name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
instWellFoundedLTOrderDualOfWellFoundedGT | Mathlib.Order.RelClasses | [
"WellFoundedLT",
"WellFoundedGT",
"OrderDual.instLT",
"OrderDual",
"LT"
] | true |
Std.IteratorAccess.ctorIdx | Init.Data.Iterators.Consumers.Monadic.Access | [
"Std.Iterator",
"Nat",
"Std.IteratorAccess"
] | false |
_private.Mathlib.LinearAlgebra.Lagrange.0.Lagrange.basisDivisor_inj._simp_1_6 | Mathlib.LinearAlgebra.Lagrange | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
ContinuousMap.linearIsometryBoundedOfCompact_apply_apply | Mathlib.Topology.ContinuousMap.Compact | [
"LinearIsometryEquiv.instEquivLike",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"UniformContinuousConstSMul.to_continuousConstSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousMap",
"AddMonoid.toAddZeroClass",
"IsBoundedSMul.toUniformContinuousConstSMul",
"Pse... | true |
LinearMap.mkContinuous_norm_le | Mathlib.Analysis.Normed.Operator.Basic | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"Real.instLE",
"Real",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"HMul.hMul",
"NormedSpace",
"Real.instZero",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"LinearMap.instFunLike",
"PseudoMetricSpace.toUniformSpace",
"RingHom",
"... | true |
Lean.TheoremVal.mk._flat_ctor | Lean.Declaration | [
"Lean.Expr",
"Lean.ConstantVal.mk",
"List",
"Lean.TheoremVal.mk",
"Lean.Name",
"Lean.TheoremVal"
] | false |
SuccOrder.prelimitRecOn._proof_2 | Mathlib.Order.SuccPred.Limit | [
"Preorder.toLT",
"Order.succ",
"Order.IsSuccPrelimit",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"PartialOrder",
"And",
"Order.not_isSuccPrelimit_iff_succ_eq",
"Iff.mp",
"SuccOrder",
"Eq",
"Not",
"IsMax"
] | false |
AlternativeMonad.map._inherited_default | Batteries.Control.AlternativeMonad | [
"Function.comp",
"id"
] | false |
Ideal.Filtration.Stable.exists_pow_smul_eq | Mathlib.RingTheory.Filtration | [
"Eq.mpr",
"Submodule",
"MulOne.toOne",
"Semigroup.toMul",
"Ideal.one_eq_top",
"CommRing",
"Nat.recAux",
"instHSMul",
"Semiring.toModule",
"HMul.hMul",
"IsScalarTower.right",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.instNo... | true |
Lean.Meta.DiscrTree.casesOn | Lean.Meta.DiscrTree.Types | [
"Lean.Meta.DiscrTree.instHashableKey",
"Lean.Meta.DiscrTree.instBEqKey",
"Lean.Meta.DiscrTree.Key",
"Lean.PersistentHashMap",
"Lean.Meta.DiscrTree.mk",
"Lean.Meta.DiscrTree.Trie",
"Lean.Meta.DiscrTree",
"Lean.Meta.DiscrTree.rec"
] | false |
MeasureTheory.Measure.measure_support_eq_zero_iff._auto_1 | Mathlib.MeasureTheory.Measure.MeasureSpace | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.MeasureTheory.Measure.Haar.Basic.0.MeasureTheory.Measure.haar.chaar_sup_le._simp_1_2 | Mathlib.MeasureTheory.Measure.Haar.Basic | [
"Set.Ici",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"Set.mem_Ici",
"propext",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | false |
_private.Mathlib.NumberTheory.Primorial.0.primorial_add._proof_1_3 | Mathlib.NumberTheory.Primorial | [
"Lean.RArray.leaf",
"False",
"of_decide_eq_true",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"HSub.hSub",
"Nat.not_le_eq",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Lean.RArray.branch",
"DistribLattice.toLattice",
"id",
"False.casesOn",
"Nat.Simproc.add_le_add_ge",
... | false |
Lean.Grind.Config.splitImp._default | Init.Grind.Config | [
"id",
"Bool",
"Bool.false"
] | false |
Complex.mul_cpow_ofReal_nonneg | Mathlib.Analysis.SpecialFunctions.Pow.Complex | [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"add_mul",
"Eq.mpr",
"Complex.log",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorder.toLT",
"HMul.hMul",
"Complex.exp_add",
