name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.LinearAlgebra.Matrix.Notation.0.Matrix.diagonal_fin_three._simp_1_2 | Mathlib.LinearAlgebra.Matrix.Notation | [
"instNeZeroNatHAdd_1",
"Fin.succ",
"Fin.instOfNat",
"instOfNatNat",
"instHAdd",
"And",
"Fin.forall_fin_succ",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"propext",
"instAddNat",
"OfNat.ofNat",
"Fin",
"Eq"
] | false |
ContinuousMultilinearMap.smulRightL._proof_8 | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"NormedCommRing.toSeminormedCommRing",
"SeminormedAddCommGroup",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"ContinuousSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toU... | false |
Topology.RelCWComplex.finiteType_mkFiniteType | Mathlib.Topology.CWComplex.Classical.Finite | [
"Real",
"pseudoMetricSpacePi",
"ChainCompletePartialOrder.instOfCompleteLattice",
"outParam",
"Pi.topologicalSpace",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Real.instZero",
"PartialEquiv.target",
"PartialEquiv",
"Set.univ",
"Finite",
"Set.PairwiseDisjoint",
"PseudoMetricSpace.toU... | true |
TopHomClass.rec | Mathlib.Order.Hom.Bounded | [
"TopHomClass",
"TopHomClass.mk",
"Top.top",
"Eq",
"DFunLike.coe",
"Top",
"FunLike"
] | false |
List.getLast_range' | Init.Data.List.Nat.Range | [
"List.getLast",
"False",
"List.getLast?",
"congrArg",
"False.elim",
"List.range'",
"Nat.add_eq_zero_iff._simp_1",
"HSub.hSub",
"Option.some",
"Eq.mp",
"not_true_eq_false",
"instSubNat",
"Ne",
"instOfNatNat",
"Nat.casesAuxOn",
"Option.none",
"List",
"instHAdd",
"And",
"instHSub"... | true |
AddLocalization.r'._proof_4 | Mathlib.GroupTheory.MonoidLocalization.Basic | [
"Std.Commutative",
"Eq.mpr",
"AddMonoid.toAddSemigroup",
"Lean.Data.AC.Expr.var",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddCommMagma.to_isCommutative",
"IsAddCommutative.is_comm",
"Lean.Data.AC.Variable",
"Lean.Data.AC.Context.mk",
"Option.some",
"Membership.mem",
"AddZeroClass.toAddZero"... | false |
_private.Lean.Server.FileWorker.0.Lean.Server.FileWorker.reportSnapshots.match_1 | Lean.Server.FileWorker | [
"Lean.Syntax.Range",
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
CochainComplex.mkHomAux | Mathlib.Algebra.Homology.HomologicalComplex | [
"PSigma.snd",
"CategoryTheory.Limits.HasZeroMorphisms",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.mkHomAux._f",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.brecOn",
"Nat.instAddCancelCommMonoid",
"instOfNat... | true |
IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation' | Mathlib.RingTheory.DedekindDomain.AdicValuation | [
"Int.instAddCommGroup",
"Int.instAddCommMonoid",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"UniformSpace.Completion.coe'",
"Multiplicative.linearOrder",
"Int.instIsStrictOrderedRing",
"CommRing",
"Int.instLinearOrder",
"IsFractionRing",
"RingEquiv.instEquivLike",
"WithV... | true |
Equiv.toHomeomorphOfContinuousClosed_symm_apply | Mathlib.Topology.Homeomorph.Defs | [
"Continuous",
"Equiv.instEquivLike",
"Equiv",
"IsClosedMap",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Equiv.toHomeomorphOfContinuousClosed",
"Homeomorph.symm",
"Homeomorph",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
Matroid.eRk_le_encard | Mathlib.Combinatorics.Matroid.Rank.ENat | [
"Eq.mpr",
"Set.encard",
"congrArg",
"Matroid.IsBasis'",
"Exists",
"id",
"Matroid.IsBasis'.eRk_eq_encard",
"LE.le",
"instLEENat",
"Set.encard_mono",
"Exists.casesOn",
"ENat",
"Matroid.eRk",
"Matroid.IsBasis'.subset",
"Matroid.exists_isBasis'",
"Eq",
"Matroid",
"Set"
] | true |
FintypeCat.botTopology | Mathlib.Topology.Category.Profinite.Basic | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"Finite",
"OrderBot.toBot",
"FintypeCat",
"PartialOrder.toPreorder",
"Preorder.toLE",
"TopologicalSpace.instCompleteLattice",
"CompleteLattice.toBoundedOrder",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"Bot.bot",
"TopologicalS... | true |
