name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
FDerivMeasurableAux.B | Mathlib.Analysis.Calculus.FDeriv.Measurable | [
"Real",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"FDerivMeasurableAux.A",
"Set.instInter",
"Field.toSemifield",
"Inter.inter",
"ContinuousLinearMap",
"Semifield.toDivisionSemiring",
"... | true |
OmegaCompletePartialOrder.Chain.map_comp | Mathlib.Order.OmegaCompletePartialOrder | [
"OrderHom.comp",
"OmegaCompletePartialOrder.Chain",
"OmegaCompletePartialOrder.Chain.map",
"Eq",
"OrderHom",
"rfl",
"Preorder"
] | true |
Std.DTreeMap.Raw.minKey!_alter_eq_self | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.get?",
"Std.DTreeMap.Raw.instMembership",
"Ord.mk",
"Membership.mem",
"Std.DTreeMap.Raw.alter",
"Ordering",
"Std.DTreeMap.Raw.isEmpty",
"Std.TransCmp",
"Bool.true",
"And",
"Iff",
"Std.DTreeMap.Raw.WF.out",
"Std.LawfulEqCmp",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Inter... | true |
one_lt_iff_ne_one | Mathlib.Algebra.Order.IsBotOne | [
"Preorder.toLT",
"One",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Ne",
"IsBotOneClass",
"Iff",
"LT.lt",
"LE.le.lt_iff_ne",
"Iff.trans",
"ne_comm",
"One.toOfNat1",
"one_le",
"OfNat.ofNat"
] | true |
CauSeq.le_total | Mathlib.Algebra.Order.CauSeq.Basic | [
"Iff.mpr",
"CauSeq.instLTAbs._proof_1",
"CauSeq.instLTAbs",
"AddGroupWithOne.toAddGroup",
"abs",
"LinearOrder",
"IsAbsoluteValue.abs_isAbsoluteValue",
"IsStrictOrderedRing",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"CauSeq.instLEAbs",
"DivisionRing... | true |
MeasureTheory.tendstoInMeasure_of_tendsto_eLpNorm_top | Mathlib.MeasureTheory.Function.ConvergenceInMeasure | [
"edist_eq_enorm_sub",
"MeasureTheory.ae",
"Iff.mpr",
"Eq.mpr",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"ENNReal.ofNat_ne_top",
"MeasureTheory.Measure",
"Preorder.toLT",
"instHDiv",
"SeminormedAddCommGroup",
"MeasureTheory.eLpNorm_exponent_top",
"ENNReal.div_pos_iff",
"congrArg",
"Fi... | true |
Nat.RecursiveIn.below.pair | Mathlib.Computability.RecursiveIn | [
"Part",
"PFun",
"Monad.toApplicative",
"Nat.RecursiveIn.below",
"Nat.RecursiveIn.pair",
"Seq.seq",
"Nat.pair",
"Unit",
"Nat",
"Nat.RecursiveIn",
"Nat.RecursiveIn.below.pair",
"Applicative.toFunctor",
"Applicative.toSeq",
"Functor.map",
"Part.instMonad",
"Set"
] | true |
Lean.mkCIdentFromRef | Init.Meta.Defs | [
"Pure.pure",
"Lean.MonadRef.getRef",
"Lean.identKind",
"Monad.toApplicative",
"Lean.Syntax",
"Lean.TSyntax.raw",
"Lean.mkCIdentFrom",
"Applicative.toPure",
"List.cons",
"Lean.MonadRef",
"Bool",
"Lean.Name",
"Monad.toBind",
"Bind.bind",
"optParam",
"Lean.SyntaxNodeKind",
"Monad",
"B... | true |
MeasureTheory.Measure.completion._proof_1 | Mathlib.MeasureTheory.Measure.NullMeasurable | [
"Eq.mpr",
"MeasureTheory.Measure",
"congrArg",
"MeasurableSet.nullMeasurableSet",
"PartialOrder.toPreorder",
"Preorder.toLE",
"MeasureTheory.OuterMeasure",
"id",
"MeasureTheory.OuterMeasure.trim_anti_measurableSpace",
"MeasureTheory.Measure.trimmed",
"LE.le",
"MeasurableSpace",
"MeasureTheor... | false |
HomotopicalAlgebra.PathObject.recOn | Mathlib.AlgebraicTopology.ModelCategory.PathObject | [
"HomotopicalAlgebra.PathObject",
"HomotopicalAlgebra.PathObject.mk",
"HomotopicalAlgebra.PrepathObject.P",
"HomotopicalAlgebra.CategoryWithWeakEquivalences",
"HomotopicalAlgebra.WeakEquivalence",
"HomotopicalAlgebra.PathObject.rec",
"HomotopicalAlgebra.PrepathObject",
"CategoryTheory.Category",
"Hom... | false |
Subsemiring.center.smulCommClass_right | Mathlib.Algebra.Ring.Subsemiring.Basic | [
"Subsemiring.instSetLike",
"instSMulOfMul",
"Subsemiring.smul",
"Membership.mem",
"Subtype",
"Subsemiring",
"instDistribOfSemiring",
"Distrib.toMul",
"Submonoid.center.smulCommClass_right",
"Semiring.toMonoid",
"Semiring",
"Subsemiring.center",
"Semiring.toNonAssocSemiring",
"SetLike.instM... | true |
IsCompact.exists_bound_of_continuousOn' | Mathlib.Analysis.Normed.Group.Bounded | [
"Norm.norm",
"isBounded_iff_forall_norm_le'",
"Real.instLE",
"Real",
"PseudoMetricSpace.toBornology",
"IsCompact.isBounded",
"SeminormedGroup",
"PseudoMetricSpace.toUniformSpace",