"MulZeroClass.toMul",
"Real.instZero",
"congrArg",
"MulZeroClass.zero_mul",
"Complex.ofReal_log",
"NormedDivision... | true |
CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero | Mathlib.CategoryTheory.Preadditive.Projective.Resolution | [
"CategoryTheory.ProjectiveResolution.π",
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.single_obj_d",
"congrArg",
"Add... | true |
Equiv.normedCommGroup.eq_1 | Mathlib.Analysis.Normed.Module.TransferInstance | [
"Equiv.normedCommGroup._proof_2",
"MulEquiv.instEquivLike",
"Monoid.toMulOneClass",
"Equiv.normedCommGroup",
"NormedCommGroup.toSeminormedCommGroup",
"SeminormedCommGroup.toPseudoMetricSpace",
"Equiv.commGroup",
"Mul",
"NormedCommGroup.dist_eq",
"Equiv.normedCommGroup._proof_1",
"Equiv",
"MulO... | true |
Std.DTreeMap.Internal.Impl.containsThenInsert_fst_eq_containsₘ | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"Eq.mpr",
"False",
"Decidable.casesOn",
"beq_eq_false_iff_ne._simp_1",
"BEq.rfl",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"congrArg",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.Ordered",
"Decidable",
"Std.DTreeMap.Internal.Impl.Balanced",
"Nat.instTransOrd",
"Eq.mp",
... | true |
Lean.Compiler.LCNF.MonadFVarSubst | Lean.Compiler.LCNF.CompilerM | [
"Lean.Compiler.LCNF.MonadFVarSubst.mk",
"outParam",
"Lean.Compiler.LCNF.Purity",
"Bool"
] | true |
MeasureTheory.Measure.quasiMeasurePreserving_smul | Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | [
"Eq.mpr",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"NormedSpace.toIsBoundedSMul",
"Real.lattice",
"IsScalarTower.right",
"NormedSpace",
"Real.instZero",
"ENNReal.ofReal",
"abs",
"congrArg",
"CommSemiring.toSemiring",
"Real.instInv",
"DistribMulAction.toDistribSMul... | true |
Metric.closedBall_eq_sphere_of_nonpos | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"Set.ext",
"Real.partialOrder",
"Real.instLE",
"Real",
"Real.instZero",
"dist_nonneg",
"LE.le",
"LE.le.ge_iff_eq'",
"PseudoMetricSpace",
"Zero.toOfNat0",
"Dist.dist",
"PseudoMetricSpace.toDist",
"LE.le.trans",
"Metric.closedBall",
"OfNat.ofNat",
"Eq",
"Real.instPreorder",
"Metric.s... | true |
Rack.PreEnvelGroupRel'.symm | Mathlib.Algebra.Quandle | [
"Rack.PreEnvelGroupRel'",
"Rack",
"Rack.PreEnvelGroup",
"Rack.PreEnvelGroupRel'.symm"
] | true |
Lean.ErrorExplanation.declLoc? | Lean.ErrorExplanation | [
"Lean.DeclarationLocation",
"Option",
"Lean.ErrorExplanation"
] | true |
Module.rankAtStalk_tensorProduct_of_isScalarTower | Mathlib.RingTheory.Spectrum.Prime.FreeLocus | [
"TensorProduct.AlgebraTensorModule.cancelBaseChange",
"LinearEquiv.symm",
"CommRing",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"HMul.hMul",
"Module.rankAtStalk",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid... | true |
WithTop.insertTop | Mathlib.Order.Interval.Finset.Defs | [
"Finset.cons",
"WithTop.insertTop._proof_1",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Finset.map",
"Finset.partialOrder",
"WithTop.insertTop._proof_2",
"WithTop.top",
"OrderEmbedding.ofMapLEIff",
"OrderEmbedding",
"Top.top",
"Function.Embedding.coeWithTop",
"WithTop"
] | true |
_private.Mathlib.Topology.MetricSpace.PiNat.0.PiCountable.pseudoEMetricSpace._simp_8 | Mathlib.Topology.MetricSpace.PiNat | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
SemiNormedGrp.explicitCokernelDesc._proof_1 | Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"congr",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"Zero.toOfNat0",
"SemiNormedGrp.instLargeCategory",
"CategoryTheory.Category.toCategoryStruct",
"... | false |
GroupExtension.Splitting.instFunLike | Mathlib.GroupTheory.GroupExtension.Defs | [
"MulOne.toOne",
"GroupExtension.Splitting.instFunLike._proof_3",
