name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ContinuousMultilinearMap.curryRight | Mathlib.Analysis.Normed.Module.Multilinear.Curry | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"ContinuousMultilinearMap.norm_map_snoc_le",
"MultilinearMap.mk",
"Real",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"Finset.univ",
"Nor... | true |
ProbabilityTheory.Kernel.partialTraj_comp_partialTraj'' | Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj | [
"Eq.mpr",
"ProbabilityTheory.Kernel.deterministic_comp_eq_map",
"congrArg",
"ProbabilityTheory.Kernel.comp",
"Finset",
"ProbabilityTheory.Kernel.map",
"Nat.instLocallyFiniteOrder",
"Membership.mem",
"LocallyFiniteOrder.toLocallyFiniteOrderBot",
"Preorder.measurable_frestrictLe₂",
"id",
"Subtyp... | true |
instFaithfulVAdd | Mathlib.Algebra.Group.Action.Faithful | [
"instVAddOfAdd",
"congrArg",
"AddZeroClass.toAddZero",
"FaithfulVAdd.mk",
"Eq.mp",
"FaithfulVAdd",
"HVAdd.hVAdd",
"AddZero.toZero",
"AddZeroClass",
"congr",
"instHVAdd",
"AddZero.toAdd",
"Zero.toOfNat0",
"add_zero",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1.splitter | Mathlib.Data.Nat.Squarefree | [
"Nat.minSqFacAux.match_1",
"Nat"
] | true |
_private.Mathlib.GroupTheory.Finiteness.0.AddMonoid.fg_iff_exists_freeAddGroup_hom_surjective_finite.match_1_1 | Mathlib.GroupTheory.Finiteness | [
"AddMonoid.toAddZeroClass",
"FreeAddMonoid.instAddCancelMonoid",
"AddCancelMonoid.toAddRightCancelMonoid",
"Set.Finite",
"Exists",
"AddZeroClass.toAddZero",
"Set.Elem",
"Exists.casesOn",
"AddRightCancelMonoid.toAddMonoid",
"AddMonoid",
"Exists.intro",
"AddMonoidHom",
"AddMonoidHom.instFunLik... | false |
spectrum.add_singleton_eq | Mathlib.Algebra.Algebra.Spectrum.Basic | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"spectrum",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Eq.rec",
"Set.instSingletonSet",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssoc... | true |
USize.ofFin_shiftLeft | Init.Data.UInt.Bitwise | [
"USize.toFin_inj",
"congrArg",
"HShiftLeft.hShiftLeft",
"USize.ofFin",
"Fin.instShiftLeft",
"USize.toFin_ofFin",
"Fin.val",
"System.Platform.numBits",
"USize.toFin_shiftLeft",
"Nat",
"congr",
"LT.lt",
"True",
"eq_self",
"Iff.mp",
"of_eq_true",
"USize.size",
"instHShiftLeftOfShiftLe... | true |
Matrix.invertibleOfFromBlocks₂₂Invertible | Mathlib.LinearAlgebra.Matrix.SchurComplement | [
"Matrix.fromBlocks",
"MulOne.toOne",
"CommRing",
"instFintypeSum",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Equiv.instEquivLike",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"Invertible.mulRight",
"Mat... | true |
String.Slice.all_prop_eq_all_decide | Init.Data.String.Lemmas.Pattern.Pred | [
"congrArg",
"String.Slice",
"String.Slice.all",
"String.Slice.isEmpty",
"String.Slice.Pattern.CharPred.instForwardPatternForallCharBool",
"DecidablePred",
"True",
"eq_self",
"Bool",
"of_eq_true",
"String.Slice.dropWhile_prop_eq_dropWhile_decide",
"congrFun'",
"Char",
"String.Slice.Pattern.... | true |
Std.Http.URI.Authority.recOn | Std.Internal.Http.Data.URI.Basic | [
"Std.Http.URI.Host",
"Std.Http.URI.Authority.rec",
"Std.Http.URI.Authority",
"Std.Http.URI.Authority.mk",
"Std.Http.URI.Port",
"Option",
"Std.Http.URI.UserInfo"
] | false |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex.0.Complex.tan_eq_zero_iff._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex | [
"eq_comm",
"propext",
"Eq"
] | false |
Polynomial.Splits.degree_eq_one_of_irreducible | Mathlib.Algebra.Polynomial.Splits | [
"Iff.mpr",
"WithBot.instPreorder",
"WithBot",
"Preorder.toLT",