"SeminormedGroup.toPseudoMetricSpace",
"Membership.mem",
"Exists",
"Bornology.IsBounded",
"Exists.imp",
"LE.le... | true |
NonemptyInterval.instPartialOrderLex | Mathlib.Order.Interval.Lex | [
"NonemptyInterval.instPartialOrderLex._proof_1",
"Lex",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"NonemptyInterval.instPreorderLex",
"PartialOrder.mk",
"NonemptyInterval"
] | true |
CategoryTheory.Quotient.comp_natTransLift | Mathlib.CategoryTheory.Quotient | [
"CategoryTheory.Functor",
"CategoryTheory.Quotient.natTransLift",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Quotient",
"Quiver.Hom",
"CategoryTheory.Quotient.category",
"CategoryTheory.Functor.category",
"CategoryTheory.Quotient.functor",
"CategoryTheory.Functor.comp",
"HomRel",
... | true |
Algebra.Extension.h1Cotangentι_apply | Mathlib.RingTheory.Extension.Cotangent.Basic | [
"Submodule",
"CommRing",
"Algebra.Extension.commRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Algebra.Extension.instModuleCotangent",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"instAddCommGroupKaehlerDifferential",
"Algebra.Extension.cotangentComplex._p... | true |
_private.Mathlib.Data.Finset.Pi.0.Finset.pi_nonempty._simp_1_1 | Mathlib.Data.Finset.Pi | [
"Classical.skolem",
"Exists",
"propext",
"Eq"
] | false |
RCLike.ofReal_re_ax | Mathlib.Analysis.RCLike.Basic | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"RCLike.toNormedAlgebra",
"AddMonoid.toAddSemigroup",
"Algebra.algebraMap",
"Real.instAddMonoid",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"SeminormedRing.toRing",
"RingHom",
"NormedField.toField",
"AddZeroClass... | true |
UInt64.reduceDiv._regBuiltin.UInt64.reduceDiv.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt.4002762760._hygCtx._hyg.99 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | [
"IO",
"UInt64.reduceDiv",
"Bool.true",
"Unit",
"Sum.inr",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"Lean.Meta.Simp.addSimprocBuiltinAttr",
"Lean.Meta.Simp.Simproc"
] | false |
SSet.Subcomplex.image_comp | Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex | [
"Set.ext",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"exists_exists_and_eq_and._simp_1",
"Set.mem_image._simp_1",
"CategoryTheory.Functor.category",
"CategoryTheory.Subfunctor.ext",
"TypeCat.instFunLikeFun",
"Membersh... | true |
_private.Lean.Server.Completion.CompletionCollectors.0.Lean.Server.Completion.idCompletionCore._sparseCasesOn_1 | Lean.Server.Completion.CompletionCollectors | [
"Lean.SourceInfo.rec",
"Nat.ne_of_beq_eq_false",
"Lean.SourceInfo.original",
"Lean.SourceInfo.ctorIdx",
"Lean.SourceInfo",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.SourceInfo.synthetic",
"String.Pos.Raw",
"Substring.Raw",
"Nat.land",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofN... | false |
_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_61 | Mathlib.Data.List.Induction | [
"False",
"Lean.Grind.nestedProof",
"eq_false",
"False.elim",
"Lean.Grind.Bool.ne_of_eq_false_of_eq_true",
"noConfusion_of_Nat",
"Lean.Grind.imp_false_eq",
"cast",
"Eq.mp",
"instDecidableEqBool",
"List.dropLast",
"Lean.Grind.not_eq_of_eq_false",
"List.cons",
"List.dropLast_append",
"List.... | false |
Mathlib.Tactic.RingNF.instBEqConfig.beq | Mathlib.Tactic.Ring.RingNF | [
"Mathlib.Tactic.instBEqBehaviorIfUnchanged",
"Bool.and",
"Mathlib.Tactic.BehaviorIfUnchanged",
"BEq.beq",
"_private.Mathlib.Tactic.Ring.RingNF.0.Mathlib.Tactic.RingNF.instBEqConfig.beq.match_1",
"Bool",
"Bool.false",
"Mathlib.Tactic.AtomM.Recurse.instBEqConfig",
"Mathlib.Tactic.AtomM.Recurse.Config"... | true |
_private.Mathlib.Algebra.Polynomial.Div.0.Polynomial.rootMultiplicity_eq_zero_iff._simp_1_3 | Mathlib.Algebra.Polynomial.Div | [
"Polynomial.C",
"CommRing",
"Dvd.dvd",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Polynomial.IsRoot",
"semigroupDvd",
"HSub.hSub",
"RingHom",
"SemigroupWithZero.toSemigroup",
"NonUnitalSemiring.toSemigroupWithZero",
"Polynomial",
"NonUnitalCommSemiring.toNonUnitalSemiring",
... | false |
MulSemiringActionHom.map_one' | Mathlib.GroupTheory.GroupAction.Hom | [
