name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
nodup_permsOfList | Mathlib.Data.Fintype.Perm | [
"List.brecOn",
"nodup_permsOfList._f",
"List.Nodup",
"List",
"Equiv.Perm",
"permsOfList",
"DecidableEq"
] | true |
_private.Lean.Meta.Sym.Simp.Main.0.Lean.Meta.Sym.Simp.simpImpl._sparseCasesOn_1 | Lean.Meta.Sym.Simp.Main | [
"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 |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.emod_lt_of_neg._proof_1_3 | Init.Data.Int.DivMod.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Lean.Omega.Int.le_of_not_lt",
"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",
"Op... | false |
TopCat.PrelocalPredicate.sheafify | Mathlib.Topology.Sheaves.LocalPredicate | [
"TopCat.PrelocalPredicate",
"TopCat.PrelocalPredicate.sheafify._proof_2",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"TopCat.PrelocalPredicate.pred",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Membership.mem",
"Exists",
"Subtype"... | true |
HasDerivWithinAt.cos | Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"RCLike.toNormedAlgebra",
"HMul.hMul",
"IsTopologicalRing.toIsTopologicalSemiring",
"Real.denselyNormedField",
"Real.cos",
"Real.instRCLike",
"IsTopologicalSemiring.toContinuousMu... | true |
AddMonoidAlgebra.infDegree_withTop_some_comp | Mathlib.Algebra.MonoidAlgebra.Degree | [
"Finset.coe_inf'",
"Eq.mpr",
"Finset.inf'",
"congrArg",
"AddMonoidAlgebra.infDegree",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Finsupp.support",
"Function.comp",
"SemilatticeInf.toPartialOrder",
"id",
"OrderTop",
"WithTop.some",
"SemilatticeInf",
"Finset.Nonempty",
"Semiring",
"W... | true |
_private.Mathlib.CategoryTheory.Sites.Pretopology.0.CategoryTheory.Pretopology.instInfSet._simp_2 | Mathlib.CategoryTheory.Sites.Pretopology | [
"Set.iInter",
"Membership.mem",
"Set.mem_iInter",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
AlgCat.limitSemiring._proof_12 | Mathlib.Algebra.Category.AlgCat.Limits | [
"Subalgebra.instSetLike",
"AlgCat.instAlgebraObjForgetAlgHomCarrier",
"Equiv.ring._proof_3",
"CategoryTheory.Functor",
"CommRing",
"Equiv.instEquivLike",
"CategoryTheory.Limits.Types.Small.limitCone",
"AlgCat.limitSemiring._aux_4",
"AddMonoid.toAddSemigroup",
"Equiv.addGroupWithOne",
"AlgCat.ins... | false |
Std.Http.Headers.mk._flat_ctor | Std.Internal.Http.Data.Headers | [
"Std.Http.Header.Name.instBEq",
"Std.Http.Header.Name",
"Std.Http.Header.Value",
"Std.Http.Header.Name.instHashable",
"Std.Http.Headers.mk",
"Std.Http.Headers",
"Std.Internal.IndexMultiMap"
] | false |
add_tsub_tsub_cancel | Mathlib.Algebra.Order.Sub.Unbundled.Basic | [
"PartialOrder.toPreorder",
"HSub.hSub",
"AddLeftMono",
"Preorder.toLE",
"PartialOrder",
"OrderedSub",
"LE.le",
"ExistsAddOfLE",
"AddLECancellable.add_tsub_tsub_cancel",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"AddLeftReflectLE",
"AddCommSemigroup.toAddCommMagma",
"AddCommSemigroup",
"Eq",... | true |
MeasureTheory.MeasurePreserving.integral_comp | Mathlib.MeasureTheory.Integral.Bochner.Basic | [
"MeasureTheory.MeasurePreserving",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"MeasurableEmbedding.integral_map",
"Eq.rec",
"MeasureTheory.MeasurePreserving.map_eq",
"MeasurableSpace",
"MeasureTheory.integral",
"MeasureTheory.Measure.map",
"MeasurableEmbedding",
"Real.normedField",
"Eq.... | true |
Decidable.iff_congr_right | Init.PropLemmas | [
"False",
"eq_false",
"congrArg",
"Decidable",
"true_iff",
"false_iff",
"dite",
"iff_self",
"Iff",
"congr",
"True",
"eq_true",
"of_eq_true",
"congrFun'",
"Not",
"_private.Init.PropLemmas.0.Decidable.iff_congr_right._simp_1_1",
"Eq.trans"
] | true |
_private.Mathlib.Algebra.Algebra.Spectrum.Basic.0.spectrum.«term↑ₐ_1» | Mathlib.Algebra.Algebra.Spectrum.Basic | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
Multiset.range.eq_1 | Mathlib.Data.Multiset.Range | [
"Multiset",
"List.range",
"Multiset.ofList",