Std.DTreeMap.Internal.Impl.toListModel_inner | Std.Data.DTreeMap.Internal.Def | [
"Std.DTreeMap.Internal.Impl.inner",
"List.cons",
"instHAppendOfAppend",
"List",
"Nat",
"Std.DTreeMap.Internal.Impl.toListModel",
"Sigma.mk",
"List.instAppend",
"Eq",
"Std.DTreeMap.Internal.Impl",
"HAppend.hAppend",
"Sigma",
"rfl"
] | true |
instCompleteAtomicBooleanAlgebraLanguage | Mathlib.Computability.Language | [
"SemilatticeSup.mk",
"instCompleteAtomicBooleanAlgebraLanguage._proof_18",
"LT.mk",
"Lattice.toSemilatticeSup",
"instCompleteAtomicBooleanAlgebraLanguage._proof_21",
"instCompleteAtomicBooleanAlgebraLanguage._aux_34",
"PartialOrder.toPreorder",
"instCompleteAtomicBooleanAlgebraLanguage._aux_32",
"Co... | true |
Real.toNNReal_le_ofNat._simp_1 | Mathlib.Data.NNReal.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.instLE",
"Real",
"Real.toNNReal_le_ofNat",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddMonoidWithOne.toNatCast",
"NNReal",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"LE.le",
"Nat.cast",
"NNReal.instPartialOrder",
"Nat",
"propext",
"NN... | false |
NonUnitalStarAlgebra.range_eq_top | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"Lattice.toSemilatticeSup",
"instSMulOfMul",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"NonUnitalStarAlgebra.instCompleteLatticeNonUnitalStarSubalgebra",
"AddZ... | true |
_private.Mathlib.Analysis.Analytic.Within.0.analyticWithinAt_of_singleton_mem._simp_1_7 | Mathlib.Analysis.Analytic.Within | [
"Set.univ",
"Membership.mem",
"True",
"Set.mem_univ",
"eq_true",
"Eq",
"Set.instMembership",
"Set"
] | false |
IsSepClosed.of_exists_root | Mathlib.FieldTheory.IsSepClosed | [
"CommMonoidWithZero.toCommMonoid",
"Iff.mpr",
"Units.val",
"Eq.mpr",
"inv_eq_zero._simp_1",
"Polynomial.C",
"Polynomial.eval",
"GroupWithZero.toMonoidWithZero",
"RingHom.instRingHomClass",
"False",
"IsDomain.to_noZeroDivisors",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"DivisionCommMo... | true |
Subtype.isEmpty_of_false | Mathlib.Logic.IsEmpty.Defs | [
"Subtype",
"IsEmpty",
"IsEmpty.mk",
"Subtype.val",
"Not",
"Subtype.property"
] | true |
ContinuousLinearMap.range_coeFn_eq | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic | [
"Set.ext",
"Continuous",
"ContinuousLinearMap.mk",
"ContinuousLinearMap.funLike",
"setOf",
"LinearMap.instFunLike",
"RingHom",
"Membership.mem",
"ContinuousLinearMap.toLinearMap",
"Set.instInter",
"LinearMap",
"AddCommMonoid",
"Inter.inter",
"And.casesOn",
"ContinuousLinearMap",
"Topol... | true |
Turing.PartrecToTM2.instDecidableEqCont'.decEq._proof_5 | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.Cont'.ctorIdx",
"Turing.PartrecToTM2.Cont'",
"False",
"False.elim",
"noConfusion_of_Nat",
"Turing.PartrecToTM2.Cont'.comp",
"Turing.PartrecToTM2.Cont'.halt",
"Eq",
"Not",
"Turing.ToPartrec.Code"
] | false |
Lean.CollectMVars.State.rec | Lean.Util.CollectMVars | [
"Lean.MVarId",
"Lean.ExprSet",
"Array",
"Lean.CollectMVars.State",
"Lean.CollectMVars.State.mk"
] | false |
SemidirectProduct.rightHom_eq_right | Mathlib.GroupTheory.SemidirectProduct | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"SemidirectProduct",
"MulAut.instGroup",
"SemidirectProduct.right",
"Group",
"MulAut",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"SemidirectProduct.instGroup",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"SemidirectProduct.ri... | true |
AlgebraicGeometry.StructureSheaf.sectionsSubmodule._proof_5 | Mathlib.AlgebraicGeometry.StructureSheaf | [
"CommRing",
"instSMulOfMul",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra.toSMul",
"Algebra.id",
"instDistribOfSemiring",
"CommRing.toCommSemiring",
"Distrib.toMul"
] | false |
_private.Lean.Meta.Basic.0.Lean.Meta.lambdaMetaTelescope.process.match_1 | Lean.Meta.Basic | [
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Expr.lam",
"Lean.Name",
"_private.Lean.Meta.Basic.0.Lean.Meta.lambdaMetaTelescope.process._sparseCasesOn_1",
