name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ModularGroup.exists_eq_T_zpow_of_c_eq_zero | Mathlib.NumberTheory.Modular | [
"Int.instAddCommGroup",
"Eq.mpr",
"NegZeroClass.toNeg",
"instNeZeroNatHAdd_1",
"Real",
"Fintype.card_fin_two",
"instHSMul",
"Matrix.SpecialLinearGroup",
"Fintype.elems",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"UpperHalfPlane.SLAction",
"Equiv.instEquivLike",
"Matrix.SpecialLinearGr... | true |
Function.Embedding.codRestrict_apply | Mathlib.Logic.Embedding.Set | [
"Function.Embedding.codRestrict",
"Membership.mem",
"Set.Elem",
"Function.Embedding",
"Subtype.mk",
"Function.instFunLikeEmbedding",
"Eq",
"Set.instMembership",
"DFunLike.coe",
"rfl",
"Set"
] | true |
AddSubmonoid.neg_le | Mathlib.Algebra.Group.Submonoid.Pointwise | [
"AddGroup.toSubtractionMonoid",
"SubtractionMonoid.toInvolutiveNeg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"AddSubmonoid",
"HasSubset.Subset",
"LE.le",
"SetLike.coe_subset_coe",
"Set.neg_subset",
"AddGroup",
"Iff",
"AddGroup.toSubNegMonoi... | true |
Std.Http.Status.proxyAuthenticationRequired | Std.Internal.Http.Data.Status | [
"Std.Http.Status",
"Std.Http.Status.proxyAuthenticationRequired"
] | true |
MvPowerSeries.trunc_one | Mathlib.RingTheory.MvPowerSeries.Trunc | [
"MvPowerSeries.truncFinset_one",
"Eq.mpr",
"Nat.instMulZeroClass",
"Finsupp.partialorder",
"Preorder.toLT",
"Semiring.toModule",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"Finset",
"Finsupp.instIsBotZeroClass",
"LinearMa... | true |
Std.Tactic.BVDecide.LRAT.Internal.lratChecker.match_3.congr_eq_2 | Std.Tactic.BVDecide.LRAT.Internal.LRATCheckerSound | [
"Unit.unit",
"Std.Tactic.BVDecide.LRAT.Action.addEmpty",
"Std.Tactic.BVDecide.LRAT.Action.casesOn",
"Std.Tactic.BVDecide.LRAT.Action",
"Std.Tactic.BVDecide.LRAT.Action.del",
"id",
"Std.Tactic.BVDecide.LRAT.Action.addRat",
"List.cons",
"Std.Tactic.BVDecide.LRAT.Internal.lratChecker.match_3",
"Array... | true |
Lean.Options.get? | Lean.Data.Options | [
"Lean.NameMap.find?",
"Option.bind",
"Lean.KVMap.Value.ofDataValue?",
"_private.Lean.Data.Options.0.Lean.Options.map",
"Lean.Name",
"Lean.KVMap.Value",
"Lean.DataValue",
"Lean.Options",
"Option"
] | true |
List.Lex.decidableRel._proof_3 | Mathlib.Data.List.Lex | [
"False",
"List.Lex.casesOn",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"List.Lex.nil",
"List.Lex.rel",
"List.cons",
"List",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"List.ctorIdx",
"List.Lex",
"List.Lex.cons",
"List.nil"
] | false |
KaehlerDifferential.mvPolynomialBasis_repr_D | Mathlib.RingTheory.Kaehler.Polynomial | [
"Derivation",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Finsupp.module",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"instAddCommGroupKaehlerDifferential",
"AddM... | true |
FreeAddGroup.reduceCyclically.eq_1 | Mathlib.GroupTheory.FreeGroup.CyclicallyReduced | [
"Bool.not",
"instDecidableEqBool",
"Prod.fst",
"List.cons",
"instHAppendOfAppend",
"List",
"And",
"List.bidirectionalRec",
"Bool",
"Eq.refl",
"instDecidableAnd",
"List.instAppend",
"Prod",
"FreeAddGroup.reduceCyclically",
"Eq",
"Prod.snd",
"HAppend.hAppend",
"List.nil",
"Decidabl... | true |
_private.Mathlib.Algebra.Module.Submodule.Pointwise.0.Submodule.smul_inductionOn_pointwise._simp_1_1 | Mathlib.Algebra.Module.Submodule.Pointwise | [
"Monoid",
"Submodule.pointwiseDistribMulAction",
"Submodule",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Set.instSingletonSet",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"AddZero.toZero",
"Submodule.singleton_set_smul",
"Submod... | false |
_private.Mathlib.Condensed.Light.Sequence.0.LightCondensed.internallyProjective_free_natUnionInfty._proof_1_10 | Mathlib.Condensed.Light.Sequence | [
"instTopologicalSpaceNat",
"LightProfinite.instMetrizableSpaceOnePointNat",
"Nat",
"T2Space",
"TopologicalSpace.t2Space_of_metrizableSpace",
"OnePoint.instTopologicalSpace",
