name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
MeasureTheory.lintegral_sum_measure | Mathlib.MeasureTheory.Integral.Lebesgue.Basic | [
"MeasureTheory.lintegral_def",
"MeasureTheory.SimpleFunc.lintegral",
"Eq.mpr",
"MeasureTheory.SimpleFunc.lintegral_sum",
"MeasureTheory.Measure",
"ENNReal.instAddCommMonoid",
"Iff.of_eq",
"congrArg",
"iSup",
"Finset",
"CompletelyDistribLattice.toCompleteLattice",
"MeasureTheory.SimpleFunc.lint... | true |
HasEnoughRootsOfUnity.natCard_rootsOfUnity | Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity | [
"Units.val",
"IsPrimitiveRoot.eq_orderOf",
"Eq.mpr",
"MulOne.toOne",
"Nat.instMulZeroClass",
"Dvd.dvd",
"Subgroup.instSubgroupClass",
"_private.Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity.0.HasEnoughRootsOfUnity.natCard_rootsOfUnity._simp_1_1",
"SubmonoidClass.toMonoid._proof_6",
"Monoid.to... | true |
ENNReal.ofReal_ne_top._simp_1 | Mathlib.Data.ENNReal.Basic | [
"False",
"Real",
"eq_false",
"ENNReal.ofReal",
"ENNReal",
"ENNReal.instTop",
"ENNReal.ofReal_ne_top",
"Top.top",
"Eq"
] | false |
_private.Mathlib.RingTheory.Ideal.AssociatedPrime.Localization.0.Module.associatedPrimes.mem_associatedPrimes_of_comap_mem_associatedPrimes_of_isLocalizedModule._simp_1_9 | Mathlib.RingTheory.Ideal.AssociatedPrime.Localization | [
"Submodule",
"Submodule.colon",
"instHSMul",
"Semiring.toModule",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Set.instSingletonSet",
"DistribSMul.toSMulZeroClass",
"Ideal",
"AddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMon... | false |
_private.Mathlib.GroupTheory.Subgroup.Center.0.Subgroup.center_eq_top_iff._simp_1_2 | Mathlib.GroupTheory.Subgroup.Center | [
"HMul.hMul",
"Mul",
"IsMulCommutative",
"propext",
"Eq",
"isMulCommutative_iff",
"instHMul"
] | false |
ArchimedeanClass.instLinearOrderedAddCommGroupWithTop._proof_6 | Mathlib.Algebra.Order.Ring.Archimedean | [
"IsDomain.to_noZeroDivisors",
"IsOrderedRing",
"LinearOrder",
"IsStrictOrderedRing",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"DivisionRing.toRing",
"Field.toSemifield",
"instIsDomain",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
... | false |
Aesop.Match.casesOn | Aesop.Forward.Match.Types | [
"Aesop.PremiseIndex",
"Aesop.Match.mk",
"Aesop.SlotIndex",
"Aesop.Substitution",
"Aesop.Match.rec",
"Aesop.Match",
"Array"
] | false |
CategoryTheory.SimplicialObject.Splitting.PInfty_toNondegComplex | Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject | [
"CategoryTheory.Idempotents.Karoubi.Hom.f",
"ChainComplex",
"HomologicalComplex.instCategory",
"Opposite",
"CategoryTheory.Idempotents.Karoubi",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.SimplicialObject.Splitting.d._proof_1",
"CategoryThe... | true |
Std.DHashMap.Internal.AssocList.getCast?._f | Std.Data.DHashMap.Internal.AssocList.Basic | [
"Std.DHashMap.Internal.AssocList.below",
"congrArg",
"Option.some",
"cast",
"LawfulBEq",
"Std.DHashMap.Internal.AssocList.nil",
"_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.toList.match_1",
"instDecidableEqBool",
"dite",
"Bool.true",
"Option.none",
"BE... | false |
Set.preimage_const_mul_Iic | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"Set.ext",
"instHDiv",
"HMul.hMul",
"IsOrderedMonoid",
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"le_div_iff_mul_le'",
"Preorder.toLE",
"PartialOrder",
"MulOne.toMul",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"LE.le",
"CommGroup",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
... | true |
RootPairingCat.coweightIsAddCommGroup | Mathlib.LinearAlgebra.RootSystem.RootPairingCat | [
"CommRing",
"RootPairingCat.coweight",
"AddCommGroup",
"RootPairingCat"
] | true |
Finset.falling.eq_1 | Mathlib.Combinatorics.SetFamily.LYM | [
"Lattice.toSemilatticeSup",
"Finset",
"Finset.decidableEq",
"Finset.powersetCard",
"Nat",
"Finset.instLattice",