"Lean.BinderInfo",
"Lean.Expr.ctorIdx"
] | false |
MvPolynomial.degrees_one | Mathlib.Algebra.MvPolynomial.Degrees | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"CommSemiring.toSemiring",
"MvPolynomial.degrees_C",
"Multiset",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"CommSemiring",
"AddMonoidWithOne.toOne",
"AddMonoidAlgebra.zero",
"Nat",
"MvPolynomial",
"One.toOfNat1",
"Zero.toOfN... | true |
Real.not_summable_indicator_one_div_natCast | Mathlib.Analysis.PSeries | [
"Iff.mpr",
"zero_le",
"Real.instIsOrderedRing",
"div_le_div₀",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"summable_nat_add_iff",
"le_refl",
"Nat.instMulZeroClass",
"Real.partialOrder",
"Real",
"NeZero.mk",
"Set.indicator_apply",
"Preorder.toLT",
"instHDiv",
"Nat.instIsOrderedAddMonoid... | true |
CategoryTheory.Limits.biproduct.isLimit | Mathlib.CategoryTheory.Limits.Shapes.Biproducts | [
"CategoryTheory.Limits.biproduct.bicone",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.HasBiproduct",
"CategoryTheory.Limits.LimitBicone.isBilimit",
"CategoryTheory.Limits.Bicone.toCone",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.discreteCa... | true |
List.mergeSort_of_sorted | Init.Data.List.Sort.Lemmas | [
"List.Pairwise",
"Bool.true",
"List",
"List.mergeSort_of_pairwise",
"Bool",
"Eq",
"List.mergeSort"
] | true |
QuasispectrumRestricts.nonUnitalStarAlgHom | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict | [
"QuasispectrumRestricts.nonUnitalStarAlgHom._proof_9",
"QuasispectrumRestricts.nonUnitalStarAlgHom._proof_6",
"QuasispectrumRestricts.nonUnitalStarAlgHom._proof_16",
"Subtype.map",
"QuasispectrumRestricts.nonUnitalStarAlgHom._proof_1",
"QuasispectrumRestricts.nonUnitalStarAlgHom._proof_3",
"NonUnitalCom... | true |
_private.Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities.0.MvPolynomial.NewtonIdentities.disjoint_filter_pairs_lt_filter_pairs_eq | Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | [
"Eq.mpr",
"Preorder.toLT",
"lt_irrefl",
"congrArg",
"Finset",
"Disjoint",
"Eq.subst",
"Membership.mem",
"Finset.disjoint_filter",
"id",
"Finset.partialOrder",
"Prod.fst",
"Fintype",
"Finset.instSetLike",
"Nat.instPreorder",
"Nat",
"LT.lt",
"propext",
"Finset.card",
"Nat.decLt",... | true |
EStateM.Result.map_error | Batteries.Lean.EStateM | [
"EStateM.Result",
"EStateM.Result.map",
"EStateM.Result.error",
"Eq",
"rfl"
] | true |
DFinsupp.mkAddGroupHom | Mathlib.Data.DFinsupp.Defs | [
"AddGroup.toSubtractionMonoid",
"DFinsupp.mk",
"Finset",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddMonoidHom.mk",
"Set.Elem",
"DFinsupp.addZeroClass",
"DFinsupp.mkAddGroupHom._proof_2",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",... | true |
MonoidHom.noncommPiCoprod.eq_1 | Mathlib.GroupTheory.NoncommPiCoprod | [
"Monoid",
"MonoidHom.noncommPiCoprod._proof_3",
"MulOne.toOne",
"MonoidHom.instFunLike",
"Finset.univ",
"MonoidHom",
"Monoid.toMulOneClass",
"OneHom.mk",
"Commute",
"MulOne.toMul",
"MonoidHom.noncommPiCoprod._proof_1",
"MonoidHom.mk",
"Finset.noncommProd",
"Pi.mulOneClass",
"MulOneClass.... | true |
MulEquiv.monoidHomCongrLeftEquiv._proof_1 | Mathlib.Algebra.Group.Equiv.Basic | [
"Monoid",
"MulEquiv.instEquivLike",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"MonoidHom.ext",
"MulOne.toMul",
"MonoidHom.comp",
"MulEquiv.toMonoidHom",
"MulOneClass.toMulOne",
"True",
"eq_self",
"of_eq_true",
"MulEquiv",
"congrFun'",
"MulOneClass",
... | false |
Pi.involutiveNeg._proof_1 | Mathlib.Algebra.Group.Pi.Basic | [
"Pi.instNeg",
"neg_neg",
"funext",
"InvolutiveNeg",
"InvolutiveNeg.toNeg",
"Eq",
"Neg.neg"
] | false |
String.Slice.SplitIterator.instIteratorIdSubslice._proof_7 | Init.Data.String.Slice | [
"String.Slice.Subslice",
"False",
"Std.IterStep",
"String.Slice.SplitIterator.instIteratorIdSubslice.match_1",
"String.Slice.Pattern.SearchStep",
"String.Slice",
"Std.Iter.IsPlausibleSuccessorOf",
"Std.IterM.mk",