"OnePoint"
] | false |
_private.Mathlib.Analysis.Normed.Field.Basic.0.NormedField.denselyOrdered_range_norm.match_1 | Mathlib.Analysis.Normed.Field.Basic | [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Real.instLT",
"Membership.mem",
"Exists",
"NormedField.toNorm",
"Subtype.mk",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"And",
"DenselyNormedField",
"Exists.casesOn",
"NonUnitalSeminormedCommRing... | false |
ConvexCone.coe_add._simp_1 | Mathlib.Geometry.Convex.Cone.Basic | [
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"ConvexCone.instSetLike",
"AddZeroClass.toAddZero",
"PartialOrder",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"AddZero.toZero",
"instHAdd",
"Set.add",
"SetLike.coe",
"HAdd.hAdd",
"ConvexCone.coe_add",
"ConvexCone",
"Semi... | false |
LinearMap.BilinMap.toQuadraticMap._proof_3 | Mathlib.LinearAlgebra.QuadraticForm.Basic | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LinearMap.BilinMap",
"LinearMap.BilinMap.toQuadraticMap._proof_2",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Exists",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.instAdd",
"SMulCommClass.symm",
"L... | false |
Matrix.PosSemidef.ofNat | Mathlib.LinearAlgebra.Matrix.PosDef | [
"Matrix.PosSemidef.natCast",
"Ring.toNonAssocRing",
"Matrix",
"AddGroupWithOne.toAddMonoidWithOne",
"PartialOrder",
"Matrix.instNatCastOfZero",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"AddMonoidWithOne.toNatCast",
"NonAssocRing.toNonUnitalNonAssocRing",
"Matrix.PosSemidef",
"StarOrd... | true |
List.takeI_left' | Mathlib.Data.List.TakeDrop | [
"Eq.mpr",
"congrArg",
"id",
"List.takeI",
"instHAppendOfAppend",
"List",
"Nat",
"Inhabited",
"List.takeI_left",
"List.instAppend",
"Eq.symm",
"Eq",
"List.length",
"HAppend.hAppend"
] | true |
OrderHom.nextFixed._proof_1 | Mathlib.Order.FixedPoints | [
"OrderHom.prevFixed",
"Equiv.instEquivLike",
"ChainCompletePartialOrder.instOfCompleteLattice",
"PartialOrder.toPreorder",
"Function.fixedPoints",
"Preorder.toLE",
"Membership.mem",
"Equiv",
"LE.le",
"ChainCompletePartialOrder.toPartialOrder",
"OrderHom.instFunLike",
"OrderDual.instCompleteLat... | false |
Std.DHashMap.getKey_eq_getKeyD | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.Raw",
"Membership.mem",
"Std.DHashMap.instMembership",
"Std.DHashMap.wf",
"Std.DHashMap.Internal.Raw₀.getKey_eq_getKeyD",
"instOfNatNat",
"Std.DHashMap.getKeyD",
"LawfulHashable",
"Subtype.mk",
"EquivBEq",
"Std.DHashMap.inner",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"S... | true |
Lean.Meta.Grind.Var | Lean.Meta.Tactic.Grind.VarRename | [
"Nat"
] | true |
ConcaveOn.continuousOn_interior | Mathlib.Analysis.Convex.Continuous | [
"Real.partialOrder",
"Real",
"instSMulOfMul",
"NormedSpace",
"ConcaveOn.locallyLipschitzOn_interior",
"NormedAddCommGroup.toMetricSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"A... | true |
WeierstrassCurve.IsGoodReduction | Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | [
"IsDomain",
"CommRing",
"CommSemiring.toSemiring",
"IsFractionRing",
"IsDiscreteValuationRing",
"Algebra",
"WeierstrassCurve",
"Field.toSemifield",
"CommRing.toCommSemiring",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemiring",
"WeierstrassCurve.HasGoodR... | true |
ENNReal.zpow_add | Mathlib.Data.ENNReal.Inv | [
"GroupWithZero.toMonoidWithZero",
"ENNReal.canLift",
"ENNReal.ofNNReal",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"MulZeroClass.toMul",
"NNReal.zpow",
"congrArg",
"CommSemiring.toSemiring",
"ENNReal.coe_zpow",
"DivInvMonoid.toZPow",
"DivisionSemiring.toGroupWithZero",
"Exists",
"Eq.mp"... | true |
CondensedMod.epi_iff_locallySurjective_on_compHaus | Mathlib.Condensed.Epi | [
"ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier",
"ModuleCat.forget_preservesLimits",
"CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions",