"GroupExtension.Splitting.toMonoidHom",
"DFunLike.mk",
"Monoid.toMulOneClass",
"GroupExtension.Splitting",
"Group",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"OneHom.toFun",
"MonoidHom.toOneHom",
... | true |
SimpleGraph.cliqueFinset.congr_simp | Mathlib.Combinatorics.SimpleGraph.Clique | [
"instSubsingletonDecidable",
"Finset",
"SimpleGraph.Adj",
"DecidableRel",
"Decidable",
"Eq.rec",
"Pi.instSubsingleton",
"SimpleGraph",
"Fintype",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Subsingleton.elim",
"SimpleGraph.cliqueFinset",
"Eq",
"DecidableEq"
] | true |
LocallyConstant.instInhabited._proof_1 | Mathlib.Topology.LocallyConstant.Basic | [
"Inhabited.default",
"IsLocallyConstant",
"IsLocallyConstant.const",
"TopologicalSpace",
"Function.const",
"Inhabited"
] | false |
Batteries.Random.MersenneTwister.State.noConfusion | Batteries.Data.Random.MersenneTwister | [
"Vector",
"HEq.refl",
"BitVec",
"Batteries.Random.MersenneTwister.State",
"Batteries.Random.MersenneTwister.Config",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Batteries.Random.MersenneTwister.Config.wordSize",
"Batteries.Random.MersenneTwister.State.noConfusionType",
"Fin",
"Eq",
"Batteries.Random.Me... | false |
String.mk | Init.Data.String.Bootstrap | [
"String",
"List",
"Char",
"String.mk._proof_1",
"List.utf8Encode",
"String.ofByteArray"
] | true |
Option.decidableForallMem._proof_3 | Init.Data.Option.Instances | [
"Option.instMembership",
"Option.some",
"Membership.mem",
"mt",
"Not",
"rfl",
"Option"
] | false |
_private.Init.Data.SInt.Bitwise.0.Int16.shiftRight_and._simp_1_1 | Init.Data.SInt.Bitwise | [
"Int16",
"BitVec",
"instOfNatNat",
"Nat",
"Int16.toBitVec",
"propext",
"OfNat.ofNat",
"Eq.symm",
"Int16.toBitVec_inj",
"Eq"
] | false |
_private.Lean.Meta.SynthInstance.0.Lean.Meta.SynthInstance.removeUnusedArguments? | Lean.Meta.SynthInstance | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.instantiateMVars",
"Lean.MessageData",
"Lean.mkAppN",
"Bool.not",
"Lean.Meta.forallTelescope",
"instMonadControlTOfPure",
"String",
"Lean.Expr.fvarId!",
"Lean.instMonadTraceOfMonadLift",
"Lean.Meta.State",
"Lean.MetavarContext",
"Lean.Mes... | true |
_private.Lean.Elab.Match.0.Lean.Elab.Term.withElaboratedLHS | Lean.Elab.Match | [
"Lean.Core.instMonadTraceCoreM",
"Lean.MessageData",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"_private.Lean.Elab.Match.0.Lean.Elab.Term.withElaboratedLHS.match_1",
"Lean.Meta.Match.AltLHS",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"monadFunctorRefl",
"String",
"Lean.instMonadTraceO... | true |
Denumerable.raise'._unsafe_rec | Mathlib.Logic.Equiv.Finset | [
"Denumerable.raise'._unsafe_rec",
"instOfNatNat",
"List.cons",
"List",
"instHAdd",
"Denumerable.lower'.match_1",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"List.nil"
] | false |
Int16.ofBitVec_ofNat | Init.Data.SInt.Lemmas | [
"Int16",
"Int16.ofBitVec",
"instOfNatNat",
"BitVec.ofNat",
"Int16.ofNat",
"Nat",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctor | Mathlib.CategoryTheory.Limits.Constructions.Over.Products | [
"CategoryTheory.Limits.BinaryFan.isLimitMk",
"CategoryTheory.Over",
"CategoryTheory.Limits.BinaryFan.fst",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.BinaryFan",
"CategoryTheory.Over.mk",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.p... | true |
CategoryTheory.Abelian.Preradical.toColon_hom_left_colonπ | Mathlib.CategoryTheory.Abelian.Preradical.Colon | [
"CategoryTheory.Abelian.Preradical.colonπ",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Functor.rightU... | true |
_private.Mathlib.RingTheory.Invariant.Basic.0.Ideal.Quotient.exists_algHom_fixedPoint_quotient_under._simp_1_2 | Mathlib.RingTheory.Invariant.Basic | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