"String.Slice.SplitIterator.operating",
"String.Slice.Pattern.ToForwardSearcher",
"... | false |
Lean.Elab.Term.elabRunElab._regBuiltin.Lean.Elab.Term.elabRunElab.declRange_5 | Lean.Elab.BuiltinNotation | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"IO",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk",
"Lean.Name.mkStr4"
] | false |
abs_eq_abs | Mathlib.Algebra.Order.Group.Unbundled.Abs | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"abs_neg",
"SubtractionMonoid.toInvolutiveNeg",
"abs",
"congrArg",
"LinearOrder",
"DistribLattice.toLattice",
"neg_neg",
"neg_eq_iff_eq_neg",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"... | true |
_private.Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace.0.RestrictedProduct.continuous_dom_pi._simp_1_4 | Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace | [
"Filter.map",
"Filter.tendsto_map'_iff",
"Function.comp",
"Filter.Tendsto",
"propext",
"Eq",
"Filter"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKeyD_minKey!._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
UInt32.and_not_self | Init.Data.UInt.Bitwise | [
"instComplementUInt32",
"UInt32.toBitVec",
"BitVec.instAndOp",
"UInt32.toBitVec_and",
"BitVec.instOfNat",
"congrArg",
"_private.Init.Data.UInt.Bitwise.0.UInt32.and_not_self._simp_1_1",
"BitVec",
"UInt32.toBitVec_ofNat",
"instOfNatNat",
"BitVec.ofNat",
"Nat",
"BitVec.and_not_self",
"congr",... | true |
OrderRingHom | Mathlib.Algebra.Order.Hom.Ring | [
"NonAssocSemiring",
"OrderRingHom.mk",
"Preorder"
] | true |
Std.DTreeMap.Internal.Impl.minView.eq_1 | Std.Data.DTreeMap.Internal.Model | [
"Std.DTreeMap.Internal.Impl.Tree.mk",
"Std.DTreeMap.Internal.Impl.View",
"Std.DTreeMap.Internal.Impl.minView",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.size",
"instHAdd",
"Std.DTreeMap.Internal.Impl.BalancedAtRoot",
"HAdd.hAdd",
"Std.DTreeMap.Internal.Impl.leaf",
"Std.DTr... | true |
TopCat.effectiveEpiStructOfQuotientMap._proof_2 | Mathlib.Topology.Category.TopCat.EffectiveEpi | [
"Continuous",
"continuous_const",
"TopCat.str",
"TopCat.carrier",
"TopCat"
] | false |
NormedAddGroup.induced._proof_7 | Mathlib.Analysis.Normed.Group.Basic | [
"Real",
"NormedAddGroup.induced._proof_5",
"PseudoMetricSpace.toBornology",
"NormedAddGroup.induced._proof_6",
"Real.instZero",
"Dist.mk",
"uniformity",
"NormedAddGroup.toSeminormedAddGroup",
"NormedAddGroup.induced._proof_1",
"SeminormedAddGroup.induced._proof_11",
"PseudoMetricSpace.toUniformS... | false |
IsUltrametricDist.closedBall_openSubgroup._proof_3 | Mathlib.Analysis.Normed.Group.Ultra | [
"Norm.norm",
"Real.instLE",
"Real",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"SeminormedGroup",
"SeminormedGroup.toGroup",
"SeminormedGroup.toPseudoMetricSpace",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"LE.le",
"norm_inv'",
... | false |
OpenSubgroup.mem_inf._simp_2 | Mathlib.Topology.Algebra.OpenSubgroup | [
"OpenSubgroup",
"Group",
"OpenSubgroup.instSetLike",
"Membership.mem",
"OpenSubgroup.mem_inf",
"TopologicalSpace",
"And",
"propext",
"OpenSubgroup.instInfOpenSubgroup",
"Eq",
"SetLike.instMembership",
"Min.min"
] | false |
Std.DHashMap.Raw.contains_inter | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.inter",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Internal.Raw.inter_eq",
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.contains",
"Std.DHashMap.Raw.instInterOfBEqOfHashable",
"id",
"Bool.and",
"instOfNatNat",
"Std.D... | true |
_private.Mathlib.Algebra.DirectSum.Basic.0.DirectSum.id._proof_3 | Mathlib.Algebra.DirectSum.Basic | [
"Inhabited.default",
"False",
"AddMonoidHom.instAddMonoidHomClass",
"eq_false",
"instAddCommMonoidDirectSum",
"congrArg",
"HEq.refl",
"Unique",
"AddMonoid.toAddZeroClass",
"Classical.byContradiction",
"DFunLike.coe.hcongr_6",
"AddMonoidHom.id",
"AddZeroClass.toAddZero",
"Eq.mp",
"map_add... | false |
Lean.Firefox.ProfileMeta.sampleUnits._default | Lean.Util.Profiler | [