"CategoryTheory.GrothendieckTopology.instPreservesSheafificationForgetOfPreservesLimitsOfHasColimitsOfShapeOfPreservesColimitsOfShapeOpposit... | true |
_private.Init.Data.Iterators.Lemmas.Consumers.Access.0.Std.Iter.atIdxSlow?_eq_match.match_3.splitter | Init.Data.Iterators.Lemmas.Consumers.Access | [
"Std.IterStep",
"Std.Iter.atIdxSlow?_eq_match.match_3",
"Std.IterStep.skip",
"Unit",
"Std.Iter",
"Std.IterStep.yield",
"Std.IterStep.done"
] | true |
OreLocalization.instDivisionRingNonZeroDivisors | Mathlib.RingTheory.OreLocalization.Ring | [
"Nontrivial",
"Semiring.toNatCast",
"Rat.castRec",
"NNRat.castRec",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"OreLocalization.OreSet",
"OreLocalization",
"Rat",
"OreLocalization.instDivisionRingNonZeroDivisors._proof_10",
"nonZeroDivisors",
"Ore... | true |
MoritaEquivalence.ofAlgEquiv._proof_1 | Mathlib.RingTheory.Morita.Basic | [
"AlgEquiv.symm",
"ModuleCat",
"CommSemiring.toSemiring",
"CategoryTheory.Functor.Linear",
"Algebra",
"ModuleCat.restrictScalarsEquivalenceOfRingEquiv",
"CategoryTheory.Equivalence.functor",
"ModuleCat.Algebra.instLinear",
"CommSemiring",
"AlgEquiv",
"ModuleCat.moduleCategory",
"AlgEquiv.toRing... | false |
_private.Mathlib.Analysis.RCLike.Sqrt.0.RCLike.sqrt_neg_I._proof_1_3 | Mathlib.Analysis.RCLike.Sqrt | [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"NormedCommRing.toNormedRing",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"RingHom.instRingHomClass",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Real.partialOrder",
"Real",
"Lean.Grind.CommRing.Mon.mult",
... | false |
_private.Mathlib.Tactic.LinearCombinationPrime.0.Mathlib.Tactic.LinearCombinationPrime.expandLinearCombo.match_3 | Mathlib.Tactic.LinearCombinationPrime | [
"Mathlib.Tactic.LinearCombinationPrime.Expanded.const",
"Mathlib.Tactic.LinearCombinationPrime.Expanded",
"Lean.Syntax.Term",
"Mathlib.Tactic.LinearCombinationPrime.Expanded.proof",
"Mathlib.Tactic.LinearCombinationPrime.Expanded.casesOn"
] | false |
FunctionField.inftyValuation.X_zpow | Mathlib.NumberTheory.FunctionField | [
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"Int.instIsStrictOrderedRing",
"RatFunc.X",
"Int.instLinearOrder",
"PartialOrder.toPreorder",
"DivInvMonoid.toZPow",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DivisionRing.toDivInvMonoid",
"DistribLattice.toLattice",
"Multi... | true |
LinearMap.iterateFrobenius | Mathlib.Algebra.CharP.Frobenius | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"LinearMap.iterateFrobenius._proof_3",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"ExpChar",
"Algebra.toModule",
"NonAssocSemiring.toMulZeroOneClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"LinearMap",
"MulZeroOneClass.toMul... | true |
inner_gradientWithin_right | Mathlib.Analysis.Calculus.Gradient.Basic | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"CompleteSpace",
"Semiring.toModule",
"NormedRing.toRing",
"Inner.inner",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"... | true |
Field.Emb.Cardinal.embEquivPi._proof_6 | Mathlib.FieldTheory.CardinalEmb | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Algebra",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Field.toSemifield",
"WithTop.some",
"Field.toCommRing",
"Cardinal.ord",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"WithTop.coe_... | false |
RingCon.quotientKerEquivRangeₐ_comp_mkₐ | Mathlib.RingTheory.Congruence.Hom | [
"Subalgebra.instSetLike",
"AlgHom.algHomClass",
"AlgEquiv.toAlgHom",
"AlgHom",
"RingCon.quotientKerEquivRangeₐ",
"AlgHom.funLike",
"AlgHom.rangeRestrict",
"Algebra",
"Membership.mem",
"RingCon.ker",
"Subtype",
"Distrib.toAdd",
"RingCon.instSemiringQuotient",
"RingCon.Quotient",
"RingCon.... | true |
NonUnitalStarRingHom.mk.sizeOf_spec | Mathlib.Algebra.Star.StarRingHom | [
"NonUnitalStarRingHom._sizeOf_inst",
"NonUnitalStarRingHom.mk",
"NonUnitalStarRingHom",
"NonUnitalRingHom._sizeOf_inst",
"instOfNatNat",
"instHAdd",