"Nat",
"Multiset.range",
"Eq.refl",
"Eq"
] | true |
Algebra.algebraMapSubmonoid_le_comap | Mathlib.Algebra.Algebra.Hom | [
"Eq.mpr",
"RingHom.instRingHomClass",
"AlgHom.algHomClass",
"Submonoid.le_comap_map",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"RingHom",
"id",
"RingHomClass.toMonoidWithZeroHomClass",
"NonAssocSemiring.toMu... | true |
Mathlib.Tactic.Ring.Common.RingCompare.mk | Mathlib.Tactic.Ring.Common | [
"Mathlib.Tactic.Ring.Common.RingCompare.mk",
"Ordering",
"Lean.Expr.sort",
"Lean.Level",
"Qq.Quoted",
"Bool",
"Lean.Level.succ",
"Mathlib.Tactic.Ring.Common.RingCompare"
] | true |
UInt16.and_assoc | Init.Data.UInt.Bitwise | [
"UInt16.toBitVec",
"BitVec.and_assoc",
"BitVec",
"instOfNatNat",
"UInt16",
"Nat",
"Iff.mp",
"HAnd.hAnd",
"OfNat.ofNat",
"UInt16.toBitVec_inj",
"instAndOpUInt16",
"Eq",
"instHAndOfAndOp"
] | true |
_private.Mathlib.NumberTheory.LSeries.ZMod.0.ZMod.LFunction_one_sub._simp_1_3 | Mathlib.NumberTheory.LSeries.ZMod | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
WithConv.toConv.injEq | Mathlib.Algebra.WithConv | [
"WithConv.toConv",
"Eq.propIntro",
"WithConv.toConv.inj",
"Eq.ndrec",
"Eq.refl",
"WithConv",
"Eq"
] | true |
BddAbove.isBoundedUnder_of_range | Mathlib.Order.Filter.IsBounded | [
"Eq.mpr",
"Set.image_univ",
"congrArg",
"Set.univ",
"Preorder.toLE",
"BddAbove.isBoundedUnder",
"id",
"LE.le",
"BddAbove",
"Set.image",
"Set.range",
"Filter.univ_mem",
"Eq",
"Filter.IsBoundedUnder",
"Filter",
"Preorder",
"Set"
] | true |
intervalIntegrable_of_odd₀ | Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic | [
"Left.neg_pos_iff._simp_1",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"Real.partialOrder",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"IntervalIntegrable.neg",
"Real.instZero",
"congrArg",
"IntervalIntegrable",
"instIsLeftCancelAddOfAddLeftReflectLE",
"AddMonoi... | true |
_private.Lean.Elab.PreDefinition.MkInhabitant.0.Lean.Elab.mkInhabitantForAux? | Lean.Elab.PreDefinition.MkInhabitant | [
"Inhabited.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"Array",
"Lean.Meta.instInhabitedMetaM",
"Bool",
"Option"
] | true |
continuous_neg_iff._simp_1 | Mathlib.Topology.Algebra.Group.Basic | [
"Pi.instNeg",
"Continuous",
"ContinuousNeg",
"TopologicalSpace",
"InvolutiveNeg",
"propext",
"continuous_neg_iff",
"InvolutiveNeg.toNeg",
"Eq",
"Neg.neg"
] | false |
Lean.Meta.Match.instInhabitedProblem.default | Lean.Meta.Match.Basic | [
"Inhabited.default",
"Lean.Meta.Match.Example",
"Lean.Meta.Match.Alt",
"Lean.MVarId",
"Lean.instInhabitedMVarId",
"Lean.Expr",
"Lean.Meta.Match.Problem",
"Lean.Meta.Match.Problem.mk",
"List",
"instInhabitedList"
] | true |
Complex.I_ne_zero._simp_1 | Mathlib.Data.Complex.Basic | [
"False",
"eq_false",
"Complex.instZero",
"Complex.I_ne_zero",
"Zero.toOfNat0",
"Complex",
"OfNat.ofNat",
"Eq",
"Complex.I"
] | false |
Array.setIfInBounds_append_left | Init.Data.Array.Lemmas | [
"Array.instAppend",
"congrArg",
"Array.setIfInBounds_append",
"HSub.hSub",
"instSubNat",
"ite_cond_eq_true",
"Array",
"instHAppendOfAppend",
"instHSub",
"Nat",
"LT.lt",
"True",
"eq_self",
"eq_true",
"of_eq_true",
"Nat.decLt",
"congrFun'",
"Array.setIfInBounds",
"instLTNat",
"Eq... | true |
Mathlib.Tactic.ITauto.instInhabitedAndKind | Mathlib.Tactic.ITauto | [
"Mathlib.Tactic.ITauto.AndKind",
"Mathlib.Tactic.ITauto.AndKind.and",
"Inhabited",
"Inhabited.mk"
] | true |
Real.noConfusionType | Mathlib.Data.Real.Basic | [
"Real",
"abs",
"IsAbsoluteValue.abs_isAbsoluteValue",
"Rat",
"CauSeq.Completion.Cauchy",
"Rat.linearOrder",
"Rat.instLattice",
"Rat.instDivisionRing",
"DivisionRing.toRing",
"Rat.instField",
"Rat.instIsStrictOrderedRing",
"Rat.addGroup",
"Eq",
"Real.casesOn"
] | false |
genLoopEquivOfUnique._proof_7 | Mathlib.Topology.Homotopy.HomotopyGroup | [
"Real.instIsOrderedRing",
"Inhabited.default",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"Pi.topologicalSpace",