"DistribMulActionHom.toMulActionHom",
"Monoid",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"NonAs... | true |
HasCompactSupport.convolutionExists_left_of_continuous_right | Mathlib.Analysis.Convolution | [
"MeasureTheory.ConvolutionExists",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MeasureTheory.Measure",
"Continuous",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"congrArg",
"DistribMulAction.toDi... | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital.0._auto_252 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
WeakDual.CharacterSpace.equivAlgHom_symm_coe | Mathlib.Analysis.Normed.Algebra.Spectrum | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"NormedRing.toRing",
"Equiv.instEquivLike",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"AlgHom",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"SeparatelyContinuousMul.to_continuo... | true |
Simps.ProjectionRule.erase.injEq | Mathlib.Tactic.Simps.Basic | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Syntax",
"Simps.ProjectionRule.erase",
"Simps.ProjectionRule",
"And",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Simps.ProjectionRule.erase.inj",
"Eq"
] | true |
_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.withInductiveLocalDecls.loop._unary | Lean.Elab.MutualInductive | [
"Pure.pure",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.withInductiveLocalDecls.match_4",
"Subarray",
"Array.push",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"instMonadControlTOfPure",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.withInductiveLocalDecls.match_1",
"Lean.... | false |
mem_residual_iff | Mathlib.Topology.GDelta.Basic | [
"Filter.instMembership",
"Eq.mpr",
"Filter.mem_countableGenerate_iff",
"_private.Mathlib.Topology.GDelta.Basic.0.mem_residual_iff._simp_1_3",
"congrArg",
"residual",
"setOf",
"Membership.mem",
"Exists",
"Dense",
"_private.Mathlib.Topology.GDelta.Basic.0.mem_residual_iff._simp_1_2",
"id",
"Ha... | true |
Submonoid.map_coe_toMonoidHom | Mathlib.Algebra.Group.Submonoid.Operations | [
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"MonoidHom",
"MonoidHomClass.toMonoidHom",
"Submonoid.map",
"MulOneClass.toMulOne",
"MonoidHomClass",
"MulOneClass",
"Eq",
"Submonoid",
"rfl",
"FunLike"
] | true |
CategoryTheory.Equivalence.functor_map_ε_inverse_comp_counit_app | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.LaxMonoidal.ε",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Equivalence.IsMonoidal",
"CategoryTheory.Equivalence.functor",
... | true |
lowerSemicontinuous_biSup | Mathlib.Topology.Semicontinuity.Basic | [
"ChainCompletePartialOrder.instOfCompleteLattice",
"iSup",
"CompletelyDistribLattice.toCompleteLattice",
"PartialOrder.toPreorder",
"lowerSemicontinuous_iSup",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"ChainCompletePartialOrder.toPartialOrder",
"LowerSemicontinuous",
"Topol... | true |
_private.Mathlib.Order.SuccPred.WithBot.0.WithBot.succ_eq_succ.match_1_1 | Mathlib.Order.SuccPred.WithBot | [
"Unit.unit",
"WithBot",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit"
] | false |
Metric.Snowflaking.dist_ofSnowflaking_ofSnowflaking | Mathlib.Topology.MetricSpace.Snowflaking | [
"Metric.Snowflaking.instDist",
"Real.instPow",
"Real.instLE",
"Real",
"Equiv.instEquivLike",
"Metric.Snowflaking.toSnowflaking",
"Real.instZero",
"congrArg",
"Real.instInv",
"dist_nonneg",
"Metric.Snowflaking.casesOn_toSnowflaking",
"Real.instLT",
"Equiv",
"LE.le",
"Real.instOne",
"LT.... | true |
SimpleGraph.Partition.partOfVertex._proof_1 | Mathlib.Combinatorics.SimpleGraph.Partition | [
"SimpleGraph.Partition.isPartition",
"Membership.mem",
"SimpleGraph.Partition",
"SimpleGraph",
"And",
"SimpleGraph.Partition.parts",
"And.right",
"ExistsUnique",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Set.instMembership",
"Not",
"Set"
] | false |
_private.Mathlib.Data.Sigma.Basic.0.Sigma.eq.match_1_1 | Mathlib.Data.Sigma.Basic | [
"Eq.recOn",
"HEq.refl",
"Eq.casesOn",
"Sigma.fst",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Sigma.mk",
"Sigma.casesOn",
"Eq.symm",
"Sigma.snd",