"MulHom.toFun",
"Distrib.toMul",
"HAdd.hAdd",
"Star",
"Nat",
"NonUnitalRingHom.toMulHom",
"SizeOf.sizeOf",
"NonUnitalNonAssocSemiring.toDistr... | true |
CompHausLike.instPreservesLimitWalkingCospanCospanToCompHausLike | Mathlib.Topology.Category.CompHausLike.Limits | [
"CategoryTheory.Limits.fullyFaithful_reflectsLimits",
"CompHausLike.toCompHausLike",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.finCategoryWidePullback",
"TopCat.instCategory",
"CompHausLike.instFullTopCatCompHausLikeToTop",
... | true |
CategoryTheory.Limits.ChosenPullback.p₁ | Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.ChosenPullback.pullback",
"CategoryTheory.Limits.ChosenPullback",
"CategoryTheory.Category"
] | true |
groupHomology.indIso._proof_3 | Mathlib.RepresentationTheory.Homological.GroupHomology.Shapiro | [
"CommRing",
"CommSemiring.toSemiring",
"Group",
"Rep.instCategory",
"Membership.mem",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"CommRing.toCommSemiring",
"Rep",
"CategoryTheory.Limits.HasZeroObject",
"Subgroup.toGroup",
"SetLike.instMembership",
"Subgroup.i... | false |
PolishSpace.measurableEquivNatBoolOfNotCountable._proof_2 | Mathlib.MeasureTheory.Constructions.Polish.Basic | [
"PolishSpace.measurableEquivNatBoolOfNotCountable._proof_1",
"isClosed_univ",
"StandardBorelSpace",
"MeasurableSpace.countablySeparated_of_separatesPoints",
"Continuous",
"Pi.topologicalSpace",
"TopologicalSpace.IsCompletelyMetrizableSpace.MetrizableSpace",
"Set.univ",
"upgradeStandardBorel",
"Mea... | false |
CategoryTheory.ShortComplex.fFunctor_map | Mathlib.Algebra.Homology.ShortComplex.Basic | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ShortComplex.Hom.comm₁₂",
"Quiver.Hom",
"CategoryTheory.ShortComplex.Hom.τ₁",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheo... | true |
differentialIdeal_le_fractionalIdeal_iff | Mathlib.RingTheory.DedekindDomain.Different | [
"Eq.mpr",
"FractionalIdeal.dual",
"Submodule",
"IsIntegralClosure",
"IsDomain",
"IsDedekindDomain.toIsDomain",
"RingHomSurjective.ids",
"False",
"CommRing",
"LinearMap.restrictScalars",
"FractionalIdeal.instNontrivialNonZeroDivisors",
"IsDomain.to_noZeroDivisors",
"NonUnitalCommRing.toNonUni... | true |
MeasureTheory.weightedSMul._proof_1 | Mathlib.MeasureTheory.Integral.Bochner.L1 | [
"Real",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Real.semiring",
"smulCommClass_self",
"CommMonoid.toMonoid",
"Monoid.toSemigroup",
"NormedAddCommGroup.toAddCommGroup",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMonoid.toAddMonoid",
"Real.no... | false |
_private.Mathlib.CategoryTheory.Bicategory.Modification.Oplax.0.CategoryTheory.Oplax.LaxTrans.Modification.ext.match_1 | Mathlib.CategoryTheory.Bicategory.Modification.Oplax | [
"CategoryTheory.Oplax.LaxTrans.Modification",
"CategoryTheory.Oplax.LaxTrans.instCategoryStructOplaxFunctor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Bicategory.toCategoryStruct",
"... | false |
Filter.map_mapsTo_Iic_iff_mapsTo | Mathlib.Order.Filter.Tendsto | [
"Eq.mpr",
"congrArg",
"Filter.map",
"Iff.rfl",
"PartialOrder.toPreorder",
"Membership.mem",
"Filter.map_mapsTo_Iic_iff_tendsto",
"id",
"Iff",
"Set.MapsTo.eq_1",
"Filter.Tendsto",
"Set.MapsTo",
"propext",
"Filter.principal",
"Set.Iic",
"Eq",
"Set.instMembership",
"Filter",
"Filter... | true |
CategoryTheory.WithTerminal.opEquiv_counitIso_hom_app | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.WithInitial.of",
"CategoryTheory.CategoryStruct.opposite",
"CategoryTheory.WithTerminal.id.match_1",
"Quiver.Hom.op",
"CategoryTheory.WithTerminal.... | true |
Int.ediv_mul | Init.Data.Int.DivMod.Lemmas | [
"Int.decidableDvd",
"instDecidableNot",
"Int.instDiv",
"Dvd.dvd",
"instHDiv",
"HMul.hMul",
"HSub.hSub",
"Int.instDecidableEq",
"_private.Init.Data.Int.DivMod.Lemmas.0.Int.ediv_mul._proof_1_1",
"Int.sign",
"HDiv.hDiv",
"Int",
"Int.instDvd",
"Int.instMul",
"Int.instLTInt",
"instHAdd",