"id",
"Lean.Firefox.SampleUnits",
"Lean.Firefox.SampleUnits.mk"
] | false |
Lean.EffectiveImport.mk.noConfusion | Lean.Environment | [
"Lean.EffectiveImport",
"Lean.Import",
"id",
"Lean.EffectiveImport.noConfusion",
"Lean.EffectiveImport.mk",
"Eq",
"Lean.IRPhases"
] | false |
Set.Ioi_insert | Mathlib.Order.Interval.Set.Basic | [
"Set.ext",
"Set.Ioi",
"Preorder.toLT",
"Set.Ici",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Insert.insert",
"LE.le",
"Set.instInsert",
"le_iff_eq_or_lt'",
"LT.lt",
"Or",
"Eq",
"Iff.symm",
"Set"
] | true |
Lean.Compiler.LCNF.MonadCodeBind.recOn | Lean.Compiler.LCNF.Bind | [
"Lean.Compiler.LCNF.MonadCodeBind.rec",
"Lean.FVarId",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Code",
"Lean.Compiler.LCNF.MonadCodeBind.mk",
"Lean.Compiler.LCNF.MonadCodeBind"
] | false |
CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit._proof_1 | Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty | [
"Iff.mpr",
"Order.IsSuccLimit.succ_lt_iff",
"Eq.mpr",
"lt_of_le_of_lt",
"le_refl",
"Preorder.toLT",
"Order.succ",
"CategoryTheory.SmallObject.SuccStruct",
"congrArg",
"LinearOrder",
"WellFoundedLT",
"PartialOrder.toPreorder",
"CategoryTheory.SmallObject.SuccStruct.toSuccArrow",
"CategoryTh... | false |
_private.Mathlib.MeasureTheory.Measure.Restrict.0.MeasureTheory.ae_restrict_iff₀._simp_1_3 | Mathlib.MeasureTheory.Measure.Restrict | [
"and_comm",
"And",
"propext",
"Eq"
] | false |
CategoryTheory.DifferentialObject.Hom.mk.congr_simp | Mathlib.CategoryTheory.DifferentialObject | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.DifferentialObject.Hom.mk",
"CategoryTheory.shiftFunctor",
"Eq.rec",
"CategoryTheory.DifferentialObject.obj",
"CategoryTheory.Functor.map",
"CategoryTheory.DifferentialObject.Hom",
"Ad... | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.alterKey_cons_perm.match_1.splitter | Std.Data.Internal.List.Associative | [
"Option.some",
"Option.none",
"Unit",
"Std.Internal.List.alterKey_cons_perm.match_1",
"Option"
] | true |
ComplexShape.Embedding.extendFunctor_obj | Mathlib.Algebra.Homology.Embedding.Extend | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"ComplexShape.Embedding.extendFunctor",
"HomologicalComplex",
"HomologicalComplex.extend",
"ComplexShape",
"CategoryTheory.Limits.HasZeroObject",
"ComplexShape.Embedding",
"Eq.refl",
"Eq",
"CategoryTheory.Functor.obj",
... | true |
GradedAlgebra.algebraMap_apply | Mathlib.RingTheory.GradedAlgebra.TensorProduct | [
"Submodule",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"Algebra",
"RingHom",
"Membership.mem",
"AddZeroClass.toAddZero",
"Algebra.toModule",
"Subtype",
"AddCommMonoid",
"Com... | true |
WittVector.truncateFun_add | Mathlib.RingTheory.WittVector.Truncated | [
"Eq.mpr",
"CommRing",
"Nat.Prime",
"congrArg",
"TruncatedWittVector.instAdd",
"Fact",
"id",
"WittVector.init_add",
"TruncatedWittVector.out_injective",
"WittVector.init",
"instHAdd",
"WittVector",
"WittVector.truncateFun",
"HAdd.hAdd",
"Nat",
"WittVector.instAdd",
"TruncatedWittVecto... | true |
MessageActionItem.title | Lean.Data.Lsp.Window | [
"String",
"MessageActionItem"
] | true |
Pi.vaddAssocClass | Mathlib.Algebra.Group.Action.Pi | [
"Pi.instVAdd",
"vadd_assoc",
"VAdd",
"HVAdd.hVAdd",
"funext",
"VAddAssocClass.mk",
"instHVAdd",
"VAddAssocClass"
] | true |
instPseudoEMetricSpaceULift | Mathlib.Topology.EMetricSpace.Defs | [
"ULift",
"PseudoEMetricSpace.induced",
"PseudoEMetricSpace",
"ULift.down"
] | true |
Action.forget._proof_2 | Mathlib.CategoryTheory.Action.Basic | [
"Monoid",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"id",
"Action",
"Action.instCategory",
"CategoryTheory.CategoryStruct.comp",
"Eq.refl",
"Action.V",
"CategoryTheory.Category.toCategoryStruct",
"Action.Hom.hom",
"Eq",
"CategoryTheory.Category"
] | false |
_private.Mathlib.Algebra.Polynomial.FieldDivision.0.Polynomial.dvd_C_mul.match_1_1 | Mathlib.Algebra.Polynomial.FieldDivision | [