"Eq",
"Sigma",
"rfl"
] | false |
Lean.instBEqDeclaration.beq | Lean.Declaration | [
"_private.Lean.Declaration.0.Lean.instBEqDeclaration.beq.match_1",
"Lean.InductiveType",
"Bool.and",
"Lean.instBEqAxiomVal",
"instDecidableEqBool",
"Lean.instBEqInductiveType",
"instBEqOfDecidableEq",
"Lean.instBEqTheoremVal",
"Bool.true",
"Lean.Declaration",
"List",
"BEq.beq",
"Unit",
"Le... | true |
HasDerivAt.const_mul | Mathlib.Analysis.Calculus.Deriv.Mul | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Set.univ",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"HasDerivAt",
"PseudoMetricSpace.toU... | true |
AlgebraicGeometry.Scheme.IdealSheafData.recOn | Mathlib.AlgebraicGeometry.IdealSheaf.Basic | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"CommRingCat.Hom.hom",
"Semiring.toModule",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"TopologicalSpace.Opens.instPartialOr... | false |
CategoryTheory.projective_iff_llp_epimorphisms_of_isZero | Mathlib.CategoryTheory.Preadditive.Projective.LiftingProperties | [
"CategoryTheory.HasLiftingProperty",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Epi",
"CategoryTheory.MorphismProperty.llp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CommSq",
"congrArg",
"CategoryTheory.sq_hasLift_of_hasLiftingProperty",
"CategoryTheor... | true |
TwoSidedIdeal.instSubSubtypeMem | Mathlib.RingTheory.TwoSidedIdeal.Basic | [
"NonUnitalNonAssocRing",
"TwoSidedIdeal",
"NonUnitalNonAssocRing.toAddCommGroup",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Sub.mk",
"Subtype",
"Subtype.mk",
"SubNegMonoid.toSub",
"instHSub",
"AddGroup.toSubNegMonoid",
"TwoSidedIdeal.setLike",
"TwoSidedIdeal.instSubSubtype... | true |
CategoryTheory.Discrete.productEquiv_functor_map | Mathlib.CategoryTheory.Discrete.SumsProducts | [
"ULift.rec",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Discrete.productEquiv",
"CategoryTheory.Discrete.functor._proof_2",
"CategoryTheory.eqToHom",
"Function.comp",
"PLift",
"Prod.mk",
"CategoryTheory.Equivalence.functor",
"PLift.down",
"CategoryTheory.Functor.ma... | true |
le_inv_iff_mul_le_one_left | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"Eq.mpr",
"MulOne.toOne",
"DivInvMonoid.toInv",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"Iff.rfl",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulLeftMono",
"id",
"MulOne.toMul",
"DivInvMonoid.to... | true |
Lean.Grind.AC.Seq.endsWithVar_k | Init.Grind.AC | [
"Nat.beq",
"Lean.Grind.AC.Seq.rec",
"Bool",
"Lean.Grind.AC.Var",
"Lean.Grind.AC.Seq"
] | true |
WeierstrassCurve.Jacobian.neg_X | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | [
"CommRing",
"Fin.instOfNat",
"instOfNatNat",
"WeierstrassCurve.Jacobian",
"Nat.instNeZeroSucc",
"Nat",
"WeierstrassCurve.Jacobian.neg",
"OfNat.ofNat",
"Fin",
"Eq",
"rfl"
] | true |
AddSubgroup.neg_mem_iff | Mathlib.Algebra.Group.Subgroup.Defs | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"neg_mem_iff",
"Membership.mem",
"SubtractionMonoid.toSubNegZeroMonoid",
"AddSubgroupClass.toNegMemClass",
"SubNegZeroMonoid.toNegZeroClass",
"AddSubgroup",
"AddGroup",
"Iff",
"AddGroup.toSubNegMonoid",
... | true |
Lean.AttributeApplicationTime.afterCompilation.elim | Lean.Attributes | [
"PULift.up",
"Lean.AttributeApplicationTime",
"Lean.AttributeApplicationTime.ctorIdx",
"Lean.AttributeApplicationTime.afterCompilation",
"Nat",
"Eq.symm",
"Eq",
"Lean.AttributeApplicationTime.ctorElim"
] | false |
AlgebraicGeometry.StructureSheaf.Localizations.comapFun._proof_6 | Mathlib.AlgebraicGeometry.StructureSheaf | [
"CommRing",
"Semiring.toModule",
"LocalizedModule",
"PrimeSpectrum.isPrime",
"CommSemiring.toSemiring",
"AlgebraicGeometry.StructureSheaf.Localizations.comapFun._proof_3",
"AddCommGroup.toAddCommMonoid",
"AlgebraicGeometry.StructureSheaf.sectionsSubmodule._proof_2",
"IsLocalizedModule",
"RingHom",... | false |
Mathlib.Tactic.ModCases.NatMod.onModCases_succ | Mathlib.Tactic.ModCases | [
"_private.Mathlib.Tactic.ModCases.0.Mathlib.Tactic.ModCases.NatMod.onModCases_succ._proof_2",
"_private.Mathlib.Tactic.ModCases.0.Mathlib.Tactic.ModCases.NatMod.onModCases_succ._proof_1",