... | true |
_private.Mathlib.Algebra.Ring.Int.Parity.0.Int.natAbs_even._proof_1_1 | Mathlib.Algebra.Ring.Int.Parity | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"of_eq_false",
"Lean.RArray.leaf",
"Int.instDiv",
"False",
"Int.Nonneg.toPoly",
"Lean.Grind.CommRing.Mon.mult",
"Int.Linear.le_coeff",
"instHDiv",
"Lean.Grind.not_not",
... | false |
_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.match_16 | Std.Sat.AIG.CNF | [
"Std.Sat.AIG.Decl",
"Subtype.casesOn",
"Subtype",
"instHashableNat",
"Subtype.mk",
"Std.Sat.AIG",
"Nat",
"LT.lt",
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.State.IsExtensionBy",
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.State",
"instDecidableEqNat",
"instLTNat",
"Array.size",
"Std.... | false |
_private.Mathlib.RingTheory.Etale.QuasiFinite.0.Localization.exists_finite_awayMapₐ_of_surjective_awayMapₐ._simp_1_11 | Mathlib.RingTheory.Etale.QuasiFinite | [
"Monoid",
"HMul.hMul",
"instMulNat",
"pow_mul",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"instHPow",
"Eq.symm",
"Eq",
"instHMul"
] | false |
TwoSidedIdeal.instNegSubtypeMem._proof_1 | Mathlib.RingTheory.TwoSidedIdeal.Basic | [
"NonUnitalNonAssocRing",
"NegZeroClass.toNeg",
"TwoSidedIdeal",
"TwoSidedIdeal.neg_mem",
"NonUnitalNonAssocRing.toAddCommGroup",
"Membership.mem",
"Subtype",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"TwoSidedIdeal.set... | false |
Lean.Lsp.InitializeResult.noConfusion | Lean.Data.Lsp.InitShutdown | [
"Lean.Lsp.ServerInfo",
"Lean.Lsp.InitializeResult",
"Lean.Lsp.ServerCapabilities",
"Lean.Lsp.InitializeResult.noConfusionType",
"Eq.ndrec",
"Eq.refl",
"Lean.Lsp.InitializeResult.casesOn",
"Eq",
"Option"
] | false |
FreeLieAlgebra.instZero | Mathlib.Algebra.Lie.Free | [
"CommRing",
"FreeNonUnitalNonAssocAlgebra",
"CommSemiring.toSemiring",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"CommRing.toCommSemiring",
"FreeLieAlgebra",
"Zero.mk",
"Zero.toOfNat0",
"MonoidAlgebra.nonUnitalNonAssocSemiring",
"FreeMagma.instMul",
"FreeLieAlgebra.Rel",
"OfNat.ofNat",
"Mu... | true |
totallyBounded_interUnionBalls | Mathlib.Topology.UniformSpace.Cauchy | [
"UniformSpace",
"Set.iUnion_iUnion_eq_right",
"Eq.mpr",
"TotallyBounded",
"Preorder.toLT",
"SetRel",
"Finset.coe_range",
"Iff.of_eq",
"congrArg",
"interUnionBalls",
"Set.iInter",
"Finset",
"uniformity",
"setOf",
"Classical.propDecidable",
"Set.Finite",
"Membership.mem",
"Exists",
... | true |
CategoryTheory.Limits.coker._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"congrArg",
"CategoryTheory.Limits.comp_zero",
"CategoryTheory.Limits.cokernel",
"CategoryTheory.Limits.cokernel.condition",
"CategoryTheory.Arrow.left",
"CategoryThe... | false |
Bool.bne_self_right | Init.Data.Bool | [
"bne",
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"instBEqOfDecidableEq",
"Bool.true",
"Bool",
"Eq.refl",
"Decidable.decide",
"Eq"
] | true |
CategoryTheory.Functor.ranCompLimIso_hom_app | Mathlib.CategoryTheory.Functor.KanExtension.Adjunction | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.ranCompLimIso",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Limits.lim",
"CategoryT... | true |
CategoryTheory.ShortComplex.RightHomologyData.canonical | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"CategoryTheory.ShortComplex.opcycles",
"CategoryTheory.ShortComplex.RightHomologyData.mk",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.RightHomologyData",
"CategoryTheory.ShortComplex.homologyIsKernel",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",... | true |
String.toByteArray | Init.Prelude | [
"String",
"ByteArray"
] | true |
VectorBundle.finrank_eq | Mathlib.Topology.VectorBundle.FiniteDimensional | [
"VectorBundle.continuousLinearEquivAt",
"NormedSpace",
"FiberBundle",
"ContinuousLinearEquiv.toLinearEquiv",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"AddCommGroup",
"LinearEquiv.finrank_eq",
"Field.toSemifield",