"ContinuousMap",
"Unique",
"PseudoMetricSpace.toUniformSpace",
"GenLoop.instFunLike",
"Membership.mem",
"Real.semiring",
"Set.Elem",
"GenLoop",
"TopologicalSpace",
"Ex... | false |
ProbabilityTheory.Kernel.isSFiniteKernel_prodMkRight_unit | Mathlib.Probability.Kernel.Composition.MapComap | [
"Unit.unit",
"ProbabilityTheory.Kernel.comap",
"ProbabilityTheory.IsSFiniteKernel",
"inferInstance",
"id",
"Measurable.prodMk",
"Prod.mk",
"ProbabilityTheory.Kernel.prodMkRight",
"MeasurableSpace",
"ProbabilityTheory.Kernel.IsSFiniteKernel.prodMkRight",
"Unit",
"Iff",
"Iff.intro",
"PUnit.i... | true |
IsSpectralMap.mk | Mathlib.Topology.Spectral.Hom | [
"Continuous",
"IsSpectralMap",
"TopologicalSpace",
"IsSpectralMap.mk",
"Set.preimage",
"IsOpen",
"IsCompact",
"Set"
] | true |
ExceptT.pure | Init.Control.Except | [
"Pure.pure",
"Except.ok",
"Monad.toApplicative",
"Applicative.toPure",
"ExceptT",
"ExceptT.mk",
"Except",
"Monad"
] | true |
hasStrictFDerivAt_apply | Mathlib.Analysis.Calculus.FDeriv.Prod | [
"NormedSpace",
"Pi.topologicalSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Pi.module",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Field.toSemifield",
"ContinuousLinearMap.proj",
"ContinuousLinearMap.hasStrictFDerivAt",
"Semifield.toDivisionSemiring",
"Semin... | true |
String.Pos.prev_induction | Init.Data.String.Termination | [
"Eq.mpr",
"congrArg",
"String",
"id",
"String.startPos",
"Ne",
"String.Pos.prev_lt_iff_le._simp_1",
"LE.le",
"dite",
"WellFounded.induction",
"String.instLTPos",
"String.Pos.prev",
"LT.lt",
"True",
"String.Pos",
"of_eq_true",
"String.instLEPos",
"String.Pos.le_refl._simp_1",
"Eq"... | true |
Module.dualProdDualEquivDual | Mathlib.LinearAlgebra.Dual.Lemmas | [
"Algebra.to_smulCommClass",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Module.dualProdDualEquivDual._proof_1",
"Algebra.id",
"LinearMap.module",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"RingHomInvPair.ids... | true |
_private.Init.Data.Array.Basic.0.Array.findSomeRevM?.find._unsafe_rec | Init.Data.Array.Basic | [
"Pure.pure",
"Monad.toApplicative",
"_private.Init.Data.Array.Basic.0.Array.findSomeRevM?.find._unsafe_rec",
"Nat.lt_succ_self",
"instOfNatNat",
"LE.le",
"instLENat",
"Applicative.toPure",
"Nat.le_of_lt",
"Array",
"GetElem.getElem",
"_private.Init.Data.Array.Basic.0.Array.findSomeRevM?.find.ma... | false |
Std.DHashMap.Raw.any_eq_true_iff_exists_contains_get | Std.Data.DHashMap.RawLemmas | [
"Iff.mpr",
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.contains",
"Iff.of_eq",
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw.get_eq",
"LawfulBEq",
"Exists",
"Std.DHashMap.Raw.contains",
"id",
"Std.DHashMap.Internal.Raw.get_eq._proof_2",
"instOfNatNat",
"Std.... | true |
_private.Mathlib.CategoryTheory.NatIso.0.CategoryTheory.NatIso.cancel_natIso_inv_left._simp_1_1 | Mathlib.CategoryTheory.NatIso | [
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.cancel_epi",
"Eq",
"CategoryTheory.Category"
] | false |
IsRelPrime.add_mul_right_right_iff._simp_1 | Mathlib.RingTheory.Coprime.Basic | [
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"IsRelPrime",
"Distrib.toAdd",
"instDistribOfSemiring",
"instHAdd",
"CommRing.toCommSemiring",
"Distrib.toMul",
"HAdd.hAdd",
"Semiring.toMonoid",
"propext",
"Eq",
"IsRelPrime.add_mul_right_right_iff",
"instHMul"
] | false |
_private.Mathlib.Tactic.GCongr.Core.0.Mathlib.Tactic.GCongr.initFn._proof_1._@.Mathlib.Tactic.GCongr.Core.2213018204._hygCtx._hyg.2 | Mathlib.Tactic.GCongr.Core | [
"Nat.le_refl",
"Lean.Expr",
"LE.le",
"instLENat",
"Array",
"Nat",
"Array.size"
] | false |
Std.Do.SPred.or_comm | Std.Do.SPred.DerivedLaws | [
"Iff.mpr",
"Std.Do.SPred.entails",
"Std.Do.SPred.or",
"Std.Do.SPred.or_symm",
"Std.Do.SPred.bientails",
"List",
"And",
"And.intro",
"Std.Do.SPred",
"Std.Do.SPred.bientails.iff"
] | true |
dirSupClosedOn_Iic | Mathlib.Order.DirSupClosed | [
"dirSupClosed_Iic",