CategoryTheory.ComposableArrows.isoMkSucc_inv | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ComposableArrows.map'._proof_8",
"CategoryTheory.ComposableArrows.app'",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.ComposableArrows",
"Fin.mk",
"CategoryTheory.ComposableArrows.homMk₁._proof_4... | true |
comap_abs_nhds_zero | Mathlib.Topology.Algebra.Order.Group | [
"abs_neg",
"OrderTopology",
"Preorder.toLT",
"iInf",
"Iff.of_eq",
"abs",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Filter.instInfSet",
"nhds_eq_iInf_abs_sub",
"LinearOrder",
"covariant_swap_add_of_covariant_add",
"PartialOrder.toPreorder",
"setOf",
"HSub.hSub",
"Preorder.toLE",
"A... | true |
Matrix.transpose_zero | Mathlib.LinearAlgebra.Matrix.Defs | [
"Matrix",
"Matrix.transpose",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Matrix.zero",
"rfl",
"Zero"
] | true |
RootPairing.Equiv.toEndUnit._proof_9 | Mathlib.LinearAlgebra.RootSystem.Hom | [
"Units.val",
"Eq.mpr",
"RootPairing.Hom.indexEquiv",
"MulOne.toOne",
"CommRing",
"Equiv.instEquivLike",
"HMul.hMul",
"Monoid.toMulOneClass",
"LinearMap.ext",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"RootPairing.Equiv.toEndUnit._proof_2",
"LinearMap.instFunLik... | false |
_private.Lean.Meta.Tactic.Grind.0.Lean.initFn._@.Lean.Meta.Tactic.Grind.964293774._hygCtx._hyg.2 | Lean.Meta.Tactic.Grind | [
"Lean.Name.mkNum",
"IO",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.registerTraceClass",
"Lean.Name.anonymous",
"Unit",
"Nat",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"Bool.false"
] | false |
SimpleGraph.IsMaximumClique.maximum | Mathlib.Combinatorics.SimpleGraph.Clique | [
"Finset",
"Finite",
"LE.le",
"instLENat",
"SimpleGraph",
"SetLike.coe",
"Finset.instSetLike",
"Nat",
"SimpleGraph.IsMaximumClique",
"Finset.card",
"SimpleGraph.IsClique"
] | true |
Stream'.Seq.terminates_ofList | Mathlib.Data.Seq.Basic | [
"Stream'.Seq.TerminatedAt",
"Stream'.Seq.Terminates",
"Stream'.Seq.ofList",
"List",
"Nat",
"Exists.intro",
"Stream'.Seq.terminatedAt_ofList",
"List.length"
] | true |
Std.Http.Headers.insertMany | Std.Internal.Http.Data.Headers | [
"Std.Http.Header.Name.instBEq",
"Std.Http.Header.Name.instLawfulBEq",
"Std.Http.Header.Name",
"Array",
"Std.Http.Headers.map",
"Std.Http.Header.Value",
"Std.Http.Header.Name.instHashable",
"Std.Http.Headers.mk",
"Std.Http.Header.Name.instLawfulHashable",
"Std.Http.Headers",
"instEquivBEqOfLawful... | true |
Std.TreeMap.instSliceableRooSlice._auto_1 | Std.Data.TreeMap.Slice | [
"Lean.Syntax.node",
"Lean.Syntax.ident",
"Array.push",
"String.toRawSubstring",
"Lean.Syntax",
"Array.empty",
"Lean.Syntax.Preresolved",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom",
"List.nil"
] | false |
_private.Init.Data.Array.Lemmas.0.Array.foldlM_loop_empty._proof_1_2 | Init.Data.Array.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.LinearC... | false |
_private.Mathlib.Analysis.Calculus.Deriv.Inverse.0.HasDerivWithinAt.eventually_ne._simp_1_2 | Mathlib.Analysis.Calculus.Deriv.Inverse | [
"False",
"eq_false",
"instOfNatNat",
"two_ne_zero",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
Lean.matchConstNonRecStructure | Lean.MonadEnv | [
"Lean.getConstInfo",
"Unit.unit",
"bne",
"Lean.ConstructorVal",
"_private.Lean.MonadEnv.0.Lean.matchConstStructure.match_1",
"Lean.Expr",
"instDecidableEqBool",
"instOfNatNat",
"Lean.Level",
"instBEqOfDecidableEq",
"Lean.InductiveVal.isRec",
"Bool.true",
"List",
"Unit",
"Lean.MonadError"... | true |
emultiplicity_map_eq | Mathlib.RingTheory.Multiplicity | [
"Monoid",
"Dvd.dvd",
"Monoid.toMulOneClass",
"congrArg",
"semigroupDvd",
"MulOne.toMul",