"Finset.sup",
"Eq.refl",
"Finset.instOrderBot",
"Eq",
"Finset.falling",
"DecidableEq"
] | true |
Real.iteratedFDeriv_fourierIntegral | Mathlib.Analysis.Fourier.FourierTransformDeriv | [
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"measureSpaceOfInnerProductSpace",
"HMul.hMul",
"VectorFourier.fourierPowSMulRight",
"NormedSpace",
"Complex.commRing",
"ENat.instNatCast",
"Real.denselyNormedField",
"Real.instRCLike",
"innerSL",
... | true |
_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.offsetExpression | Lean.Compiler.LCNF.EmitC | [
"String",
"instOfNatNat",
"ToString.toString",
"instAppendString",
"GT.gt",
"instHAppendOfAppend",
"instToStringNat",
"Nat",
"Nat.decLt",
"instLTNat",
"OfNat.ofNat",
"HAppend.hAppend",
"instToStringString",
"ite"
] | true |
lTensor.inverse_of_rightInverse._proof_10 | Mathlib.LinearAlgebra.TensorProduct.RightExactness | [
"Function.Exact",
"Submodule.Quotient.eq",
"Iff.mpr",
"Submodule",
"RingHomSurjective.ids",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"instHSMul",
"instSMulOfMul",
"lTensor.inverse_of_rightInverse._proof_3",
"LinearMap.ext",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
... | false |
_private.Init.Data.UInt.Lemmas.0.UInt32.toUInt8_lt._simp_1_2 | Init.Data.UInt.Lemmas | [
"instLTUInt8",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"UInt8.lt_iff_toNat_lt",
"UInt8.toNat",
"UInt8",
"Eq"
] | false |
Holor.instModule._proof_5 | Mathlib.Data.Holor | [
"Pi.module._proof_1",
"instHSMul",
"Semiring.toModule",
"Holor.instSMulOfMul",
"Distrib.toAdd",
"DistribMulAction.mk",
"SemigroupAction.mk",
"instDistribOfSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"List",
"instHAdd",
"Holor.instModule._proof_1",
"Distrib.toMul",
"HAdd.hAdd",
... | false |
_private.Mathlib.MeasureTheory.MeasurableSpace.Constructions.0.measurableSet_inl_image._simp_1_1 | Mathlib.MeasureTheory.MeasurableSpace.Constructions | [
"MeasurableSet",
"Sum",
"measurableSet_sum_iff",
"Sum.inl",
"Sum.instMeasurableSpace",
"MeasurableSpace",
"And",
"Set.preimage",
"Sum.inr",
"propext",
"Eq",
"Set"
] | false |
List.isChain_cons_eq_iff_eq_replicate | Mathlib.Data.List.Chain | [
"List.head?",
"List.replicate",
"congrArg",
"Option.instMembership",
"Option.some.injEq",
"Option.some",
"Membership.mem",
"List.IsChain",
"List.cons",
"List.cons.injEq",
"forall_eq'._simp_1",
"iff_self",
"List",
"And",
"Iff",
"implies_congr",
"Option.mem_def._simp_1",
"True",
"e... | true |
iSupIndep_iff_pairwiseDisjoint | Mathlib.Order.SupIndep | [
"Iff.mpr",
"iSupIndep.pairwiseDisjoint",
"Function.onFun",
"iSupIndep",
"iSup",
"Disjoint",
"CompleteLattice.toConditionallyCompleteLattice",
"disjoint_iSup_iff",
"Ne",
"Ne.symm",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"Iff",
"Order.Frame.toCom... | true |
Vitali.exists_disjoint_subfamily_covering_enlargement_closedBall | Mathlib.MeasureTheory.Covering.Vitali | [
"Mathlib.Tactic.Push.not_forall_eq",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Iff.mpr",
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"False",
"Real.partialOrder"... | true |
Std.DTreeMap.Internal.Impl.foldr_eq_foldr_keysArray | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"List.foldr_toArray",
"Std.DTreeMap.Internal.Impl.foldr",
"congrArg",
"id",
"instOfNatNat",
"List.toArray",
"Array",
"Array.foldr",
"Std.DTreeMap.Internal.Impl.keysArray",
"Nat",
"Eq.refl",
"Std.DTreeMap.Internal.Impl.toArray_keys",
"Std.DTreeMap.Internal.Impl.keys",
"OfNat.ofN... | true |
Algebra.IsPushout.cancelBaseChange | Mathlib.RingTheory.IsTensorProduct | [
"IsTensorProduct.equiv._proof_1",
"LinearEquiv.symm",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScal... | true |
Prod.lex_iff | Mathlib.Data.Prod.Basic | [
"Prod.lex_def",
"Prod.Lex",
"Prod.fst",
"And",
"Iff",
"Or",
"Prod",
"Eq",
"Prod.snd"
] | true |