"Mathlib.Tactic.ModCases.NatMod.OnModCases",
"instOfNatNat",
"LE.le",
"instLENat",
"dite",
"And",
"Nat.ModEq",
... | true |
NonUnitalNormedCommRing.induced._proof_12 | Mathlib.Analysis.Normed.Ring.Basic | [
"uniformity",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"Preorder.toLE",
"Prod.mk",
"LE.le",
"Prod.fst",
"SetRel.comp",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"Filter.lift'",
"SeminormedAddGroup.toPseudoMetricSpace",
"NonUnitalNormedCommRing.toNonUnitalNormedRing",... | false |
MeasureTheory.Measure.snd_mono | Mathlib.MeasureTheory.Measure.Prod | [
"MeasureTheory.Measure",
"PartialOrder.toPreorder",
"Preorder.toLE",
"MeasureTheory.Measure.snd",
"LE.le",
"MeasurableSpace",
"measurable_snd",
"MeasureTheory.Measure.instPartialOrder",
"MeasureTheory.Measure.map_mono",
"Prod",
"Prod.snd",
"Prod.instMeasurableSpace"
] | true |
_private.Lean.Meta.Tactic.Grind.Split.0.Lean.Meta.Grind.Action.mkCasesResultSeq._proof_1 | Lean.Meta.Tactic.Grind.Split | [
"Lean.TSyntax",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.combo_sat'",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.sub_nonneg_o... | false |
_private.Mathlib.Algebra.Order.Field.Power.0.Mathlib.Meta.Positivity.evalZPow._proof_5 | Mathlib.Algebra.Order.Field.Power | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Qq.Quoted.unsafeMk",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Qq.QuotedDefEq.unsafeIntro",
"List.nil"
] | false |
CategoryTheory.HasProjectiveDimensionLT.subsingleton' | Mathlib.CategoryTheory.Abelian.Projective.Dimension | [
"CategoryTheory.Abelian",
"LE.le",
"instLENat",
"Nat",
"CategoryTheory.Abelian.Ext",
"CategoryTheory.HasProjectiveDimensionLT",
"Subsingleton",
"CategoryTheory.HasExt.standard",
"CategoryTheory.Category"
] | true |
addRightReflectLT_of_addLeftReflectLT | Mathlib.Algebra.Order.Monoid.Unbundled.Defs | [
"inferInstance",
"AddRightReflectLT",
"LT.lt",
"contravariant_swap_add_of_contravariant_add",
"AddCommSemigroup.toAddCommMagma",
"AddCommSemigroup",
"AddCommMagma.toAdd",
"LT",
"AddLeftReflectLT"
] | true |
Int8.reduceDiv._regBuiltin.Int8.reduceDiv.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt.3529513953._hygCtx._hyg.120 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt | [
"IO",
"Int8.reduceDiv",
"Bool.true",
"Unit",
"Sum.inr",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"Lean.Meta.Simp.addSimprocBuiltinAttr",
"Lean.Meta.Simp.Simproc"
] | false |
Batteries.RBSet.mem_toList | Batteries.Data.RBMap.Lemmas | [
"Batteries.RBNode.WF",
"Batteries.RBNode",
"Batteries.RBNode.mem_toList",
"Batteries.RBSet",
"Membership.mem",
"Ordering",
"Batteries.RBNode.instMembership",
"List",
"Iff",
"List.instMembership",
"Batteries.RBSet.toList",
"Subtype.val"
] | true |
Nat.Partition.powerSeriesMk_card_restricted_eq_powerSeriesMk_card_countRestricted | Mathlib.Combinatorics.Enumerative.Partition.Glaisher | [
"Nontrivial",
"IsSemitopologicalRing.toIsTopologicalAddGroup",
"Eq.mpr",
"instDecidableNot",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"Dvd.dvd",
"Lattice.toSemilatticeSup",
"MvPowerSeries.instZero",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnit... | true |
groupCohomology.shortComplexH0_g | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | [
"Pi.Function.module",
"Rep.V",
"CommRing",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Group",
"Rep.hV1",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"ModuleCat.of",
"CommRing.toCommSemir... | true |
HomologicalComplex.homology_π_ι | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.homologyπ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.HasHomology",
"CategoryTheory.ShortComplex.homology_π_ι",
"HomologicalComplex.iCycles",
"HomologicalComplex.opcycles",
"HomologicalComplex",
"Comple... | true |
ProbabilityTheory.HasSubgaussianMGF.const_mul | Mathlib.Probability.Moments.SubGaussian | [
"Real.instIsOrderedRing",
"Eq.mpr",
"Unit.unit",
"Real.partialOrder",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"ProbabilityTheory.HasSubgaussianMGF_iff_kernel",
"Real.instZero",
"congrArg",