"Polynomial.C",
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"semigroupDvd",
"RingHom",
"SemigroupWithZero.toSemigroup",
"NonUnitalSemiring.toSemigroupWithZero",
"Field.toSemifield",
"Field.toCommRing",
"Polynomial",
"NonUnitalCommSemiring.toNonUnitalSemiring",
... | false |
Std.Sat.AIG.denote._proof_4 | Std.Sat.AIG.Basic | [
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.Fanin.gate",
"Array",
"And",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"Nat.decLt",
"_private.Std.Sat.AIG.Basic.0.Std.Sat.AIG.denote._proof_3",
"instLTNat",
"Std.Sat.AIG.Fanin",
"Array.size",
"Not"
] | false |
Antitone.lowerBounds_range_comp_tendsto_atTop | Mathlib.Order.Filter.AtTopBot.Tendsto | [
"Equiv.instEquivLike",
"OrderDual.ofDual",
"lowerBounds",
"Filter.NeBot",
"Preorder.toLE",
"Function.comp",
"Equiv",
"Monotone.lowerBounds_range_comp_tendsto_atBot",
"Filter.atTop",
"Antitone",
"Antitone.dual_left",
"Filter.Tendsto",
"Set.range",
"OrderDual",
"OrderDual.instPreorder",
... | true |
CategoryTheory.ProjectiveResolution.isoExt._proof_4 | Mathlib.CategoryTheory.Abelian.Ext | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ProjectiveResolution.isoExt._proof_1",
"Nat.instOne",
"ModuleCat",
"CategoryTheory.Linear",
"ChainComplex.linearYonedaObj",
"CategoryTheory.ShortComplex.HasHomology",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMo... | false |
Lean.Meta.Rewrites.RwDirection._sizeOf_inst | Lean.Meta.Tactic.Rewrites | [
"Lean.Meta.Rewrites.RwDirection",
"Lean.Meta.Rewrites.RwDirection._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
Int.natAbs_inj_of_nonpos_of_nonneg | Mathlib.Data.Int.Lemmas | [
"Int.instAddCommGroup",
"NegZeroClass.toNeg",
"congrArg",
"SemilatticeInf.toPartialOrder",
"Eq.mp",
"Int.natAbs_inj_of_nonneg_of_nonneg",
"Int.instNegInt",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"LE.le",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
... | true |
LinearMap.BilinForm.Isometry.rec | Mathlib.LinearAlgebra.BilinearForm.Isometry | [
"Semiring.toModule",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"LinearMap.toAddHom",
"LinearMap.module",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"LinearMap.addCom... | false |
Nat.coprime_of_dvd' | Mathlib.Data.Nat.Prime.Basic | [
"Nat.Coprime",
"Nat.one_pos",
"Nat.Prime",
"Dvd.dvd",
"Nat.Prime.one_lt",
"Nat.coprime_of_dvd",
"instOfNatNat",
"Nat.instDvd",
"Nat.instPreorder",
"Nat",
"not_le_of_gt",
"OfNat.ofNat",
"Nat.le_of_dvd"
] | true |
Set.univ_inter | Mathlib.Data.Set.Basic | [
"Set.univ",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"top_inf_eq",
"Set.instInter",
"Set.instDistribLattice",
"Inter.inter",
"Set.instBoundedOrder",
"BoundedOrder.toOrderTop",
"Eq",
"Lattice.toSemilatticeInf",
"Set"
] | true |
_private.Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula.0.ModularForm.sturm_bound_levelOne_nat._simp_1_1 | Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula | [
"DFunLike.ext_iff",
"DFunLike",
"propext",
"Eq",
"DFunLike.coe"
] | false |
PreTilt.mk_comp_untilt_eq_coeff_zero | Mathlib.RingTheory.Perfectoid.Untilt | [
"CommRing",
"Nat.Prime",
"MonoidHom.instFunLike",
"Semiring.toModule",
"MonoidHom",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"ModP",
"AddGroupWithOne.toAddMonoidWithOne",
"IsUnit",
"RingHom",
"Function.comp",
"Fact",
"Perfection.mk_comp_teichmuller'",
"PreTilt.coeff",
"Set.instS... | true |
_private.Mathlib.NumberTheory.Bernoulli.0.Bernoulli.pIntegral._proof_1 | Mathlib.NumberTheory.Bernoulli | [
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"Int.instIsStrictOrderedRing",
"instConditionallyCompleteLinearOrder",
"Int.instLinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Multiplicative.commMonoid",
"IsStrictOrderedRing.toIsOrdered... | false |
Topology.WithScott.instPreorder | Mathlib.Topology.Order.ScottTopology | [
"Topology.WithScott",
"Preorder"
] | true |