SemiNormedGrp.Hom.mk | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"NormedAddGroupHom",
"SemiNormedGrp.Hom",
"SemiNormedGrp.carrier",
"SemiNormedGrp.Hom.mk",
"SemiNormedGrp.str",
"SemiNormedGrp"
] | true |
AlgebraicGeometry.StructureSheaf.IsLocalization.to_basicOpen | Mathlib.AlgebraicGeometry.StructureSheaf | [
"CategoryTheory.Functor",
"CommRing",
"Opposite",
"CommRingCat.carrier",
"PrimeSpectrum.basicOpen",
"TopologicalSpace.Opens.instPartialOrder",
"CommRingCat",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"IsLocalization.Away",
"TopologicalSpace.Opens",
"CommRingCat.instCategory... | true |
Metric.PiNatEmbed.continuous_distDenseSeq_inv | Mathlib.Topology.MetricSpace.PiNat | [
"Filter.instMembership",
"Iff.mpr",
"Pi.uniformSpace",
"Eq.mpr",
"Topology.IsInducing.nhds_eq_comap",
"instEMetricSpaceSubtype",
"Real",
"Continuous",
"Pi.topologicalSpace",
"Nat.encodable",
"congrArg",
"ContinuousAt",
"Filter.map",
"Metric.PiNatEmbed.instPseudoMetricSpace",
"Metric.PiNa... | true |
LieIdeal.lieAlgebra._proof_3 | Mathlib.Algebra.Lie.Ideal | [
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"CommRing",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LieSubmodule.instSMulMemClass",
"AddMonoid.toAddZeroClass",
"LieSubmodule",
"AddCommGroup.toAddGroup",
"SMulMem... | false |
Real.instField._proof_5 | Mathlib.Data.Real.Basic | [
"CauSeq.Completion.instInvCauchy",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"_private.Mathlib.Data.Real.Basic.0.Real.instField._simp_2",
"HMul.hMul",
"CommRing.toNonUnita... | false |
FiniteGaloisIntermediateField.noConfusionType | Mathlib.FieldTheory.Galois.GaloisClosure | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"IntermediateField",
"IntermediateField.toField",
"Algebra",
"Membership.mem",
"Field.toDivisionRing",
"DivisionRing.toDivisionSemiring",
"Algebra.toModule",
"Subtype",
"IsGalois",
"NonUnitalNon... | false |
Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.InsertUnitInvariant._proof_1 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult | [
"Eq.mpr",
"congrArg",
"Fin.isLt",
"id",
"Fin.val",
"Array",
"Nat",
"LT.lt",
"Std.Tactic.BVDecide.LRAT.Internal.Assignment",
"instLTNat",
"Fin",
"Eq",
"Array.size"
] | false |
MonoidWithZeroHom.ValueGroup₀ | Mathlib.Algebra.GroupWithZero.Range | [
"Membership.mem",
"Units",
"Subtype",
"Subgroup",
"Units.instGroup",
"MonoidWithZeroHomClass",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"WithZero",
"MonoidWithZeroHom.valueGroup",
"SetLike.instMembership",
"Subgroup.instSetLike",
"MonoidWithZero.toMonoid",
"FunLike"
] | true |
HasDerivWithinAt.hasFDerivWithinAt | Mathlib.Analysis.Calculus.Deriv.Basic | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"ContinuousSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"HasDerivWithinAt",
"AddCommGroup.to... | true |
Std.DHashMap.Raw.getKey | Std.Data.DHashMap.Raw | [
"_private.Std.Data.DHashMap.Raw.0.Std.DHashMap.Raw.get._proof_1",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Std.DHashMap.Internal.Raw₀.getKey",
"Std.DHashMap.Raw",
"Membership.mem",
"instOfNatNat",
"Subtype.mk",
"Nat",
"_private.Std.Data.DHashMap.Raw.0.Std.DHashMap.Raw.getKey._proof_1",
"... | true |
Std.IterM.toListRev.go | Init.Data.Iterators.Consumers.Monadic.Collect | [
"Pure.pure",
"Std.Shrink",
"Monad.toApplicative",
"Std.IterM.TerminationMeasures.Finite",
"InvImage",
"Std.IterM.finitelyManySteps!",
"Std.IterM.IsPlausibleStep",
"Std.IterStep.skip",
"Applicative.toPure",
"Std.IterM.toListRev.go._proof_2",
"Std.Iterator",
"List.cons",
"List",
"Std.IterM.s... | true |
Finset.inf_mem_of_nonempty | Mathlib.Data.Finset.Lattice.Fold | [
"Iff.mpr",
"Eq.mpr",
"False",
"Finset.not_nonempty_empty",
"Lattice.toSemilatticeSup",
"Finset.coe_singleton",
"Set.image_singleton",
"eq_false",
"congrArg",
"inf_of_le_left",
"Finset",
"LinearOrder",
"False.elim",
"Set.image_mono",