"PartialOrder.toPreorder",
"ProbabilityTheory.Kern... | true |
Mathlib.Tactic.Bicategory.tgtExpr | Mathlib.Tactic.CategoryTheory.Bicategory.Datatypes | [
"Pure.pure",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"String",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.MessageData.instAppend",
"Lean.throwError",
"Lean.MonadQuotation.toMonadRef",
"Lean.instToMessageDataExpr... | true |
ModuleCat.isLimitKernelFork._proof_6 | Mathlib.Algebra.Category.ModuleCat.Kernels | [
"Function.Exact",
"CategoryTheory.Limits.Cone.π",
"Submodule",
"RingHomSurjective.ids",
"CategoryTheory.Functor",
"LinearEquiv.toModuleIso._proof_3",
"LinearEquiv.symm",
"CategoryTheory.Limits.KernelFork.ofι",
"LinearMap.comp.congr_simp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
... | false |
TopologicalSpace.Fiber.sigmaIsoHom.match_1 | Mathlib.Topology.FiberPartition | [
"Membership.mem",
"Set.Elem",
"Set.instSingletonSet",
"Set.preimage",
"Sigma.mk",
"Set.range",
"Sigma.casesOn",
"Singleton.singleton",
"Subtype.val",
"Set.instMembership",
"Sigma",
"Function.Fiber",
"Set"
] | false |
SheafOfModules.IsFiniteType.rec | Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators | [
"SheafOfModules.IsFiniteType.mk",
"CategoryTheory.Over",
"AddCommGrpCat.instCategory",
"SheafOfModules.IsFiniteType",
"AddMonoid.toAddZeroClass",
"RingCat.ring",
"AddCommGroup.toAddGroup",
"RingHom",
"AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier",
"Exists",
"AddZeroClass.toAddZero",
"... | false |
cuspsSubMulAction | Mathlib.NumberTheory.ModularForms.Cusps | [
"OnePoint.instGLAction",
"Real",
"cuspsSubMulAction._proof_1",
"Matrix",
"instDecidableEqFin",
"setOf",
"SubMulAction.mk",
"Membership.mem",
"Real.semiring",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"IsCusp",
"instOfNatNat",
"Units.instGroup",
"MulAction.instMulAction",
"Fin.f... | true |
Lean.Lsp.DocumentColorParams.mk.noConfusion | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.WorkDoneProgressParams",
"Lean.Lsp.DocumentColorParams.mk",
"Lean.Lsp.DocumentColorParams",
"Lean.Lsp.PartialResultParams",
"id",
"Lean.Lsp.TextDocumentIdentifier",
"Lean.Lsp.DocumentColorParams.noConfusion",
"Eq"
] | false |
_private.Lean.Server.Test.Runner.0.Lean.Server.Test.Runner.Client.instFromJsonHighlightedMsgEmbed.fromJson.match_1 | Lean.Server.Test.Runner | [
"Unit.unit",
"String",
"dite",
"Unit",
"Eq.ndrec_symm",
"instDecidableEqString",
"Eq",
"Not"
] | false |
CategoryTheory.Abelian.SpectralObject.SpectralSequence.pageX._proof_7 | Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | [
"CategoryTheory.Abelian.SpectralObject.SpectralSequence.pageX._proof_2",
"Preorder.toLE",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.i₀",
"Int",
"LE.le",
"ComplexShape",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.i₁",
"CategoryTheory.Abelian.SpectralObject.Spe... | false |
Lean.Meta.mkId | Lean.Meta.AppBuilder | [
"Pure.pure",
"Lean.Meta.State",
"Lean.mkApp2",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Level",
"Lean.Meta.getLevel",
"Applicative.toPure",
"Lean.mkConst",
"List.cons",
"Lean.Core.CoreM",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"StateRefT'.instMonad",
"Monad.toBind",
"... | true |
Tropical.instLinearOrderTropical._proof_5 | Mathlib.Algebra.Tropical.Basic | [
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"LinearOrder.toDecidableLE",
"DistribLattice.toLattice",
"LE.le",
"Tropical",
"instHAdd",
"HAdd.hAdd",
"Tropical.instPartialOrderTropical",
"Tropical.instLinearOrderTropical._proof_1",
"Tropical.decid... | false |
AlternatingMap.domCoprod.summand._proof_1 | Mathlib.LinearAlgebra.Alternating.DomCoprod | [
"AlternatingMap",
"Eq.mpr",
"MonoidHom.range",
"Units.instMulAction",
"Semigroup.toMul",
"Equiv.Perm.sumCongrHom",
"instFintypeSum",
"TensorProduct.leftHasSMul",
"instHSMul",
"MonoidHom.instFunLike",
"Equiv.instEquivLike",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoi... | false |
Subalgebra.mem_saturation_iff._simp_1 | Mathlib.Algebra.Algebra.Subalgebra.Lattice | [
"Subalgebra.instSetLike",
"instHSMul",