Array.all_eq_false' | Init.Data.Array.Lemmas | [
"Eq.mpr",
"Array.all",
"Array.all_eq_true'",
"congrArg",
"Bool.eq_false_iff",
"Array.instMembership",
"Membership.mem",
"Exists",
"id",
"Ne",
"instOfNatNat",
"Array",
"iff_self",
"Bool.true",
"funext",
"And",
"Iff",
"Nat",
"Bool.not_eq_true",
"congr",
"True",
"Ne.eq_1",
"... | true |
_private.Init.Data.Nat.SOM.0.Nat.SOM.Poly.mulMon.eq_1 | Init.Data.Nat.SOM | [
"Nat.SOM.Poly.mulMon",
"Nat.SOM.Mon",
"Nat",
"Nat.SOM.Poly",
"Eq.refl",
"_private.Init.Data.Nat.SOM.0.Nat.SOM.Poly.mulMon.go",
"Prod",
"Eq",
"List.nil"
] | true |
_private.Mathlib.CategoryTheory.WithTerminal.Cone.0.CategoryTheory.WithInitial.coconeBack._proof_7 | Mathlib.CategoryTheory.WithTerminal.Cone | [
"Eq.mpr",
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Functor",
"CategoryTheory.WithInitial.liftFromUnder",
"CategoryTheory.Limits.CoconeMorphism.w",
"CategoryTheory.Limits.Cocone",
"_private.Mathlib.CategoryTheory.WithTerminal.Cone.0.CategoryTheory.WithInitial.coconeBack._proof_5",
"_private.... | false |
CategoryTheory.Limits.CompleteLattice.hasColimits_of_completeLattice | Mathlib.CategoryTheory.Limits.Lattice | [
"CategoryTheory.Functor",
"PartialOrder.toPreorder",
"CategoryTheory.Limits.HasColimitsOfSize",
"CategoryTheory.Limits.HasColimitsOfShape.mk",
"CategoryTheory.Limits.HasColimit.mk",
"CategoryTheory.Limits.CompleteLattice.colimitCocone",
"Preorder.smallCategory",
"CompleteLattice.toCompleteSemilatticeI... | true |
nhds_bot_basis | Mathlib.Topology.Order.Basic | [
"Nontrivial",
"OrderTopology",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Set.Ici",
"nhdsWithin_univ",
"congrArg",
"LinearOrder",
"Set.univ",
"nhdsWithin",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Exists",
"SemilatticeInf.toPartialOrder",
"nhds",
... | true |
Set.sInter_subset_of_mem | Mathlib.Data.Set.Lattice | [
"Membership.mem",
"HasSubset.Subset",
"CompleteLattice.toCompleteSemilatticeInf",
"sInf_le",
"CompleteBooleanAlgebra.toCompleteLattice",
"Set.sInter",
"Set.instMembership",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
"Set.instCompleteAtomicBooleanAlgebra",
"Set.instHasSubset",
"Set"... | true |
CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv_assoc | Mathlib.CategoryTheory.Limits.HasLimits | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_inv",
"CategoryTheory.Functor.category",
"Eq.mp",
"id",
"CategoryTheory.Iso",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"Ca... | true |
_private.Mathlib.Tactic.ProxyType.0.Mathlib.ProxyType.defaultMkProxyType.mkCType._f | Mathlib.Tactic.ProxyType | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"Lean.SourceInfo",
"Lean.Meta.State",
"instMonadLiftT",
"Array.mkArray0",
"Lean.Syntax.atom... | false |
_private.Std.Data.DHashMap.Internal.AssocList.Lemmas.0.Std.DHashMap.Internal.AssocList.foldrM.eq_def | Std.Data.DHashMap.Internal.AssocList.Lemmas | [
"Pure.pure",
"Std.DHashMap.Internal.AssocList.foldrM._f",
"Std.DHashMap.Internal.AssocList.foldrM",
"Eq.mpr",
"Std.DHashMap.Internal.AssocList.below",
"congrArg",
"Std.DHashMap.Internal.AssocList.brecOn.eq",
"Monad.toApplicative",
"Std.DHashMap.Internal.AssocList.nil",
"id",
"Applicative.toPure"... | true |
Lean.Json.brecOn_2.eq | Lean.Data.Json.Basic | [
"Lean.Json",
"Std.TreeMap.Raw.mk",
"Lean.Json.below_4",
"String",
"Lean.Json.below",
"Lean.Json.brecOn_2",
"Lean.Json.below_5",
"Ord.compare",
"Array",
"Std.TreeMap.Raw",
"List",
"Lean.Json.below_3",
"Lean.Json.brecOn_2.go",
"Eq.refl",
"Lean.Json.below_1",
"String.instOrd",
"Lean.Jso... | true |
Real.holderTriple_iff | Mathlib.Data.Real.ConjExponents | [
"Real",
"Real.instZero",
"Real.instInv",
"Real.HolderTriple",
"Real.instLT",
"Real.HolderTriple.mk",
"Real.instAdd",
"And.casesOn",
"instHAdd",
"And",
"Iff",
"Inv.inv",
"HAdd.hAdd",
"And.intro",
"LT.lt",
"Iff.intro",
"Zero.toOfNat0",
"Real.HolderTriple.casesOn",
"OfNat.ofNat",
... | true |
Lean.Elab.Tactic.Conv.getRhs | Lean.Elab.Tactic.Conv.Basic | [