"DirSupClosedOn",
"DirSupClosed.dirSupClosedOn",
"Set.Iic",
"Preorder",
"Set"
] | true |
Module.Basis.addHaar_self | Mathlib.MeasureTheory.Measure.Haar.OfBasis | [
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"BorelSpace",
"Real.semiring",
"id",
"Module.Basis.definition._proof_1._@.Mathlib.MeasureTheory.Measure... | true |
Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.subst.noConfusion | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstr",
"id",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.noConfusion",
"Int.Linear.Var",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.subst",
"Eq",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstr",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof"
] | false |
Function.injective_of_isPartialInv_right | Mathlib.Logic.Function.Basic | [
"Function.IsPartialInv",
"Option.instMembership",
"Option.some",
"Membership.mem",
"Iff.mp",
"Eq.symm",
"Eq",
"Eq.trans",
"Option"
] | true |
Ideal.one_eq_top | Mathlib.RingTheory.Ideal.Operations | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Semiring.toModule",
"congrArg",
"Ideal.span_singleton_one",
"Set.instSingletonSet",
"id",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Submodule.instTop",
"Ideal",
"Submodule.one",
"Ideal.span.eq_1",
"NonUnitalNonAssocSemiri... | true |
_private.Mathlib.Combinatorics.Matroid.Basic.0.Matroid.ext_iff_isBase.match_1_1 | Mathlib.Combinatorics.Matroid.Basic | [
"Matroid.E",
"Matroid.IsBase",
"HasSubset.Subset",
"And.casesOn",
"And",
"Iff",
"And.intro",
"Eq",
"Matroid",
"Set.instHasSubset",
"Set"
] | false |
CategoryTheory.CostructuredArrow.instEssSurjCompObjPostOfFull | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor.preimage",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.comp",
"CategoryTheory.CostructuredArrow.hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso.refl",
"CategoryTheory.CostructuredArrow",... | true |
ContMDiffSection.coeFn_mk | Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | [
"ContMDiffSection.mk",
"Prod.normedSpace",
"Prod.normedAddCommGroup",
"NormedSpace",
"FiberBundle",
"ContMDiff",
"PseudoMetricSpace.toUniformSpace",
"ContMDiffSection.instDFunLike",
"instTopologicalSpaceModelProd",
"Bundle.TotalSpace.mk'",
"FiberBundle.chartedSpace",
"TopologicalSpace",
"Mod... | true |
NNReal.agm_eq_ciSup | Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean | [
"NNReal.agmSequences",
"Eq.mpr",
"Real",
"NNReal.tendsto_dist_agmSequences_atTop_zero",
"Real.instZero",
"congrArg",
"iSup",
"LinearOrder.supConvergenceClass",
"tendsto_atTop_ciSup",
"EMetricSpace.metrizableSpace",
"instArchimedeanNat",
"PseudoMetricSpace.toUniformSpace",
"NNReal.tendsto_agm... | true |
CoalgCat.MonoidalCategory.inducingFunctorData._proof_7 | Mathlib.Algebra.Category.CoalgCat.Monoidal | [
"CoalgCat.toModuleCat",
"CommRing",
"Coalgebra.toCoalgebraStruct",
"CoalgCat",
"CategoryTheory.MonoidalCategory.tensorIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CoalgCat.category",
"ModuleCat",
"CommSemiring.toSemiring",
"CoalgHom",
"CoalgCat.hasForgetToModule",
"AddCommG... | false |
ContinuousAlgHom.instContinuousMapClass | Mathlib.Topology.Algebra.Algebra | [
"ContinuousAlgHom.instFunLike",
"Algebra",
"ContinuousMapClass",
"CommSemiring",
"TopologicalSpace",
"ContinuousMapClass.mk",
"Semiring",
"ContinuousAlgHom.cont",
"ContinuousAlgHom"
] | true |
_private.Mathlib.Tactic.Linarith.Preprocessing.0.Mathlib.Tactic.Linarith.nlinarithGetSquareProofs.match_3 | Mathlib.Tactic.Linarith.Preprocessing | [
"Lean.Expr",
"Prod.mk",
"Bool",
"Prod",
"Prod.casesOn"
] | false |
Std.DHashMap.Raw.Const.get!_alter_self | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.Const.get!_alter",
"BEq.rfl",
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.Const.get!",
"instDecidableEqBool",
"Option.get!",
"ite_cond_eq_true",
"LawfulHashable",
"Bool.true",
"EquivBEq.toReflBEq",
"BEq.beq",