"PartialOrder.toPreorder",
"Classical.propDecidable",... | true |
Std.DTreeMap.Internal.Impl.ordered_containsThenInsertIfNew! | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"Eq.mpr",
"Ord",
"congrArg",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.Ordered",
"Std.DTreeMap.Internal.Impl.Balanced",
"id",
"Std.DTreeMap.Internal.Impl.ordered_insertIfNew!",
"Bool",
"Eq",
"Prod.snd",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.containsThenInsertIfNew!_snd_... | true |
Lean.Meta.Occurrences.noConfusionType | Init.MetaTypes | [
"dite",
"Lean.Meta.Occurrences.all.elim",
"Lean.Meta.Occurrences.neg.elim",
"List",
"Lean.Meta.Occurrences",
"Nat",
"Lean.Meta.Occurrences.pos.elim",
"Nat.decEq",
"Lean.Meta.Occurrences.ctorIdx",
"Eq",
"Not",
"Lean.Meta.Occurrences.casesOn"
] | false |
List.cons_diff_of_not_mem | Batteries.Data.List.Lemmas | [
"Eq.mpr",
"congrArg",
"LawfulBEq",
"Membership.mem",
"id",
"List.cons",
"List",
"List.erase",
"List.instMembership",
"Eq.refl",
"List.diff",
"List.instDecidableMemOfLawfulBEq",
"BEq",
"Eq",
"if_neg",
"Not",
"List.cons_diff",
"ite"
] | true |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic.0.WeierstrassCurve.Affine.CoordinateRing.mk_ψ._simp_1_5 | Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | [
"Monoid",
"HMul.hMul",
"instMulNat",
"pow_mul",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"instHPow",
"Eq.symm",
"Eq",
"instHMul"
] | false |
RingEquivClass.toLinearEquivClassRat | Mathlib.Algebra.Algebra.Rat | [
"RingHom.instRingHomClass",
"instHSMul",
"HMul.hMul",
"LinearEquivClass",
"map_ratCast",
"DivisionRing.toRatCast",
"Algebra.algebraMap",
"outParam",
"Ring.toNonAssocRing",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"RingEquivClass.toNonUnitalRingHomClass",
"Ad... | true |
WithTop.instSemiring._proof_9 | Mathlib.Algebra.Order.Ring.WithTop | [
"WithTop.instNonUnitalSemiring",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"NonUnitalNonAssocSemiring.toMul",
"Distrib.toAdd",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"CanonicallyOrderedAdd",
"instDistribOfSemiring",
"NonUnita... | false |
_private.Init.Data.Int.Order.0.Int.mem_toNat?.match_1_9 | Init.Data.Int.Order | [
"False",
"Int.ctorIdx",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Eq.casesOn",
"Int.ofNat",
"Int",
"Nat.cast",
"Nat",
"Eq.refl",
"HEq",
"instNatCastInt",
"Int.negSucc",
"Eq"
] | false |
Std.Time.Day.Offset.toMinutes | Std.Time.Date.Unit.Day | [
"Rat.instOfNat",
"Int.cast",
"instHDiv",
"_private.Std.Time.Date.Unit.Day.0.Std.Time.Day.Offset.toMinutes._proof_1",
"Rat",
"Rat.instIntCast",
"HDiv.hDiv",
"Int",
"Std.Time.Day.Offset",
"Std.Time.Minute.Offset",
"instOfNat",
"OfNat.ofNat",
"Std.Time.Internal.UnitVal.cast",
"Rat.instDiv",
... | true |
Turing.proj | Mathlib.Computability.TuringMachine.Tape | [
"Turing.proj._proof_1",
"Pi.instInhabited",
"Turing.PointedMap.mk",
"Inhabited",
"Turing.PointedMap"
] | true |
Std.DTreeMap.Internal.Impl.balance!.match_1 | Std.Data.DTreeMap.Internal.Balancing | [
"Unit.unit",
"Std.DTreeMap.Internal.Impl.casesOn",
"namedPattern",
"Std.DTreeMap.Internal.Impl.inner",
"Unit",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | false |
CategoryTheory.Arrow.augmentedCechConerve_right | Mathlib.AlgebraicTopology.CechNerve | [
"CategoryTheory.Arrow.augmentedCechConerve",
"CategoryTheory.Comma.right",
"CategoryTheory.CosimplicialObject",
"CategoryTheory.Functor.id",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.hom",
"instOfNatNat",
"instHAdd",
"CategoryTheory.CosimplicialObject.const",
"CategoryTheory.Limits.HasWid... | true |
ENNReal.tsum_eq_zero._simp_1 | Mathlib.Topology.Algebra.InfiniteSum.ENNReal | [
"ENNReal.instAddCommMonoid",
"tsum",
"ENNReal",
"propext",
"Zero.toOfNat0",
"ENNReal.instTopologicalSpace",
"ENNReal.instZero",
"OfNat.ofNat",
"Eq",
"ENNReal.tsum_eq_zero",