"Pure.pure",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Elab.Tactic.Conv.getLhsRhs",
"Lean.Elab.Tactic.Context",
"Lean.Expr",
"IO.RealWorld",
"Lean.Elab.Tactic.instMonadTacticM",
"Applicative.toPure",
"StateRefT'",
"StateRefT'.instMonad",
"Lean.Elab.Term.TermElabM",
"Monad.toBind",
"Bind.bin... | true |
MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group | Mathlib.MeasureTheory.Measure.EverywherePos | [
"Eq.mpr",
"MeasureTheory.measure_congr",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"Continuous",
"MeasurableSet",
"Real.instZero",
"Monoid.toMulOneClass",
"HEq.refl",
"ContinuousMap.mk",
"ContinuousMap",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"Group",
"M... | true |
FreeAlgebra.instFree | Mathlib.LinearAlgebra.FreeAlgebra | [
"MonoidAlgebra.semiring",
"CancelMonoid.toRightCancelMonoid",
"FreeMonoid",
"Semiring.toModule",
"FreeAlgebra.instSemiring",
"FreeAlgebra.instAlgebra",
"AlgEquiv.symm",
"CommSemiring.toSemiring",
"FreeMonoid.instCancelMonoid",
"MonoidAlgebra.instFree",
"Algebra.toModule",
"Algebra.id",
"Free... | true |
Polynomial.mapAlgHom_coe_ringHom | Mathlib.Algebra.Polynomial.AlgebraMap | [
"AlgHom.algHomClass",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"Algebra",
"RingHom",
"Polynomial.mapAlgHom",
"Polynomial",
"CommSemiring",
"RingHomClass.toRingHom",
"Polynomial.mapRingHom",
"Polynomial.semiring",
"Semiring",
"AlgHomClass.toRingHomClass",
"Semiring.toNon... | true |
Int.Linear.cooper_right_split.eq_1 | Init.Data.Int.Linear | [
"Dvd.dvd",
"HMul.hMul",
"Int.Linear.Poly.leadCoeff",
"Int.Linear.Poly.addConst",
"Int.Linear.Poly.mul_k",
"Int.instNegInt",
"Int",
"LE.le",
"Int.Linear.Poly.denote'",
"Nat.cast",
"Int.instDvd",
"Int.instMul",
"And",
"instOfNat",
"Nat",
"Int.Linear.Poly.combine",
"Int.Linear.Context",... | true |
List.zip_eq_zip_take_min | Init.Data.List.Nat.TakeDrop | [
"List.brecOn",
"List.zip",
"List",
"Nat",
"List.zip_eq_zip_take_min._f",
"Prod",
"Eq",
"List.take",
"List.length",
"Min.min",
"instMinNat"
] | true |
CategoryTheory.instIsRegularEpiCategorySheafTypeOfHasSheafify | Mathlib.CategoryTheory.Sites.RegularEpi | [
"CategoryTheory.Limits.Types.hasColimitsOfSize",
"CategoryTheory.Limits.hasFiniteLimits_of_hasLimits",
"CategoryTheory.Limits.factorThruImage",
"CategoryTheory.Functor.flip",
"CategoryTheory.FunctorToTypes.instHasImagesFunctorType",
"CategoryTheory.Limits.HasImages.has_image",
"CategoryTheory.Functor",
... | true |
_private.Mathlib.Data.Finset.Basic.0.Finset.erase_singleton._proof_1_1 | Mathlib.Data.Finset.Basic | [
"Lean.Grind.eq_false_of_not_eq_true",
"Finset.mem_singleton",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Finset",
"Classical.byContradiction",
"Finset.ext",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"Lean.Grind.forall_imp_eq_or",
"Ne",... | false |
MonomialOrder.lex._proof_1 | Mathlib.Data.Finsupp.MonomialOrder | [
"instIsOrderedCancelAddMonoidLexFinsupp",
"Nat.instMulZeroClass",
"Finsupp.Lex.linearOrder",
"instAddCommMonoidLex",
"Lex",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"inferInstance",
"DistribLattice.toLattice",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"N... | false |
Lean.Order.Array.monotone_mapM | Init.Internal.Order.Lemmas | [
"Pure.pure",
"dite_cond_eq_true",
"Eq.mpr",
"Lean.Order.monotone_const",
"eq_false",
"Array.push",
"congrArg",
"Monad.toApplicative",
"Lean.Order.monotone_apply",
"id",
"instOfNatNat",
"_private.Init.Data.Array.Basic.0.Array.mapM.map",
"_private.Init.Internal.Order.Lemmas.0.Array.mapM.map.eq... | true |
Std.Internal.List.DistinctKeys.casesOn | Std.Data.Internal.List.Defs | [
"Std.Internal.List.DistinctKeys",
"List.Pairwise",
"Std.Internal.List.DistinctKeys.rec",
"List",
"BEq.beq",
"Std.Internal.List.DistinctKeys.mk",
"Bool",
"Bool.false",
"Std.Internal.List.keys",
"BEq",
"Eq",
"Sigma"
] | false |
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