"Topolo... | true |
stableUnderSpecialization_iUnion | Mathlib.Topology.Inseparable | [
"StableUnderSpecialization",
"isLowerSet_iUnion",
"Preorder.toLE",
"specializationPreorder",
"TopologicalSpace",
"Set.iUnion",
"Set"
] | true |
Lean.Elab.Tactic.RCases.RCasesPatt.clear.noConfusion | Lean.Elab.Tactic.RCases | [
"Lean.Elab.Tactic.RCases.RCasesPatt",
"Lean.Elab.Tactic.RCases.RCasesPatt.clear",
"Lean.Elab.Tactic.RCases.RCasesPatt.noConfusion",
"Lean.Syntax",
"id",
"Eq"
] | false |
Equiv.funSplitAt | Mathlib.Logic.Equiv.Prod | [
"Equiv",
"Subtype",
"Ne",
"Equiv.piSplitAt",
"Prod",
"DecidableEq"
] | true |
Array.foldrM | Init.Data.Array.Basic | [
"Pure.pure",
"Array.forIn'._proof_2",
"Monad.toApplicative",
"Array.foldrM.fold",
"instOfNatNat",
"LE.le",
"instLENat",
"Applicative.toPure",
"dite",
"Array",
"Nat",
"LT.lt",
"Nat.decLt",
"instLTNat",
"optParam",
"OfNat.ofNat",
"Monad",
"Array.size",
"Not",
"Nat.decLe",
"ite"... | true |
_private.Mathlib.Algebra.Polynomial.Roots.0.Polynomial.eq_zero_of_natDegree_lt_card_of_eval_eq_zero._simp_1_1 | Mathlib.Algebra.Polynomial.Roots | [
"Finset.mem_image",
"Finset",
"Membership.mem",
"Exists",
"And",
"Finset.instSetLike",
"propext",
"Eq",
"Finset.image",
"SetLike.instMembership",
"DecidableEq"
] | false |
_private.Mathlib.Data.Set.Finite.Basic.0.Set.infinite_union._simp_1_2 | Mathlib.Data.Set.Finite.Basic | [
"And",
"not_and_or",
"propext",
"Or",
"Eq",
"Not"
] | false |
CategoryTheory.ShortComplex.leftHomologyπ_naturality'_assoc | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.leftHomologyMap'",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.c... | true |
MeasureTheory.AEEqFun.ext | Mathlib.MeasureTheory.Function.AEEqFun | [
"MeasureTheory.ae",
"Eq.mpr",
"MeasureTheory.Measure",
"congrArg",
"MeasureTheory.AEEqFun.cast",
"Filter.EventuallyEq",
"id",
"MeasureTheory.AEEqFun",
"MeasurableSpace",
"TopologicalSpace",
"MeasureTheory.AEEqFun.mk_coeFn",
"propext",
"MeasureTheory.AEEqFun.mk_eq_mk",
"MeasureTheory.AEEqFu... | true |
Subsemiring.copy_toSubmonoid | Mathlib.Algebra.Ring.Subsemiring.Defs | [
"Subsemiring.instSetLike",
"Subsemiring.copy._proof_1",
"Subsemigroup.mk",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"Subsemiring.toSubmonoid",
"Subsemiring",
"MulZeroOneClass.toMulOneClass",
"MulOneClass.toMulOne",
"NonAssocSemiring",
"SetLike.coe",
"Eq.refl",
"Submonoid.mk",
... | true |
Std.Http.URI.Host.rec | Std.Internal.Http.Data.URI.Basic | [
"Std.Http.URI.Host.ipv4",
"Std.Net.IPv6Addr",
"Std.Net.IPv4Addr",
"Std.Http.URI.Host",
"Std.Http.URI.DomainName",
"Std.Http.URI.Host.ipv6",
"Std.Http.URI.Host.name"
] | false |
Nat.boddDiv2.match_1 | Mathlib.Data.Nat.Bits | [
"Prod.mk",
"Bool.true",
"Bool.casesOn",
"Nat",
"Bool",
"Prod",
"Prod.casesOn",
"Bool.false"
] | false |
Commute.conj_iff._simp_2 | Mathlib.Algebra.Group.Commute.Basic | [
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Commute",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"propext",
"Commute.conj_iff",
"InvO... | false |
CategoryTheory.ObjectProperty.instSmallOppositeOp_1 | Mathlib.CategoryTheory.ObjectProperty.Small | [
"Eq.mpr",
"Opposite",
"CategoryTheory.ObjectProperty.Small",
"CategoryTheory.ObjectProperty.small_op_iff._simp_1",
"id",
"CategoryTheory.Category.opposite",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty.op",
"Eq",
"CategoryTheory.ObjectProperty",
"CategoryTheory.Cate... | true |
ContinuousMap.instSeminormedCommRing._proof_1 | Mathlib.Topology.ContinuousMap.Compact | [
"SeminormedCommRing",
"PseudoMetricSpace.toUniformSpace",
"NonUnitalRing.toNonUnitalNonAssocRing",
"NonUnitalSeminormedRing.toIsTopologicalRing",
"IsTopologicalRing",
"NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing",
"NonUnitalSeminormedRing.toPseudoMetricSpace",
"SeminormedCommRing.toNonUnital... | false |
CategoryTheory.sum.associativity._proof_1 | Mathlib.CategoryTheory.Sums.Associator | [