"SummationFilter.unconditional"
] | false |
_private.Mathlib.Data.List.TFAE.0.List.forall_tfae._simp_1_2 | Mathlib.Data.List.TFAE | [
"List.map",
"Membership.mem",
"List.forall_mem_map",
"List",
"List.instMembership",
"propext",
"Eq"
] | false |
Std.Format.defUnicode | Init.Data.Format.Basic | [
"Bool.true",
"Bool"
] | true |
_private.Mathlib.Topology.Sets.VietorisTopology.0.TopologicalSpace.IsTopologicalBasis.nonemptyCompacts.match_1_2 | Mathlib.Topology.Sets.VietorisTopology | [
"setOf",
"Set.Finite",
"Membership.mem",
"HasSubset.Subset",
"And.casesOn",
"And",
"And.intro",
"Set.instMembership",
"Set.instHasSubset",
"Set"
] | false |
Std.DTreeMap.Internal.Impl.recOn | Std.Data.DTreeMap.Internal.Def | [
"Std.DTreeMap.Internal.Impl.rec",
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Std.DTreeMap.Internal.Impl"
] | false |
one_div_pow | Mathlib.Algebra.Group.Basic | [
"DivInvMonoid.toInv",
"instHDiv",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"DivisionMonoid.toDivInvOneMonoid",
"DivisionMonoid",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"inv_pow",
"DivisionMonoid.toDivInvMonoid",
"Monoid.toPow",
"Inv.inv",
"HPow.hPow",
"Nat",
"co... | true |
QuadraticMap.polar_sub_right | Mathlib.LinearAlgebra.QuadraticForm.Basic | [
"Eq.mpr",
"NegZeroClass.toNeg",
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"id",
"QuadraticMap.polar",
"SubtractionMonoi... | true |
_private.Mathlib.Lean.Expr.Basic.0.Lean.Name.mapPrefix._sparseCasesOn_1 | Mathlib.Lean.Expr.Basic | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
LinearEquiv.uniqueProd_symm_apply | Mathlib.LinearAlgebra.Prod | [
"Inhabited.default",
"LinearEquiv.symm",
"Unique",
"Prod.mk",
"AddCommMonoid",
"RingHomInvPair.ids",
"LinearEquiv",
"Semiring",
"LinearEquiv.instEquivLike",
"Eq.refl",
"Unique.instInhabited",
"LinearEquiv.uniqueProd",
"Module",
"Prod",
"Prod.instModule",
"RingHom.id",
"Semiring.toNon... | true |
isOrderedModule_iff_smul_one_mono | Mathlib.Algebra.Order.Module.Defs | [
"MulOne.toOne",
"instHSMul",
"instSMulOfMul",
"SMulWithZero.toSMulZeroClass",
"IsScalarTower",
"IsOrderedModule.toSMulPosMono",
"Monotone",
"Preorder.toLE",
"IsOrderedModule",
"MulOne.toMul",
"ZeroLEOneClass",
"MulPosMono",
"MulOneClass.toMulOne",
"Iff",
"PosMulMono",
"smul_one_mono",
... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_380 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Finset.mem_singleton",
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"Equiv.instEquivLike",
"List.idxOfNth_lt_length_iff",
"eq_false",
"instLawfulBEq",
"List.Pairwise",
"Lean.Grind.iff_eq",
"Lean.Grind.CommRing.Expr.var",
... | false |
Int.eq_mul_of_fdiv_eq_left | Init.Data.Int.DivMod.Lemmas | [
"Eq.mpr",
"Dvd.dvd",
"HMul.hMul",
"congrArg",
"Int.fdiv",
"id",
"Int",
"Int.instDvd",
"Int.instMul",
"Int.eq_mul_of_fdiv_eq_right",
"Eq.refl",
"Int.mul_comm",
"Eq",
"instHMul"
] | true |
LightProfinite.instHasPropAndTotallyDisconnectedSpaceCarrierSecondCountableTopology | Mathlib.Topology.Category.LightProfinite.Basic | [
"SecondCountableTopology",
"inferInstance",
"TotallyDisconnectedSpace",
"TopologicalSpace",
"TopCat.str",
"And",
"TopCat.carrier",
"And.intro",
"TopCat",
"CompHausLike.HasProp.mk",
"TopCat.of",
"CompHausLike.HasProp"
] | true |
PFun.image_mono | Mathlib.Data.PFun | [
"PFun.graph'",
"PFun",
"PFun.image",
"HasSubset.Subset",
"SetRel.image_mono",
"Set.instHasSubset",
"Set"
] | true |
noZeroSMulDivisors_iff | Mathlib.Algebra.NoZeroSMulDivisors.Defs | [
"instHSMul",
"SMul",
"NoZeroSMulDivisors.mk",
"NoZeroSMulDivisors",
"Iff",
"NoZeroSMulDivisors.casesOn",
"Iff.intro",
"Zero.toOfNat0",
"HSMul.hSMul",
"Or",
"OfNat.ofNat",
"Eq",
"Zero"
] | true |
RootPairing.GeckConstruction.equivRootSystem._proof_14 | Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basis | [
"LieAlgebra.toModule",
"LieSubalgebra.lieAlgebra",
