonoid.toSubmonoid | Mathlib.Algebra.Group.Submonoid.Saturation | [
"SaturatedSubmonoid",
"MulOneClass",
"Submonoid"
] | true |
_private.Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureFibrant.0.HomotopicalAlgebra.FibrantObject.instWeakEquivalenceWWeakEquivalences._simp_1 | Mathlib.AlgebraicTopology.ModelCategory.DerivabilityStructureFibrant | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomotopicalAlgebra.weakEquivalence_iff",
"HomotopicalAlgebra.CategoryWithWeakEquivalences",
"propext",
"HomotopicalAlgebra.WeakEquivalence",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"HomotopicalAlgebra.weakEquivalences",
"CategoryTh... | false |
FirstOrder.Language.BoundedFormula.IsQF.isPrenex | Mathlib.ModelTheory.Complexity | [
"FirstOrder.Language.BoundedFormula.IsPrenex.of_isQF",
"FirstOrder.Language.BoundedFormula.IsQF",
"FirstOrder.Language.BoundedFormula.IsPrenex",
"Nat",
"FirstOrder.Language",
"FirstOrder.Language.BoundedFormula"
] | true |
QuaternionGroup.instGroup._proof_10 | Mathlib.GroupTheory.SpecificGroups.Quaternion | [
"Mul.mk",
"One.mk",
"HMul.hMul",
"ZMod.commRing",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Distrib.toAdd",
"instMulNat",
"instOfNatNat",
"_private.Mathlib.GroupTheory.SpecificGroups.Quaternion.0.QuaternionGroup.one",
"ZMod",
"QuaternionGro... | false |
UniformContinuous.dist | Mathlib.Topology.MetricSpace.Pseudo.Constructions | [
"UniformContinuous",
"UniformSpace",
"instUniformSpaceProd",
"Real",
"uniformContinuous_dist",
"PseudoMetricSpace.toUniformSpace",
"UniformContinuous.prodMk",
"Prod.mk",
"Prod.fst",
"UniformContinuous.comp",
"PseudoMetricSpace",
"Real.pseudoMetricSpace",
"Dist.dist",
"PseudoMetricSpace.toD... | true |
_private.Lean.Server.Requests.0.Lean.Server.RequestM.findCmdParsedSnap.containsHoverPos | Lean.Server.Requests | [
"Pure.pure",
"Lean.Syntax.Range",
"Lean.FileMap.rangeContainsHoverPos",
"Monad.toApplicative",
"Lean.Syntax.getRangeWithTrailing?",
"Lean.Server.FileWorker.EditableDocument",
"Id.run",
"Id",
"Applicative.toPure",
"String.Pos.Raw",
"Bool.true",
"_private.Lean.Server.Requests.0.Lean.Language.Sna... | true |
AddEquiv.linearEquiv | Mathlib.Algebra.Module.TransferInstance | [
"LinearEquiv.mk",
"Equiv.toFun",
"AddCommMonoid",
"AddEquiv.linearEquiv._proof_4",
"RingHomInvPair.ids",
"LinearEquiv",
"LinearMap.mk",
"AddEquiv.module",
"AddEquiv.linearEquiv._proof_3",
"Semiring",
"AddEquiv",
"AddCommSemigroup.toAddCommMagma",
"AddHom.mk",
"AddEquiv.toEquiv",
"Module"... | true |
SSet.Truncated.ι0₂._proof_3 | Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | [
"_private.Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat.0.SSet.Truncated.ι0₂._proof_2",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"SimplexCategory.mk",
"Nat",
"OfNat.ofNat",
"SimplexCategory.len"
] | false |
finSuccEquiv'_ne_last_apply | Mathlib.Logic.Equiv.Fin.Basic | [
"Iff.mpr",
"Fin.succAbove",
"Equiv.instEquivLike",
"congrArg",
"Fin.predAbove_succAbove",
"Option.some",
"Exists",
"Equiv",
"Fin.exists_succAbove_eq",
"Ne",
"instOfNatNat",
"Fin.predAbove",
"instHAdd",
"Exists.casesOn",
"HAdd.hAdd",
"Nat",
"Fin.last",
"congr",
"True",
"eq_self"... | true |
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