"MulEquivClass",
"Monoid.toPow",
"iff_self",
"MulOneClass.toMulOne",
"Iff",
"EquivLike",
"HPow.hPow",
"Nat",
"ENat",
"_private.Mathlib.RingTheory.Multiplicity.0.emultiplicity_map_eq._simp_1_1",
"... | true |
_private.Lean.Util.Recognizers.0.Lean.Expr.notNot?.match_1 | Lean.Util.Recognizers | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.Expr",
"Option.none",
"Unit",
"Option"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.Spectrum.0.LinearMap.IsSymmetric.unsortedEigenvectorBasis | Mathlib.Analysis.InnerProductSpace.Spectrum | [
"InnerProductSpace.toNormedSpace",
"instAddMonoidWithOneENat",
"AddCommGroup.toAddCommMonoid",
"LinearMap.IsSymmetric.directSumDecomposition._proof_3",
"NormedSpace.toModule",
"Module.End.eigenspace",
"RCLike.toDecidableEq",
"Module.End.instFintypeEigenvalues",
"NormedDivisionRing.toDivisionRing",
... | true |
AdicCompletion.map._proof_5 | Mathlib.RingTheory.AdicCompletion.Functoriality | [
"CommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"Algebra.id",
"AdicCompletion.map._proof_3",
"Ideal.IsTwoSided",
"Ideal",
"Ideal.instIsTwoSided_1",
"CommRing.toCommSemiring",
"HPow.hPow",
"Nat",
"instHPow",
"Submodule.instPowNat"
] | false |
CFC.abs_ofNat | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs | [
"IsSelfAdjoint",
"Real.partialOrder",
"Real",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"IsScalarTower.right",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"PseudoMetricSpace.toUni... | true |
Fin.preimage_val_uIoo_val | Mathlib.Order.Interval.Set.Fin | [
"Fin.val",
"Set.uIoo",
"Fin.instLinearOrder",
"Set.preimage",
"Nat",
"Fin",
"Eq",
"rfl",
"Set",
"Nat.instLinearOrder"
] | true |
OpenPartialHomeomorph.homeomorphOfImageSubsetSource._proof_2 | Mathlib.Topology.OpenPartialHomeomorph.Basic | [
"PartialEquiv.target",
"Set.image_mono",
"Eq.rec",
"OpenPartialHomeomorph.image_source_eq_target",
"HasSubset.Subset",
"OpenPartialHomeomorph.toFun'",
"TopologicalSpace",
"PartialEquiv.source",
"Set.image",
"OpenPartialHomeomorph.toPartialEquiv",
"Eq",
"OpenPartialHomeomorph",
"Set.instHasSu... | false |
_private.Mathlib.CategoryTheory.WithTerminal.Cone.0.CategoryTheory.WithTerminal.coneBack_obj_pt | Mathlib.CategoryTheory.WithTerminal.Cone | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Functor.category",
"CategoryTheory.Over.mk",
"CategoryTheory.instCategoryOver",
"CategoryTheory.WithTerminal",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.WithTermina... | true |
Units.cfcRpow._auto_1 | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Int64.reduceLT._regBuiltin.Int64.reduceLT.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt.4041591762._hygCtx._hyg.165 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt | [
"IO",
"Sum.inl",
"Bool.true",
"Unit",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"Lean.Meta.Simp.addSimprocBuiltinAttr",
"Int64.reduceLT",
"Lean.Meta.Simp.Simproc"
] | false |
CategoryTheory.LaxFunctor._sizeOf_inst | Mathlib.CategoryTheory.Bicategory.Functor.Lax | [
"CategoryTheory.Bicategory",
"SizeOf.mk",
"SizeOf",
"CategoryTheory.LaxFunctor._sizeOf_1",
"CategoryTheory.LaxFunctor"
] | false |
AddSubgroup.toIntSubmodule._proof_4 | Mathlib.Algebra.Module.Submodule.Lattice | [
"Submodule",
"AddSubgroup.zsmul_mem",
"Equiv.instEquivLike",
"AddSubgroup.toIntSubmodule._proof_1",
"AddCommGroup.toAddCommMonoid",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubsemigroup.carrier",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddZ... | false |
FirstOrder.Language.BoundedFormula.mapTermRel.eq_def | Mathlib.ModelTheory.Syntax | [
"FirstOrder.Language.BoundedFormula.imp",
"Eq.mpr",
"FirstOrder.Language.BoundedFormula.mapTermRel",
"congrArg",
"HEq.refl",