"RootPairing.GeckConstruction.basis._proof_2",
"RootPairing.IsReduced",
"instIsPrincipalIdealRingOfIsSemisimpleRing",
"instFintypeSum",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"LieRing.... | false |
Std.Internal.List.getValueD_filter_not_contains_map_fst_of_containsKey_eq_false_right | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"Std.Internal.List.containsKey_eq_contains_map_fst",
"Bool.not",
"congrArg",
"List.map",
"List.contains",
"Std.Internal.List.getValueD_filter_not_contains_of_containsKey_eq_false_right",
"Eq.mp",
"Sigma.fst",
"List",
"Std.Internal.List.containsKey",
"EquivBEq"... | true |
neg_add_nonpos_iff | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"congrArg",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"AddLeftMono",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
"neg_add_le_iff_le_add",
"SubNegZeroMonoid.toNegZeroClass",
"LE",
"AddZero.to... | true |
Ordinal.familyOfBFamily'._proof_1 | Mathlib.SetTheory.Ordinal.Family | [
"Eq.mpr",
"Preorder.toLT",
"Ordinal.partialOrder",
"congrArg",
"PartialOrder.toPreorder",
"PrincipalSeg.toRelEmbedding",
"Ordinal.typein_lt_type",
"Ordinal.type",
"id",
"IsWellOrder",
"RelEmbedding",
"LT.lt",
"Eq.symm",
"Eq",
"DFunLike.coe",
"RelEmbedding.instFunLike",
"Ordinal.typei... | false |
Monoid.CoprodI.NeWord.replaceHead.congr_simp | Mathlib.GroupTheory.CoprodI | [
"Monoid",
"MulOne.toOne",
"Monoid.CoprodI.NeWord",
"Monoid.toMulOneClass",
"Eq.rec",
"Ne",
"MulOneClass.toMulOne",
"Monoid.CoprodI.NeWord.replaceHead",
"Eq.ndrec",
"One.toOfNat1",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.Limits.preservesColimitsOfShape_of_reflects_of_preserves | Mathlib.CategoryTheory.Limits.Preserves.Basic | [
"CategoryTheory.Limits.PreservesColimitsOfShape.preservesColimit",
"CategoryTheory.Limits.preservesColimit_of_reflects_of_preserves",
"CategoryTheory.Functor",
"CategoryTheory.Limits.ReflectsColimitsOfShape",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.PreservesColimitsOfShape",
"CategoryTheor... | true |
_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimApp.State.rec | Lean.Elab.Tactic.Induction | [
"Lean.MVarId",
"Lean.Expr",
"Array",
"_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimApp.State.mk",
"Lean.Elab.Tactic.ElimApp.Alt",
"Nat",
"_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimApp.State",
"Option"
] | false |
_private.Mathlib.Algebra.Order.Algebra.0.Mathlib.Meta.Positivity.evalAlgebraMap._proof_6 | Mathlib.Algebra.Order.Algebra | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"Lean.Expr",
"PLift",
"Lean.Expr.sort",
"Lean.Level",
"PLift.down",
"Prod.fst",
"List.cons",
"Qq.Quoted",
"Qq.Quoted.unsafeMk",
"Bool",
"Lean.Expr.app",
"Lean.Level.succ",
"Prod",
"Lean.Name.mkStr1",
"Prod.snd",
"List.nil"
] | false |
Lean.Lsp.ColorInformation.range | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.ColorInformation",
"Lean.Lsp.Range"
] | true |
Fin.dfoldlM.loop._unary._proof_3 | Batteries.Data.Fin.Basic | [
"congrArg",
"Fin.mk",
"Fin.dfoldlM._proof_2",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Fin.last",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Fin",
"Eq",
"Not"
] | false |
Equiv.coe_inj | Mathlib.Logic.Equiv.Defs | [
"Equiv.instEquivLike",
"Equiv",
"Iff",
"DFunLike.coe_fn_eq",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
_private.Batteries.Data.List.Lemmas.0.List.getElem_idxOf_eq_idxOfNth_add._proof_1_51 | Batteries.Data.List.Lemmas | [
"List.idxsOf",
"List.countP",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"Lean.Grind.nestedProof",
"Lean.Grind.iff_eq",
"Lean.Grind.CommRing.Expr.var",
"congrArg",
"Lean.Grind.Order.le_of_eq_2_k",
"Std.IsLinearPreorder.toIsPreorder",
"HEq.trans",
... | false |
Plausible.RandT.up | Plausible.Random | [
"Pure.pure",
"StateT.run",
"Plausible.RandGT",
"RandomGen",
"StateT.instMonadLift",
"Monad.toApplicative",