"instSMulOfMul",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Subalgebra.mem_saturation_iff",
"Subalgebra.toSubsemiring",
"LE.le",
"Subsemiring.toSubmonoid",
"MulZeroOneClass.toMulOneCl... | false |
Fin.sum_univ_five | Mathlib.Algebra.BigOperators.Fin | [
"Eq.mpr",
"Fin.sum_univ_castSucc",
"Finset.univ",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"id",
"Fin.instOfNat",
"instOfNatNat",
"AddCommMonoid",
"Fin.fintype",
"instHAdd",
"Fin.sum_univ_four",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"Fin.last",
"instAdd... | true |
Mathlib.Tactic.Widget.StringDiagram.stringEqM? | Mathlib.Tactic.Widget.StringDiagram | [
"Pure.pure",
"Lean.instantiateMVars",
"ProofWidgets.Html",
"Lean.Meta.State",
"Option.some",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"_private.Mathlib.Tactic.Widget.StringDiagram.0.Mathlib.Tactic.Widget.StringDiagram.stringEqM?.match_1",
"Applicative.toPure",
"_private.Mathlib.Tactic.Wid... | true |
_private.Init.Data.String.Lemmas.Splits.0.String.Pos.Splits.nextn._simp_1_1 | Init.Data.String.Lemmas.Splits | [
"String.Pos.Splits",
"String.toSlice",
"String",
"String.Pos.toSlice",
"propext",
"String.Pos",
"Eq.symm",
"Eq",
"String.Slice.Pos.Splits",
"String.Pos.splits_toSlice_iff"
] | false |
MonadCont.Label.rec | Mathlib.Control.Monad.Cont | [
"MonadCont.Label",
"MonadCont.Label.mk"
] | false |
List.take_concat_get | Init.Data.List.TakeDrop | [
"Eq.mpr",
"List.append_assoc",
"congrArg",
"List.concat",
"List.take_append_drop",
"id",
"instOfNatNat",
"List.concat_eq_append",
"List.cons",
"GetElem.getElem",
"instHAppendOfAppend",
"List",
"instHAdd",
"List.singleton_append",
"List.drop",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Iff.mp"... | true |
range_pow_padicValNat_subset_divisors' | Mathlib.NumberTheory.Padics.PadicVal.Basic | [
"Iff.mpr",
"subset_refl._simp_1",
"instPowNat",
"Nat.one_lt_pow",
"Eq.mpr",
"False",
"Nat.Prime",
"Dvd.dvd",
"Nat.Prime.one_lt",
"congrArg",
"Finset",
"Nat.mem_divisors",
"Nat.instMonoid",
"Finset.instReflSubset",
"pow_dvd_pow",
"Membership.mem",
"Exists",
"Fact",
"Eq.mp",
"id"... | true |
DihedralGroup.oddCommuteEquiv | Mathlib.GroupTheory.SpecificGroups.Dihedral | [
"Units.val",
"ZMod.unitOfCoprime",
"HMul.hMul",
"ZMod.commRing",
"DihedralGroup.oddCommuteEquiv._proof_1",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"ZMod.add_self_eq_zero_iff_eq_zero",
"Odd",
"Commute",
"Units",
"Equiv.mk",
"Sum",
"DihedralGroup.oddCommuteEquiv._proof_5",
"Dihe... | true |
Filter.EventuallyEq.fun_comp | Mathlib.Order.Filter.Basic | [
"Function.comp",
"Filter.EventuallyEq",
"Filter.Eventually.mono",
"congr_arg",
"Eq",
"Filter"
] | true |
ShareCommonT | Init.ShareCommon | [
"ShareCommon.State",
"ShareCommon.StateFactory",
"StateT"
] | true |
StarRingEquiv.mk.inj | Mathlib.Algebra.Star.StarRingHom | [
"RingEquiv.toEquiv",
"StarRingEquiv.mk.noConfusion",
"StarRingEquiv.mk",
"Mul",
"Equiv.toFun",
"Star",
"eq_of_heq",
"HEq",
"RingEquiv",
"Eq",
"StarRingEquiv",
"Add",
"Star.star"
] | true |
MeasureTheory.FiniteMeasure.ennreal_coeFn_eq_coeFn_toMeasure | Mathlib.MeasureTheory.Measure.FiniteMeasure | [
"ENNReal.coe_toNNReal",
"MeasureTheory.FiniteMeasure",
"ENNReal.ofNNReal",
"MeasureTheory.Measure",
"MeasureTheory.measure_lt_top",
"PartialOrder.toPreorder",
"NNReal",
"MeasureTheory.FiniteMeasure.instFunLike",
"MeasurableSpace",
"ENNReal",
"ENNReal.instPartialOrder",
"ENNReal.instTop",
"To... | true |
MonoidAlgebra.coe_add._simp_2 | Mathlib.Algebra.MonoidAlgebra.Defs | [
"MonoidAlgebra.addCommMonoid",
"Finsupp.instFunLike",
"Distrib.toAdd",
"MonoidAlgebra.coe_add",
"instDistribOfSemiring",
"instHAdd",
"Pi.instAdd",
"HAdd.hAdd",
"MonoidAlgebra",
"Semiring",
"AddCommSemigroup.toAddCommMagma",
"Eq.symm",
"AddCommMonoid.toAddCommSemigroup",
"Eq",
"DFunLike.c... | false |
ConditionallyCompleteLinearOrderedField.le_inducedMap_mul_self_of_mem_cutMap | Mathlib.Algebra.Order.CompleteField | [
"exists_rat_pow_btwn",
"Iff.mpr",
"Rat.instOfNat",
"Eq.mpr",
"Nat.instMulZeroClass",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"mul_self_le_mul_self",
"pow_two",
"CommRing.toNonUnitalCommRing",
"DivisionRing.toRatCast",