"FirstOrder.Language.BoundedFormula.brecOn",
"FirstOrder.Language.Term",
"Sum",
"id",
"FirstOrder.Language.BoundedFormula.rec",
"instOfNatNat",
"FirstOrder.Language.Boun... | true |
Mathlib.Tactic.Translate.TranslateData.unfoldBoundaries? | Mathlib.Tactic.Translate.Core | [
"Mathlib.Tactic.Translate.TranslateData",
"Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaryExt",
"Option"
] | true |
normalizedGCDMonoidOfLCM._proof_5 | Mathlib.Algebra.GCDMonoid.Basic | [
"CommMonoidWithZero.toCommMonoid",
"Iff.mpr",
"Units.val",
"Eq.mpr",
"False",
"Semigroup.toMul",
"Dvd.dvd",
"trans",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"MulZeroClass.toMul",
"congrArg",
"HMul",
"Dvd.intro",
"NormalizationMonoid",
"eq_isEquiv",
"semigroupDvd",
"zero_dvd_iff"... | false |
Std.ExtHashSet.contains_iff_mem._simp_1 | Std.Data.ExtHashSet.Lemmas | [
"Std.ExtHashSet",
"Membership.mem",
"LawfulHashable",
"Bool.true",
"EquivBEq",
"propext",
"Bool",
"Hashable",
"Std.ExtHashSet.instMembershipOfEquivBEqOfLawfulHashable",
"BEq",
"Eq",
"Std.ExtHashSet.contains_iff_mem",
"Std.ExtHashSet.contains"
] | false |
Array.le_min?_iff | Init.Data.Array.MinMax | [
"Array.min?_toList._cbv_eval_1",
"List.min?",
"congrArg",
"Array.instMembership",
"Option.some",
"Membership.mem",
"Array.min?",
"Eq.mp",
"LE.le",
"Array.toList",
"LE",
"Min",
"Array",
"List",
"List.le_min?_iff",
"Iff",
"Array.mem_toList_iff._simp_1",
"List.instMembership",
"impl... | true |
Lean.pp.rawOnError | Lean.Util.PPExt | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Option",
"Lean.instInhabitedOption",
"Bool"
] | true |
QuotientGroup.quotientInfEquivProdNormalQuotient.eq_1 | Mathlib.GroupTheory.QuotientGroup.Basic | [
"Subgroup.subgroupOf",
"Lattice.toSemilatticeSup",
"Monoid.toMulOneClass",
"Group",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"MulOne.toMul",
"Subtype",
"QuotientGroup.instHasQuotientSubgroup",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDi... | true |
_private.Mathlib.Data.EReal.Operations.0.ENNReal.toEReal_sub._simp_1_1 | Mathlib.Data.EReal.Operations | [
"ENNReal.ofNNReal",
"HSub.hSub",
"NNReal",
"instHSub",
"ENNReal.coe_sub",
"ENNReal",
"ENNReal.instSub",
"Eq.symm",
"Eq",
"NNReal.instSub"
] | false |
CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIsoFactorsh_hom_app_assoc | Mathlib.Algebra.Homology.Localization | [
"HomologicalComplexUpToQuasiIso.Q",
"HomologicalComplex.homotopyEquivalences",
"CategoryTheory.Category.assoc",
"CategoryTheory.MorphismProperty.instCategoryLocalization'",
"HomologicalComplexUpToQuasiIso",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQ... | true |
SemiNormedGrp₁.coe_of | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"SeminormedAddCommGroup",
"SemiNormedGrp₁.carrier",
"Eq",
"SemiNormedGrp₁.of",
"rfl"
] | true |
AdicCompletion.ofLinearEquiv.eq_1 | Mathlib.RingTheory.AdicCompletion.Basic | [
"CommRing",
"instSMulOfMul",
"AdicCompletion.ofLinearEquiv._proof_1",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"AdicCompletion.instAddCommGroup",
"AdicCompletion.ofLinearEquiv",
"AdicCompletion.instModuleOfIsScalarTower",
"Ideal",
"IsScalarTower.left",
"instDi... | true |
Algebra.SubmersivePresentation.isStandardSmoothOfRelativeDimension | Mathlib.RingTheory.Smooth.StandardSmooth | [
"CommRing",
"Fintype.ofFinite",
"Algebra.Presentation.reindex",
"congrArg",
"CommSemiring.toSemiring",
"Algebra.SubmersivePresentation.toPreSubmersivePresentation",
"Finite",
"Algebra",
"Exists",
"Algebra.PreSubmersivePresentation.toPresentation",
"inferInstance",
"Fintype.card",
"Algebra.Su... | true |
ContinuousMap.toNNReal_algebraMap | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | [
"NNReal.instTopologicalSpace",