"ULift",
"instMonadLiftT",
"MonadState.get",
"_private.Plausible.Random.0.Plausible.RandT.up.match_1",
"liftM",
"Applicative.toPure",
"instMonadStateOfStateTOfMonad",
"PUnit",
"inst... | true |
Lean.Elab.Command.ElabHeaderResult.ctorIdx | Lean.Elab.MutualInductive | [
"Nat",
"Lean.Elab.Command.ElabHeaderResult"
] | false |
Finset.addCommMonoid._proof_3 | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"instHSMul",
"Finset",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddCommMonoid",
"AddZero.toZero",
"Finset.coe_nsmul",
"SetLike.coe",
"Finset.instSetLike",
"Nat",
"AddZero.toAdd",
"HSMul.hSMul",
"AddCommMonoid.toAddMonoid",
"Set.NSMul",
"Eq",
"Finset.nsmul",
"DecidableEq... | false |
Simps.findZeroArgs | Mathlib.Tactic.Simps.NotationClass | [
"Pure.pure",
"Inhabited.default",
"Lean.Meta.State",
"Option.getD",
"Option.some",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instOfNatNat",
"Applicative.toPure",
"Simps.findArgType",
"List.toArray",
"List.cons",
"Array",
"Lean.instInhabitedExpr",
"Lean.Core.CoreM",
"StateRefT'... | true |
_private.Mathlib.Data.Seq.Computation.0.Computation.Corec.f.match_1.eq_2 | Mathlib.Data.Seq.Computation | [
"Sum",
"Computation.Corec.f.match_1",
"Sum.inl",
"Sum.inr",
"Eq.refl",
"Eq"
] | true |
String.Pos.le_ofSliceFrom_iff | Init.Data.String.Lemmas.Order | [
"Iff.mpr",
"not_exists._simp_1",
"String.Slice.Pos.instTotalLe",
"String.Pos.sliceFrom",
"String.instLEPos_1",
"String.sliceFrom",
"Iff.of_eq",
"congrArg",
"String",
"String.Slice.Pos.instLawfulOrderLT",
"Exists",
"String.Pos.instLawfulOrderLT",
"LE.le",
"_private.Init.Data.String.Lemmas.O... | true |
Lean.Meta.RefinedDiscrTree.noConfusion | Mathlib.Lean.Meta.RefinedDiscrTree.Basic | [
"Lean.Meta.RefinedDiscrTree.instHashableKey",
"Lean.Meta.RefinedDiscrTree",
"HEq.refl",
"Std.HashMap",
"Lean.Meta.RefinedDiscrTree.casesOn",
"Lean.Meta.RefinedDiscrTree.Key",
"Lean.Meta.RefinedDiscrTree.TrieIndex",
"Array",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Lean.Meta.RefinedDiscrTr... | false |
List.erase._sunfold | Init.Data.List.Basic | [
"List.filter.match_1",
"List.cons",
"List",
"BEq.beq",
"Unit",
"List.erase",
"Bool",
"List.getLastD.match_1",
"BEq",
"List.nil"
] | false |
AddMonoidHom.toOpposite._proof_2 | Mathlib.Algebra.Group.Equiv.Opposite | [
"AddMonoidHom.map_zero",
"congrArg",
"AddZeroClass.toAddZero",
"AddOpposite",
"AddZero.toZero",
"AddZeroClass",
"Zero.toOfNat0",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"AddOpposite.op"
] | false |
Multiset.filterMap_eq_map | Mathlib.Data.Multiset.Filter | [
"Multiset.filterMap",
"Multiset.map",
"List.map",
"Option.some",
"Function.comp",
"Quot.inductionOn",
"Multiset",
"List.filterMap_eq_map",
"congr_arg",
"funext",
"List",
"Multiset.ofList",
"congr_fun",
"List.filterMap",
"List.isSetoid",
"Eq",
"Setoid.r",
"Option"
] | true |
BitVec.le_def | Init.Data.BitVec.Lemmas | [
"Iff.rfl",
"BitVec",
"BitVec.toNat",
"LE.le",
"instLENat",
"Iff",
"Nat",
"instLEBitVec"
] | true |
Std.TreeSet.empty_equiv_iff_isEmpty | Std.Data.TreeSet.Lemmas | [
"Std.TreeSet",
"Std.TreeSet.empty",
"Std.TreeSet.isEmpty",
"Ordering",
"Bool.true",
"Iff",
"Std.TreeSet.equiv_empty_iff_isEmpty",
"Iff.trans",
"Bool",
"Std.TreeSet.Equiv",
"Std.TreeSet.Equiv.comm",
"Eq"
] | true |
PolyEquivTensor.toFunLinear_mul_tmul_mul_aux_1 | Mathlib.RingTheory.PolynomialAlgebra | [
"Eq.mpr",
"RingHom.instRingHomClass",
"HMul.hMul",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"Decidable",
"Algebra",
"Classical.propDecidable",
"RingHom",
"map_zero",
"not_not_intro",
"id",
"RingHomClass.toMonoidWithZeroHomClass",
"NonAssocSemiring.toMulZeroOneClass",
... | true |
_private.Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind.0.NumberField.Ideal.primesOverSpanEquivMonicFactorsModAux._proof_7 | Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind | [
"Polynomial.instNormalizationMonoid",
"UniqueFactorizationMonoid.normalizedFactors",
"Multiset.toFinset",
"instIsPrincipalIdealRingOfIsSemisimpleRing",
"MulEquiv.instEquivLike",
"IsDomain.to_noZeroDivisors",
"Nat.Prime",
"Semiring.toModule",
"ZMod.commRing",
"congrArg",
"CommSemiring.toSemiring"... | false |
Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly | Mathlib.FieldTheory.IsAlgClosed.Basic | [
"Algebra.algebraMap",
"AlgHom",
"AlgHom.funLike",
"Polynomial.rootSet",
"Algebra",
"Field.toDivisionRing",
"DivisionRing.toRing",
"Algebra.IsAlgebraic",
"Field.toSemifield",
"Field.toCommRing",
"minpoly",
"instIsDomain",
"Semifield.toDivisionSemiring",
"IsAlgClosed",
"DivisionSemiring.to... | true |
MvPolynomial.lcoeff | Mathlib.Algebra.MvPolynomial.Basic | [
"Nat.instMulZeroClass",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"LinearMap",
"MvPolynomial.coeff",
"MvPolynomial.lcoeff._proof_1",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"M... | true |
CategoryTheory.ShortComplex.nullHomotopic | Mathlib.Algebra.Homology.ShortComplex.Preadditive | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTheory.ShortComplex.Hom.mk",
"CategoryTheory.Pr... | true |
_private.Init.Data.Vector.Lemmas.0.Vector.any_eq_false'._simp_1_1 | Init.Data.Vector.Lemmas | [
"Array.any_eq_false'",
"Array.instMembership",
"Membership.mem",
"Array.any",
"instOfNatNat",
"Array",
"Bool.true",
"Nat",
"propext",
"Bool",
"OfNat.ofNat",
"Bool.false",
"Eq",
"Array.size",
"Not"
] | false |
Nat.Coprime.symm | Init.Data.Nat.Coprime | [
"Nat.gcd",
"Nat.Coprime",
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"Nat.gcd_comm",
"Eq.trans"
] | true |
IncidenceAlgebra.instAddCommGroup._proof_4 | Mathlib.Combinatorics.Enumerative.IncidenceAlgebra | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Pi.instNeg",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"IncidenceAlgebra.coe_neg",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"LE",
"IncidenceAlgebra.instFunLike",
"IncidenceAlgebra.instNeg",
"NegZeroClass.... | false |
Nat.add_one_ne_zero | Init.Data.Nat.Basic | [
"False",
"_private.Init.Data.Nat.Basic.0.Nat.add_one_ne_zero.match_1_1",
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_51 | Mathlib.Data.List.Basic | [
"Nat.succ_lt_succ_iff",
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"GetElem",
"List.take_succ_cons",
"Lean.Grind.CommRing.Mon.mult",
"List.eraseIdx",
"_private.Mathlib.Data.List.Basic.0.List.erase_getElem._proof_1_20",
"Lean.Grind.Comm... | false |
VonNeumannAlgebra.mk.injEq | Mathlib.Analysis.VonNeumannAlgebra.Basic | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"CompleteSpace",
"instSMulOfMul",
"NormedSpace.toIsBoundedSMul",
"ContinuousLinearMap.semiring",
"UniformContinuousConstSMul.to_continuousConstSMul",
"StarSubalgebra.toSubalgebra",
"Complex.commRing",
"Eq.propIntro",
"Comm... | true |
instDecidableEqPosNum.decEq._proof_3 | Mathlib.Data.Num.Basic | [
"False",
"PosNum.ctorIdx",
"False.elim",
"PosNum.bit1",
"noConfusion_of_Nat",
"PosNum",
"Eq",
"Not",
"PosNum.one"
] | false |
AddSubsemigroup.map_iInf_comap_of_surjective | Mathlib.Algebra.Group.Subsemigroup.Operations | [
"iInf",
"AddSubsemigroup.giMapComap",
"AddHom",
"AddSubsemigroup.comap",
"AddSubsemigroup.instInfSet",
"GaloisInsertion.l_iInf_u",
"AddHom.funLike",
"AddSubsemigroup",
"AddSubsemigroup.instCompleteLattice",
"Eq",
"DFunLike.coe",
"Function.Surjective",
"Add",
"AddSubsemigroup.map"
] | true |
Nat.Linear.Expr.noConfusionType | Init.Data.Nat.Linear | [
"Nat.Linear.Expr.num.elim",
"Nat.Linear.Expr.mulL.elim",
"Nat.Linear.Expr.casesOn",
"Nat.Linear.Expr",
"dite",
"Nat.Linear.Var",
"Nat",
"Nat.decEq",
"Nat.Linear.Expr.add.elim",
"Nat.Linear.Expr.ctorIdx",
"Nat.Linear.Expr.mulR.elim",
"Eq",
"Not",
"Nat.Linear.Expr.var.elim"
] | false |
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