"Std.DHashMap.Raw.Const.alter",
... | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.length_insertListIfNewUnit_le._simp_1_4 | Std.Data.Internal.List.Associative | [
"Nat.le_refl",
"LE.le",
"instLENat",
"Nat",
"True",
"eq_true",
"Eq"
] | false |
Lean.Grind.AC.Expr.toSeq'.match_1.congr_eq_1 | Init.Grind.AC | [
"Lean.Grind.AC.Expr.op",
"Lean.Grind.AC.Expr",
"id",
"Lean.Grind.AC.Expr.casesOn",
"heq_of_eq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Lean.Grind.AC.Var",
"Eq.symm",
"Eq",
"Lean.Grind.AC.Expr.toSeq'.match_1",
"Lean.Grind.AC.Expr.var"
] | true |
Lean.Server.Watchdog.ReferenceRequestContext.mk.injEq | Lean.Server.Watchdog | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Server.Watchdog.ReferenceRequestContext",
"Ord.compare",
"Lean.Server.Watchdog.ReferenceRequestContext.mk",
"Lean.Lsp.DocumentUri",
"And",
"Lean.Server.Watchdog.ReferenceRequestContext.mk.inj",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"String.instOrd",
"... | true |
_private.Init.Data.Array.Zip.0.Array.getElem?_zipWith.match_1.eq_1 | Init.Data.Array.Zip | [
"Option.some",
"Array.getElem?_zipWith.match_1",
"Eq.refl",
"Eq",
"Option"
] | true |
DirSupClosed.of_isEmpty | Mathlib.Order.DirSupClosed | [
"isEmptyElim",
"Preorder.toLE",
"DirectedOn",
"Membership.mem",
"DirSupClosed",
"HasSubset.Subset",
"LE.le",
"IsEmpty",
"Set.Nonempty",
"IsLUB",
"Set.instMembership",
"_private.Mathlib.Order.DirSupClosed.0.DirSupClosed.of_isEmpty.match_1_1",
"Preorder",
"Set.instHasSubset",
"Set"
] | true |
Prod.indiscreteTopology | Mathlib.Topology.Constructions | [
"Iff.mpr",
"IndiscreteTopology.mk",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"and_self",
"IndiscreteTopology.eq_top",
"PartialOrder.toPreorder",
"instTopologicalSpaceProd",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toConditionallyCompleteLat... | true |
IsDedekindDomain.HeightOneSpectrum.mk.injEq | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"CommRing",
"Semiring.toModule",
"IsDedekindDomain.HeightOneSpectrum.mk",
"Eq.propIntro",
"CommSemiring.toSemiring",
"IsDedekindDomain.HeightOneSpectrum",
"Ne",
"Bot.bot",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Submodule.instBot",
"CommRing.toCommSemiring",
"NonAssocSemiring.... | true |
IO.FS.readBinFile | Init.System.IO | [
"Pure.pure",
"IO.FS.Handle.read",
"UInt64.toUSize",
"ByteArray.emptyWithCapacity",
"System.FilePath.metadata",
"Monad.toApplicative",
"IO",
"IO.FS.Handle.readBinToEndInto",
"instOfNatNat",
"instMonadEIO",
"Applicative.toPure",
"GT.gt",
"IO.FS.Metadata",
"IO.FS.Handle.mk",
"IO.FS.Mode.rea... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.edgeSet_subgraphOfAdj._simp_1_1 | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"eq_comm",
"propext",
"Eq"
] | false |
Std.ExtDTreeMap.keyAtIdx._proof_1 | Std.Data.ExtDTreeMap.Basic | [
"Std.ExtDTreeMap.mk",
"Std.DTreeMap",
"Ordering",
"Eq.rec",
"Std.TransCmp",
"Std.ExtDTreeMap.entryAtIdx._proof_1",
"Std.DTreeMap.Equiv.keyAtIdx_eq",
"Nat",
"LT.lt",
"Std.ExtDTreeMap",
"Std.ExtDTreeMap.size",
"Std.DTreeMap.Equiv",
"instLTNat",
"Std.ExtDTreeMap.entryAtIdx._proof_2",
"Eq",
... | false |
Lean.Environment.PromiseCheckedResult._sizeOf_inst | Lean.Environment | [
"Lean.Environment.PromiseCheckedResult._sizeOf_1",
"SizeOf.mk",
"Lean.Environment.PromiseCheckedResult",
"SizeOf"
] | false |
Module.End.mem_invtSubmodule_adjoint_iff | Mathlib.Analysis.InnerProductSpace.Adjoint | [
"ContinuousLinearMap.adjointAux._proof_2",
"Sublattice",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Submodule",
"complete_of_proper",
"CompleteSpace",
"NormedSpace.toIsBoundedSMul",
"Submodule.HasOrthogonalProjection.ofCompleteSpace",
"NormedAddCommGroup.toMetricSpa... | true |
Mathlib.Notation3.matchForall | Mathlib.Util.Notation3 | [
"guard",
"Pure.pure",
"Lean.PrettyPrinter.Delaborator.withBindingBodyUnusedName'",
"Mathlib.Notation3.Matcher",