"NonAssocSemiring.toAddCommMonoidWithOne",
"NNReal.instCommSemiring",
"Real",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Algebra.algebraMap",
"IsTopologicalRing.toIsTopologicalSemiring",
"congrArg",
"CommSemiring.toSemiring",
"ContinuousMap",
... | true |
_private.Mathlib.Algebra.Polynomial.Degree.TrailingDegree.0.Polynomial.natTrailingDegree_intCast._simp_1_1 | Mathlib.Algebra.Polynomial.Degree.TrailingDegree | [
"Int.cast",
"Polynomial.C",
"Polynomial.C_eq_intCast",
"Polynomial.instIntCast",
"RingHom",
"Int",
"AddGroupWithOne.toIntCast",
"Polynomial",
"RingHom.instFunLike",
"Polynomial.semiring",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Eq",
"DFunLike.coe",
"Ring",
"Ring... | false |
MeasureTheory.measure_eq_top_of_setLIntegral_ne_top | Mathlib.MeasureTheory.Integral.Lebesgue.Markov | [
"MeasureTheory.Measure",
"AEMeasurable",
"setOf",
"ENNReal.measurableSpace",
"Membership.mem",
"MeasureTheory.Measure.restrict",
"Ne",
"MeasureTheory.setLIntegral_eq_top_of_measure_eq_top_ne_zero",
"MeasurableSpace",
"And",
"ENNReal",
"of_not_not",
"Zero.toOfNat0",
"ENNReal.instTop",
"EN... | true |
_private.Lean.Elab.Notation.0.Lean.Elab.Command.expandNotationItemIntoSyntaxItem._sparseCasesOn_1 | Lean.Elab.Notation | [
"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 |
CategoryTheory.CommGrp.forget | Mathlib.CategoryTheory.Monoidal.CommGrp_ | [
"CategoryTheory.Functor",
"CategoryTheory.CommGrp.instCategory",
"CategoryTheory.Functor.comp",
"CategoryTheory.Grp.instCategory",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CommGrp.forget₂Grp",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.CommGrp... | true |
RootPairing.zero_notMem_range_root | Mathlib.LinearAlgebra.RootSystem.Defs | [
"Eq.mpr",
"CommRing",
"RootPairing.ne_zero",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"Exists",
"AddCommGroup",
"_private.Mathlib.LinearAlgebra.RootSystem.Defs.0.RootPairing.zer... | true |
Mathlib.Tactic.ITauto.Proof.andIntro.inj | Mathlib.Tactic.ITauto | [
"Mathlib.Tactic.ITauto.AndKind",
"Mathlib.Tactic.ITauto.Proof.andIntro",
"And",
"Mathlib.Tactic.ITauto.Proof",
"Mathlib.Tactic.ITauto.Proof.andIntro.noConfusion",
"And.intro",
"Eq"
] | true |
ZeroHom.casesOn | Mathlib.Algebra.Group.Hom.Defs | [
"ZeroHom.mk",
"ZeroHom",
"ZeroHom.rec",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
FractionalIdeal.isFractional_span_iff | Mathlib.RingTheory.FractionalIdeal.Operations | [
"IsLocalization.IsInteger",
"Eq.mpr",
"Submodule",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsLocalization.isInteger_smul",
"IsFractional",
"AddMonoid.to... | true |
CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt | Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | [
"CategoryTheory.Limits.FormalCoproduct",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.FormalCoproduct.isColimitCofan",
"CategoryTheory.Limits.FormalCoproduct.coproductIsoCofanPt",
"CategoryTheory.Discrete.functor",... | true |
LinearMap.coe_toContinuousLinearMap | Mathlib.Topology.Algebra.Module.FiniteDimension | [
"NormedCommRing.toSeminormedCommRing",
"CompleteSpace",
"ContinuousSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"ContinuousLinearMap.addCommMonoid",
"AddCommGroup.toAddGroup",
"NormedDivisionRing.toDivision... | true |
ENNReal.add_ne_top | Mathlib.Data.ENNReal.Operations | [
"ENNReal.instAdd",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.add_ne_top._simp_1_1",
"Preorder.toLE",
"Eq.mp",
"Ne",
"instHAdd",
"And",
"Iff",
"OrderTop.toTop",
"HAdd.hAdd",
"congr",
"LT.lt",
"ENNReal",
"ENNReal.instPar... | true |
Int.emod_zero | Init.Data.Int.DivMod.Bootstrap | [
"Nat.mod_zero",
"congrArg",
"Nat.instMod",
"instHMod",
"Int.ofNat",
"Int",
"HMod.hMod",
"instOfNat",