"Is... | true |
_private.Lean.Meta.Tactic.Grind.PP.0.Lean.Meta.Grind.isArithOfCastLike | Lean.Meta.Tactic.Grind.PP | [
"Lean.Expr",
"_private.Lean.Meta.Tactic.Grind.PP.0.Lean.Meta.Grind.isArithOfCastLike.match_1",
"_private.Lean.Meta.Tactic.Grind.PP.0.Lean.Meta.Grind.Result",
"_private.Lean.Meta.Tactic.Grind.PP.0.Lean.Meta.Grind.isArithOfCastLike.go",
"Bool.true",
"Unit",
"Bool",
"Bool.false"
] | true |
Lean.Parser.InputContext.substring | Lean.Parser.Types | [
"String.Pos.Raw.instLinearOrderPackage",
"Substring.Raw.mk",
"Lean.Parser.InputContext.endPos",
"String.Pos.Raw",
"Substring.Raw",
"Lean.Parser.InputContext",
"Std.LinearOrderPackage.toMin",
"Lean.Parser.InputContext.inputString",
"Min.min"
] | true |
Std.Time.Duration.addMilliseconds | Std.Time.Duration | [
"Std.Time.Duration.ofNanoseconds",
"Std.Time.Millisecond.Offset.toNanoseconds",
"Std.Time.Millisecond.Offset",
"Std.Time.Duration",
"Std.Time.Duration.add"
] | true |
_private.Mathlib.Data.Matrix.Invertible.0.Matrix.add_mul_mul_mul_invOf_eq_one._simp_1_2 | Mathlib.Data.Matrix.Invertible | [
"Matrix.add",
"HMul.hMul",
"Matrix",
"Matrix.instHMulOfFintypeOfMulOfAddCommMonoid",
"Distrib.toAdd",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Matrix.add_mul",
"instHAdd",
"Fintype",
"Distrib.toMul",
"HAdd.hAdd",
"NonUnitalNonAssocSemiring.toDistrib",
"NonUnitalNonAssocSemiring",
"Eq.... | false |
Std.DHashMap.Raw.mem_toList_iff_get?_eq_some._simp_1 | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw",
"Option.some",
"LawfulBEq",
"Membership.mem",
"Std.DHashMap.Raw.toList",
"Std.DHashMap.Raw.mem_toList_iff_get?_eq_some",
"List",
"List.instMembership",
"Std.DHashMap.Raw.get?",
"propext",
"Hashable",
"Sigma.mk",
"BEq",
"Eq",
"Sigma",
"Option... | false |
_private.Mathlib.RingTheory.Valuation.Discrete.Basic.0.Valuation.valuationSubring_not_isField._simp_1_1 | Mathlib.RingTheory.Valuation.Discrete.Basic | [
"Subring.instSetLike",
"AddGroupWithOne.toAddGroup",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"Subring.instSubringClass",
"Subtype",
"ZeroMemClass.zero",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"N... | false |
CategoryTheory.Bicategory.id_whiskerLeft._autoParam | Mathlib.CategoryTheory.Bicategory.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.Cat.HasLimits.limitCone_pt | Mathlib.CategoryTheory.Category.Cat.Limit | [
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.Cat.HasLimits.limitCone",
"CategoryTheory.Cat.HasLimits.limitConeX",
"CategoryTheory.SmallCategory",
"CategoryTheory.Cat",
"CategoryTheory.Limits.Cone.pt",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.Algebra.Order.BigOperators.Ring.Finset.0.Finset.prod_add_prod_le._simp_1_7 | Mathlib.Algebra.Order.BigOperators.Ring.Finset | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
mem_emetric_ball_one_iff | Mathlib.Analysis.Normed.Group.Basic | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Preorder.toLT",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"SeminormedGroup",
"SeminormedGroup.toGroup",
"PartialOrder.toPreorder",
"SeminormedGroup.toPseudoMetricSpace",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivI... | true |
TensorProduct.ext_iff_inner_right_threefold | Mathlib.Analysis.InnerProductSpace.TensorProduct | [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"ContinuousLinearMap.coe_inj",
"ContinuousLinearMap.topologicalSpace",
"In... | true |
Complex.re_nonneg_iff_nonneg | Mathlib.Analysis.Complex.Basic | [
"Eq.mpr",
"IsSelfAdjoint",
"Real.instLE",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"AddMonoid.toAddSemigroup",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
"RCLike.re_nonneg_of_nonneg",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"PartialOrder.toPreorder",
"Comple... | true |
CategoryTheory.Limits.KernelFork.IsLimit.ofι'._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"id",
"Subtype",
"CategoryTheory.cancel_mono",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"propext",
"CategoryTheory.CategoryStruct.comp",
"Zero.... | false |
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