"Lean.PrettyPrinter.Delaborator.instMonadReaderOfSubExprDelabM",
"Lean.PrettyPrinter.Delaborator.Context",
"Mathlib.Notation3.MatchState",
"Lean.Syntax",
"ReaderT.instMonad",
"Lean.Prett... | true |
_private.Mathlib.LinearAlgebra.Complex.Module.0.skewAdjoint.negISMul._simp_2 | Mathlib.LinearAlgebra.Complex.Module | [
"Membership.mem",
"StarAddMonoid.toInvolutiveStar",
"AddSubgroup",
"AddGroup",
"AddGroup.toSubNegMonoid",
"selfAdjoint",
"AddSubgroup.instSetLike",
"propext",
"selfAdjoint.mem_iff",
"StarAddMonoid",
"InvolutiveStar.toStar",
"SubNegMonoid.toAddMonoid",
"Eq",
"SetLike.instMembership",
"Sta... | false |
CategoryTheory.Abelian.SpectralObject.dShortComplex_f | Mathlib.Algebra.Homology.SpectralObject.Homology | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.SpectralObject.E",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.dShortComplex._auto_7",
"CategoryTheory.Abelian",
"CategoryTheory.Abelian.SpectralObject",
"Int",
"CategoryTheory.Abelian.... | true |
CategoryTheory.PreOneHypercover.IsStronglySheafFor.isLimitMultifork._proof_3 | Mathlib.CategoryTheory.Sites.Hypercover.SheafOfTypes | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.Limits.MulticospanIndex.sections.ext",
"CategoryTheory.PreOneHypercover.IsStronglySheafFor.amalgamate",
"CategoryTheory.PreOneHypercover",
"CategoryTheory.PreOneHypercover.I₁",
"CategoryTheory.PreOneHyper... | false |
Lean.Grind.IntInterval.ci.inj | Init.Grind.ToInt | [
"Int",
"Lean.Grind.IntInterval.ci.noConfusion",
"Lean.Grind.IntInterval.ci",
"Eq",
"Lean.Grind.IntInterval"
] | true |
Matrix.reindexLinearEquiv._proof_2 | Mathlib.LinearAlgebra.Matrix.Reindex | [
"instHSMul",
"Matrix.module",
"DistribMulAction.toDistribSMul",
"Matrix",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Equiv",
"DistribSMul.toSMulZeroClass",
"Matrix.addCommMonoid",
"Equiv.toFun",
"AddCommMonoid",
"AddZero.toZero",
"Semiring.toMonoid",
"Matrix.reindex",
"Semiri... | false |
ProfiniteAddGrp.instHasForget₂ContinuousAddMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteAddGrpCatAddMonoidHomCarrier.eq_1 | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"ProfiniteAddGrp.Hom.hom",
"CategoryTheory.HasForget₂.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ContinuousAddMonoidHom",
"AddGrpCat.instCategory",
"CategoryTheory.Functor.mk",
"AddMonoid.toAddZeroClass",
"ProfiniteAddGrp.instHasForget₂ContinuousAddMonoidHomCarrierToTopTotallyDisc... | true |
_private.Mathlib.MeasureTheory.Function.LocallyIntegrable.0.MeasureTheory.LocallyIntegrableOn.norm.match_1_1 | Mathlib.MeasureTheory.Function.LocallyIntegrable | [
"Filter.instMembership",
"MeasureTheory.Measure",
"nhdsWithin",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"SeminormedAddGroup.toContinuousENorm",
"MeasureTheory.IntegrableOn",
"And.casesOn",
"MeasureTheory.IntegrableAtFilter",
"MeasurableSpace",
"SeminormedAddCommGroup.toSeminormedAd... | false |
CommRingCat.Colimits.Relation.left_distrib | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"CommRingCat",
"CommRingCat.instCategory",
"CategoryTheory.SmallCategory",
"CommRingCat.Colimits.Relation",
"CommRingCat.Colimits.Prequotient.add",
"CommRingCat.Colimits.Prequotient.mul",
"CommRingCat.Colimits.Prequotient",
"CommRingCat.Colimits.Relation.left_distrib"
] | true |
PrimeSpectrum.height_eq_orderHeight | Mathlib.RingTheory.Ideal.Height | [
"CommRing",
"PrimeSpectrum.isPrime",
"PartialOrder.toPreorder",
"PrimeSpectrum.instPartialOrder",
"CommRing.toCommSemiring",
"ENat",
"PrimeSpectrum",
"Order.height",
"Ideal.height",
"Eq",
"PrimeSpectrum.asIdeal",
"_private.Mathlib.RingTheory.Ideal.Height.0.Ideal.height_eq_primeHeight"
] | true |
Filter.Germ.instPow | Mathlib.Order.Filter.Germ.Basic | [
"Pow",
"Pow.mk",
"HPow.hPow",
"Filter.Germ",
"Filter.Germ.map",
"instHPow",
"Filter"
] | true |
CategoryTheory.Cat.FreeRefl.instUniqueHom | Mathlib.CategoryTheory.Category.ReflQuiv | [
"Inhabited.default",