"CategoryTheory.sum.associativity._proof_8",
"CategoryTheory.Functor",
"CategoryTheory.sum",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.sum.associativity._proof_5",
"CategoryTheory.sum.inrCompInrCompInverseAssociator",
"CategoryTheory.Functor.category",
"CategoryTheory.s... | false |
Lean.Compiler.LCNF.Check.Pure.Context.mk._flat_ctor | Lean.Compiler.LCNF.Check | [
"Lean.Compiler.LCNF.Check.Pure.Context.mk",
"Lean.Compiler.LCNF.Check.Pure.Context",
"Lean.FVarIdSet"
] | false |
Module.AEval.instAddCommGroup._proof_11 | Mathlib.Algebra.Polynomial.Module.AEval | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Module.AEval",
"Algebra",
"AddCommGroup.toAddGroup",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"instOfNa... | false |
Nat.Linear.Poly.denote_eq | Init.Data.Nat.Linear | [
"Nat.Linear.Poly.denote",
"Nat.Linear.Poly",
"Prod.fst",
"Nat",
"Nat.Linear.Context",
"Prod",
"Eq",
"Prod.snd"
] | true |
_private.Mathlib.ModelTheory.Algebra.Field.CharP.0.FirstOrder.Field.charP_iff_model_fieldOfChar._simp_1_5 | Mathlib.ModelTheory.Algebra.Field.CharP | [
"FirstOrder.Language.Formula.realize_bot",
"False",
"instOfNatNat",
"Bot.bot",
"FirstOrder.Language.BoundedFormula.instBot",
"FirstOrder.Language.Structure",
"Nat",
"FirstOrder.Language.Formula",
"propext",
"FirstOrder.Language",
"OfNat.ofNat",
"Eq",
"FirstOrder.Language.Formula.Realize"
] | false |
Lean.Doc.MathMode.recOn | Lean.DocString.Types | [
"Lean.Doc.MathMode.rec",
"Lean.Doc.MathMode.inline",
"Lean.Doc.MathMode",
"Lean.Doc.MathMode.display"
] | false |
ContinuousNeg.continuous_neg | Mathlib.Topology.Algebra.Group.Defs | [
"Continuous",
"ContinuousNeg",
"TopologicalSpace",
"Neg",
"Neg.neg"
] | true |
CategoryTheory.ComposableArrows.mk₀ | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"CategoryTheory.Functor",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.ComposableArrows",
"Preorder.smallCategory",
"instOfNatNat",
"Fin.instPartialOrder",
"Nat",
"CategoryTheory.Functor.const",
"OfNat.ofNat",
"Fin",
"CategoryTheory.Functor.obj",
"CategoryThe... | true |
ProbabilityTheory.setBernoulli_real_singleton | Mathlib.Probability.Distributions.SetBernoulli | [
"Real",
"ENNReal.ofNNReal",
"MeasureTheory.Measure",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"Real.instSub",
"ProbabilityTheory.setBernoulli_singleton",
"ProbabilityTheory.setBernoulli",
"MeasureTheory.Measure.real",
"HSub.hSub",
"Set.Finite",
"Membership.mem",
"unitInterval.to... | true |
linearIndependent_le_basis | Mathlib.LinearAlgebra.Dimension.StrongRankCondition | [
"Fintype.card_congr",
"Eq.mpr",
"linearIndependent_le_span",
"PSum.casesOn",
"invariantBasisNumber_of_rankCondition",
"Cardinal",
"congrArg",
"PLift.fintype",
"PSum",
"Classical.propDecidable",
"Cardinal.mk",
"PSum.inr",
"Set.Elem",
"Fintype.card",
"id",
"nontrivial_of_invariantBasisNu... | true |
MeasureTheory.diracProbaHomeomorph | Mathlib.MeasureTheory.Measure.DiracProba | [
"Homeomorph.mk",
"MeasureTheory.continuous_diracProbaEquiv",
"MeasureTheory.diracProba",
"Membership.mem",
"Set.Elem",
"CompletelyRegularSpace",
"MeasureTheory.ProbabilityMeasure",
"MeasureTheory.diracProbaEquiv",
"MeasureTheory.ProbabilityMeasure.instTopologicalSpace",
"MeasurableSpace",
"Topol... | true |
_private.Mathlib.Topology.UniformSpace.UniformConvergence.0.tendstoUniformlyOn_iff_tendsto._simp_1_1 | Mathlib.Topology.UniformSpace.UniformConvergence | [
"UniformSpace",
"tendstoUniformlyOn_iff_tendstoUniformlyOnFilter",
"TendstoUniformlyOnFilter",
"TendstoUniformlyOn",
"propext",
"Filter.principal",
"Eq",
"Filter",
"Set"
] | false |
List.mapIdxMAux'.match_1 | Mathlib.Data.List.Defs | [
"List.cons",
"List",
"Nat",
"List.casesOn",
"List.nil"
] | false |
CocompactMap.mk | Mathlib.Topology.ContinuousMap.CocompactMap | [
"ContinuousMap",
"CocompactMap.mk",
"Filter.cocompact",
"TopologicalSpace",
"Filter.Tendsto",
"ContinuousMap.toFun",
"CocompactMap"