"Nat",
"Int.natAbs",
"Int.instMod",
"Int.negSucc",
"OfNat.ofNat",
"Eq",
"_private.Init.Data.Int.DivMod.Bootstrap.0.Int.emod_zero.match_1_1"
] | true |
MeasureTheory.tendsto_measure_of_null_frontier | Mathlib.MeasureTheory.Measure.Portmanteau | [
"Iff.mpr",
"frontier",
"MeasureTheory.Measure",
"interior_subset",
"Filter.liminf",
"subset_closure",
"isOpen_interior",
"nhds",
"MeasureTheory.limsup_measure_closed_le_iff_liminf_measure_open_ge",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"Filter.limsup",
"... | true |
RingEquiv.map_sum | Mathlib.Algebra.BigOperators.RingEquiv | [
"RingEquivClass.toNonUnitalRingHomClass",
"RingEquiv.instEquivLike",
"Finset",
"RingEquiv.instRingEquivClass",
"Distrib.toAdd",
"map_sum",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"RingEquiv",
"NonUnitalNonAssocSemiring",
"Eq",
"DFu... | true |
Polynomial.Splits.eval_derivative | Mathlib.Algebra.Polynomial.Splits | [
"Multiset.sum",
"Polynomial.derivative",
"Polynomial.eval_multiset_prod",
"Eq.mpr",
"Polynomial.C",
"Polynomial.eval",
"IsDomain",
"Polynomial.derivative_mul",
"Polynomial.instOne",
"CommRing",
"Polynomial.roots",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.... | true |
Std.TreeMap.Raw.mem_toList_iff_getElem?_eq_some._simp_1 | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.toList",
"Option.some",
"Membership.mem",
"Ordering",
"Std.TreeMap.Raw.instMembership",
"Prod.mk",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw",
"List",
"List.instMembership",
"Std.LawfulEqCmp",
"propext",
"Std.TreeMap.Raw.instGetElem?Mem",
"Std.TreeMap.Raw.me... | false |
CategoryTheory.Limits.MultispanIndex.SymmStruct.noConfusionType | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.MultispanIndex.snd",
"CategoryTheory.Limits.MultispanShape.prod",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.MultispanIndex.fst",
"CategoryTheory.Iso",
"CategoryTheory.Limits.MultispanIndex.right",
"CategoryTheory.Limits.MultispanIndex",
"Pr... | false |
CochainComplex.Lifting.cocycle₁._proof_5 | Mathlib.Algebra.Homology.ModelCategory.Lifting | [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CochainComplex.Lifting.π_f_cochain₁_v_ι_f",
"MulOne.toOne",
"CochainComplex.Lifting.cochain₁",
"Units.instMulAction",
"HomologicalComplex.instCategory",
"instHSMul",
"CategoryTheory.Limits.KernelFork.ofι",
"Categ... | false |
CategoryTheory.Quiv.comp_eq_comp | Mathlib.CategoryTheory.Category.Quiv | [
"CategoryTheory.Quiv.str'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Prefunctor.comp",
"CategoryTheory.Quiv.category",
"CategoryTheory.Bundled.α",
"CategoryTheory.Quiv",
"CategoryTheory.CategoryStruct.comp",
"Quiver",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"rfl"
] | true |
ZMod.ringHom_map_cast | Mathlib.Data.ZMod.Basic | [
"Int.cast",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"instNeZeroNatHAdd_1",
"ZMod.cast",
"ZMod.commRing",
"congrArg",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"RingHom",
"map_intCast",
"id",
"AddMonoidWithOne.toNatCast",
"in... | true |
Finsupp.lattice._proof_5 | Mathlib.Order.Preorder.Finsupp | [
"Lattice",
"SemilatticeInf.inf_le_right",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"LE.le",
"SemilatticeInf.inf",
"Finsupp.semilatticeInf",
"Finsupp",
"Lattice.toSemilatticeInf",
"Zero"
] | false |
Lean.Elab.Tactic.iterateExactly'._unsafe_rec | Mathlib.Tactic.Core | [
"Pure.pure",
"Unit.unit",
"Monad.toApplicative",
"_private.Mathlib.Tactic.Core.0.Lean.Elab.Tactic.iterateAtMost.match_1",
"Applicative.toPure",
"Unit",
"Nat",
"Lean.Elab.Tactic.iterateExactly'._unsafe_rec",
"Applicative.toSeqRight",
"Monad",
"SeqRight.seqRight"
] | false |
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