"CategoryTheory.Cat.FreeRefl.instCategory",
"Unique.mk",
"Quiver.Hom",
"CategoryTheory.catToReflQuiver",
"Unique",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"CategoryTheory.Cat.FreeRefl.instUniqueHom._proof_1",
"CategoryTheory.Quotient.as",
"CategoryTheor... | true |
LinearIndepOn.id_insert | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"LinearIndepOn.insert",
"Membership.mem",
"Eq.rec",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"id",
"Insert.insert",
"Set.instInsert",
"Submodule.setLike",
"Submodule.span",
"DivisionSemiring.toSemiring",
"Set.image",
"DivisionRing",
... | true |
FreeAbelianGroup.support_of | Mathlib.Algebra.FreeAbelianGroup.Finsupp | [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Finsupp.support_single",
"FreeAbelianGroup.support",
"Int.instNeZeroOfNatOfNat",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"FreeAbelianGroup.support.eq_1",
"AddGroupWithOne.toAddMonoidWithOne",
"AddCommGroup.toAddGroup",
"Finsupp.support",
"AddZ... | true |
Affine.Simplex.independent | Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | [
"Affine.Simplex.points",
"AffineIndependent",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Affine.Simplex",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"AddTorsor",
"instAddNat",
"Module",
"OfNat.ofNat",
"Fin",
"Ring.toSemiring",
"Ring"
] | true |
OreLocalization.instCommGroupWithZeroNonZeroDivisors._proof_1 | Mathlib.RingTheory.OreLocalization.NonZeroDivisors | [
"GroupWithZero.div_eq_mul_inv",
"Nontrivial",
"GroupWithZero.toMonoidWithZero",
"Semigroup.toMul",
"instHDiv",
"GroupWithZero.toInv",
"HMul.hMul",
"MulZeroClass.toMul",
"OreLocalization.OreSet",
"OreLocalization",
"nonZeroDivisors",
"GroupWithZero.toDiv",
"HDiv.hDiv",
"CommMonoidWithZero.t... | false |
Std.HashMap.Equiv.symm | Std.Data.HashMap.Lemmas | [
"_private.Std.Data.HashMap.Lemmas.0.Std.HashMap.Equiv.symm.match_1_1",
"Std.DHashMap.Equiv",
"Std.DHashMap.Equiv.symm",
"Std.HashMap",
"Std.HashMap.Equiv.mk",
"Std.HashMap.Equiv",
"Hashable",
"Std.HashMap.inner",
"BEq"
] | true |
Mathlib.Tactic.Ring.Common.ExtractCoeff._sizeOf_inst | Mathlib.Tactic.Ring.Common | [
"Lean.Expr.const",
"Mathlib.Tactic.Ring.Common.ExtractCoeff._sizeOf_1",
"Lean.Level",
"Qq.Quoted",
"SizeOf.mk",
"Mathlib.Tactic.Ring.Common.ExtractCoeff",
"SizeOf",
"Lean.Name.mkStr1",
"List.nil"
] | false |
CategoryTheory.Limits.CreatesFiniteLimits.mk._flat_ctor | Mathlib.CategoryTheory.Limits.Preserves.Creates.Finite | [
"CategoryTheory.Limits.CreatesFiniteLimits.mk",
"CategoryTheory.Functor",
"CategoryTheory.Limits.CreatesFiniteLimits.createsFiniteLimits._autoParam",
"CategoryTheory.CreatesLimitsOfShape",
"CategoryTheory.SmallCategory",
"autoParam",
"CategoryTheory.FinCategory",
"CategoryTheory.Limits.CreatesFiniteLi... | false |
_private.Init.Data.Nat.Bitwise.Lemmas.0.Nat.eq_0_of_lt | Init.Data.Nat.Bitwise.Lemmas | [
"instPowNat",
"_private.Init.Data.Nat.Bitwise.Lemmas.0.Nat.eq_0_of_lt_one",
"instOfNatNat",
"instNatPowNat",
"Iff",
"HPow.hPow",
"Nat",
"LT.lt",
"instHPow",
"instLTNat",
"OfNat.ofNat",
"Eq"
] | true |
_private.Std.Sync.Channel.0.Std.CloseableChannel.Consumer.noConfusion | Std.Sync.Channel | [
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Consumer",
"HEq.refl",
"Std.Internal.IO.Async.Waiter",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Consumer.casesOn",
"IO.Promise",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Consumer.noConfusionType",
"... | false |
TensorProduct.quotTensorEquivQuotSMul._proof_1 | Mathlib.LinearAlgebra.TensorProduct.Quotient | [
"LinearMap.id",
"Eq.mpr",
"Submodule",
"Submodule.smul_eq_map₂",
"RingHomSurjective.ids",
"CommRing",
"instHSMul",
"TensorProduct.mapIncl",
"Semiring.toModule",
"Submodule.topEquiv",
"LinearEquiv.range_comp",
"TensorProduct.map₂_eq_range_lift_comp_mapIncl",
"congrArg",
"CommSemiring.toSemi... | false |
List.forall₂_cons_left_iff | Mathlib.Data.List.Forall2 | [