] | true |
Shrink.instNSMul.eq_1 | Mathlib.Algebra.Group.Shrink | [
"SMul",
"Shrink.instNSMul",
"Eq.refl",
"Shrink",
"Equiv.symm",
"equivShrink",
"Eq",
"Equiv.smul",
"Small"
] | true |
Set.smul_set_inter | Mathlib.Algebra.Group.Action.Pointwise.Set.Basic | [
"instHSMul",
"Group",
"Set.image_inter",
"DivInvMonoid.toMonoid",
"Set.instInter",
"Inter.inter",
"Group.toDivInvMonoid",
"MulAction",
"Monoid.toSemigroup",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Eq",
"Set.smulSet",
"MulAction.injective",
"Set"
] | true |
_private.Mathlib.AlgebraicGeometry.Morphisms.Separated.0.AlgebraicGeometry.Scheme.Pullback.diagonalCoverDiagonalRange_eq_top_of_injective._simp_1_5 | Mathlib.AlgebraicGeometry.Morphisms.Separated | [
"Sigma.exists",
"Exists",
"propext",
"Sigma.mk",
"Eq",
"Sigma"
] | false |
NonUnitalSubalgebra.ext | Mathlib.Algebra.Algebra.NonUnitalSubalgebra | [
"NonUnitalSubalgebra",
"CommSemiring.toSemiring",
"Membership.mem",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Iff",
"NonUnitalSubalgebra.instSetLike",
"SetLike.ext",
"Module",
"NonUnitalNonAssocSemiring",
"Eq",
"SetLike.instMembership"
] | true |
Module.Dual.extendRCLikeₗ._proof_3 | Mathlib.Analysis.RCLike.Extend | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"NormedCommRing.toNormedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"RingHom.instRingHomClass",
"IsSca... | false |
CategoryTheory.Limits.reflectsLimit_of_unop | Mathlib.CategoryTheory.Limits.Preserves.Opposites | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"Opposite",
"CategoryTheory.Limits.ReflectsLimit",
"CategoryTheory.Limits.isColimitCoconeLeftOpOfCone",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.unop",
"Nonempty.intro",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Limits.is... | true |
CategoryTheory.tensorRightHomEquiv_symm_coevaluation_comp_whiskerLeft | Mathlib.CategoryTheory.Monoidal.Rigid.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Equiv.instEquivLike",
"CategoryTheory.HasLeftDual.exact",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategory",... | true |
Matrix.charpoly_fromBlocks_zero₂₁ | Mathlib.LinearAlgebra.Matrix.Charpoly.Basic | [
"Polynomial.C",
"Matrix.fromBlocks",
"CommRing",
"instFintypeSum",
"Polynomial.instNeg",
"HMul.hMul",
"Matrix.map_zero",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"Polynomial.C_0",
"instDecidableEqSum",
"Matrix.addCommGroup",
"RingHom",
"Matrix.charmatrix",
"Sum",
"Matrix.char... | true |
List.foldl | Init.Prelude | [
"List.brecOn",
"List",
"List.foldl._f"
] | true |
CategoryTheory.PreZeroHypercover.HasPullbacks | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.PreZeroHypercover",
"CategoryTheory.Category"
] | true |
CommRingCat.Colimits.instCommRingColimitType._proof_25 | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"Mul.mk",
"HMul.hMul",
"Quot.sound",
"CommRingCat",
"Quot.map₂",
"CommRingCat.instCategory",
"CategoryTheory.SmallCategory",
"CommRingCat.Colimits.Relation.mul_1",
"CommRingCat.Colimits.ColimitType",
"CommRingCat.Colimits.Relation.mul_2",
"CommRingCat.Colimits.colimit... | false |
PresheafOfModules.symmetricCategory._proof_3 | Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal | [
"PresheafOfModules.map",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Opposite",
"CommRingCat.carrier",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PresheafOfModules.isoMk",
"ModuleCat",
"CommSemiring.toSemiring",
"CommRingCat"... | false |
PointedCone.maxTensorProduct_map_le | Mathlib.Geometry.Convex.Cone.TensorProduct | [
"Eq.mpr",
"Submodule",
"PointedCone.map",
"PointedCone.map._proof_2",
"CommRing",
"LinearMap.restrictScalars",
"Algebra.to_smulCommClass",
"DFunLike.congr_fun",
"Semiring.toModule",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"IsOrderedRing.toZeroLEOneClass",
"Nonneg.semiring",
"CommSemirin... | true |
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