"List.Forall₂.cons",
"_private.Mathlib.Data.List.Forall2.0.List.forall₂_cons_left_iff.match_1_1",
"Exists",
"_private.Mathlib.Data.List.Forall2.0.List.forall₂_cons_left_iff.match_1_3",
"List.cons",
"List",
"And",
"Iff",
"And.intro",
"Iff.intro",
"Exists.intro",
"List.Forall₂",
"Eq",
"rfl"
... | true |
Polynomial.expand_monomial | Mathlib.Algebra.Polynomial.Expand | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Semiring.toModule",
"SemilinearMapClass.toMulActionSemiHomClass",
"AlgHom.algHomClass",
"HMul.hMul",
"NonUnitalAlgHomClass.instLinearMapClass",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"ins... | true |
Batteries.RBNode.toList_node | Batteries.Data.RBMap.Lemmas | [
"Batteries.RBNode",
"Eq.mpr",
"Batteries.RBNode.toList",
"congrArg",
"id",
"Batteries.RBNode.toList.eq_1",
"List.cons",
"instHAppendOfAppend",
"List",
"Batteries.RBNode.foldr_cons",
"Batteries.RBNode.foldr",
"Batteries.RBColor",
"Eq.refl",
"List.instAppend",
"Batteries.RBNode.node",
"E... | true |
SFinKer.instDeterministicComul | Mathlib.Probability.Kernel.Category.SFinKer | [
"CategoryTheory.ComonObj.comul",
"SFinKer.instMonoidalCategory",
"SFinKer.deterministic_deterministic",
"ProbabilityTheory.Kernel.instIsDeterministicDeterministic",
"SFinKer",
"Measurable.prodMk",
"Prod.mk",
"ProbabilityTheory.Kernel.deterministic",
"SFinKer.str",
"ProbabilityTheory.Kernel.isMarko... | true |
Matrix.isSymm_transpose_iff._simp_1 | Mathlib.LinearAlgebra.Matrix.Symmetric | [
"Matrix",
"Matrix.transpose",
"propext",
"Matrix.IsSymm",
"Eq",
"Matrix.isSymm_transpose_iff"
] | false |
_private.Lean.Elab.PreDefinition.FixedParams.0.Lean.Elab.FixedParamPerm.instantiateLambda.go._f | Lean.Elab.PreDefinition.FixedParams | [
"Pure.pure",
"Option.isNone",
"List.all",
"instMonadControlTOfPure",
"String",
"Lean.Meta.State",
"panicWithPosWithDecl",
"Option.some",
"_private.Lean.Elab.PreDefinition.FixedParams.0.Lean.Elab.FixedParamPerm.instantiateForall.match_1",
"Lean.Meta.lambdaBoundedTelescope",
"Lean.Expr",
"Lean.M... | false |
Std.Do.Spec.IterM.forIn_mapWithPostcondition | Std.Do.Triple.SpecLemmas | [
"Eq.mpr",
"LawfulMonadLiftT",
"congrArg",
"Std.IterM.forIn_mapWithPostcondition",
"Monad.toApplicative",
"Std.Iterators.Types.Map.instIterator",
"Std.Do.PostCond",
"MonadLiftT.monadLift",
"Std.Do.Assertion",
"Std.IteratorLoop",
"Std.Iterators.Finite",
"Std.Do.WPMonad.toWP",
"id",
"Std.Do.P... | true |
SimpleGraph.chromaticNumber_mono_of_hom | Mathlib.Combinatorics.SimpleGraph.Coloring.VertexColoring | [
"SimpleGraph.Colorable.of_hom",
"SimpleGraph.chromaticNumber_le_of_forall_imp",
"LE.le",
"instLEENat",
"SimpleGraph",
"Nat",
"ENat",
"SimpleGraph.Hom",
"SimpleGraph.chromaticNumber"
] | true |
NNReal.sqrt_pos_of_pos | Mathlib.Data.Real.Sqrt | [
"Iff.mpr",
"Preorder.toLT",
"NNReal.sqrt_pos",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderIso",
"NNReal",
"NNReal.instZero",
"NNReal.sqrt",
"NNReal.instPartialOrder",
"instFunLikeOrderIso",
"LT.lt",
"Zero.toOfNat0",
"OfNat.ofNat",
"DFunLike.coe"
] | true |
FP.ofRatUp | Mathlib.Data.FP.Basic | [
"Nat.Coprime",
"FP.nextUp",
"Rat",
"FP.Float.neg",
"instDecidableEqBool",
"FP.Float.zero",
"Ne",
"instOfNatNat",
"Int",
"FP.FloatCfg",
"Nat.cast",
"Prod.fst",
"Subtype.mk",
"FP.Float",
"Bool.true",
"Nat.pos_of_ne_zero",
"instOfNat",
"Nat.succPNat",
"Nat",
"FP.ofPosRatDn",
"LT... | true |
Lean.Meta.Grind.SplitStatus._sizeOf_inst | Lean.Meta.Tactic.Grind.Split | [
"Lean.Meta.Grind.SplitStatus._sizeOf_1",
"Lean.Meta.Grind.SplitStatus",
"SizeOf.mk",
"SizeOf"
] | false |
Lean.IR.modifyJPsM | Lean.Compiler.IR.Basic | [
"Pure.pure",
"Lean.IR.FnBody.jdecl",
"Monad.toApplicative",
"Lean.IR.Param",
"Applicative.toPure",
"Lean.IR.FnBody",
"Array",
"Lean.IR.JoinPointId",
"Monad.toBind",
"_private.Lean.Compiler.IR.Basic.0.Lean.IR.modifyJPs.match_1",
"Bind.bind",
"Monad",
"Array.mapM"
] | true |
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