"Nat.instOne",
"Polynomial.Splits.degree_le_one_of_irreducible",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Nat.instZeroLEOneClass",
"WithBot.zero",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"Irreducible",
"instOf... | true |
Algebra.intNorm_intNorm | Mathlib.RingTheory.IntegralClosure.IntegralRestrict | [
"Eq.mpr",
"IsDomain",
"FractionRing.field",
"FractionRing.instIsScalarTower",
"CommRing",
"IsDomain.to_noZeroDivisors",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"Module.Free.instFaithfu... | true |
Similar.comp_right_iff._simp_1 | Mathlib.Topology.MetricSpace.Similarity | [
"Similar",
"Function.comp",
"Similar.comp_right_iff",
"PseudoEMetricSpace",
"DilationClass",
"propext",
"Eq",
"DFunLike.coe",
"FunLike"
] | false |
OrderedFinpartition.compAlongOrderedFinpartitionL._proof_1 | Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | [
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"ContinuousMultilinearMap.seminormedAddCommGroup'",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMultilinearMap",
"NormedField.toField",
"Field.toSemifield",
"Field.toCommRing",
"ContinuousMultilinearMap.normedSpace'",
"smu... | false |
fderiv_fun_const | Mathlib.Analysis.Calculus.FDeriv.Const | [
"Eq.mpr",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Set.univ",
"NormedField.toField",
"fderivWithin_univ",
"AddCommGroup",
"id",
"Pi.instZero",
"ContinuousLinearMap.zero",
"fderiv",
"Field.toSemifield",
"ContinuousLinearMap",
"fderivWithin",
"TopologicalSpace",
"fderivWithin_fun_con... | true |
_private.Mathlib.Data.WSeq.Basic.0.Stream'.WSeq.destruct_join.match_1_1 | Mathlib.Data.WSeq.Basic | [
"Stream'.WSeq.destruct_join.aux",
"Stream'.WSeq.join",
"HEq.refl",
"Stream'.WSeq.destruct",
"Exists",
"Eq.casesOn",
"Computation",
"Or.casesOn",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Stream'.WSeq",
"Exists.intro",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Or.inl... | false |
SSet.Subcomplex.PairingCore.WeakRankFunction.mk.inj | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank | [
"SSet.Subcomplex.PairingCore.ι",
"Preorder.toLT",
"SSet.Subcomplex.PairingCore",
"SSet.Subcomplex.PairingCore.WeakRankFunction.mk.noConfusion",
"PartialOrder.toPreorder",
"SSet.Subcomplex.PairingCore.WeakRankFunction",
"PartialOrder",
"SSet",
"Nat",
"LT.lt",
"SSet.Subcomplex.PairingCore.dim",
... | true |
Subgroup.center | Mathlib.GroupTheory.Subgroup.Center | [
"Monoid.toMulOneClass",
"Group",
"Subgroup.mk",
"DivInvMonoid.toMonoid",
"Subgroup",
"Subgroup.center._proof_1",
"Group.toDivInvMonoid",
"Submonoid.center",
"Submonoid"
] | true |
Nat.zeckendorf._unsafe_rec | Mathlib.Data.Nat.Fib.Zeckendorf | [
"Nat.zeckendorf._unsafe_rec",
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"List.cons",
"Nat.greatestFib",
"List",
"instHAdd",
"Unit",
"instHSub",
"HAdd.hAdd",
"Nat.fib",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.zeckendorf.match_1",
"Eq",
"List.nil"
] | false |
IsInvariantSubring.toMulSemiringAction._proof_3 | Mathlib.Algebra.Ring.Action.Invariant | [
"Monoid",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"instHSMul",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"Monoid.toMulOneClass",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"IsInvariantSubring.smul_mem",
"Membership... | false |
Std.ExtDHashMap.size_filterMap_eq_size_iff | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"instLawfulHashableOfLawfulBEq",
"LawfulBEq",
"Membership.mem",
"Std.ExtDHashMap.inductionOn",
"Std.ExtDHashMap.get",
"Bool.true",
"Iff",
"Std.ExtDHashMap.size",
"Nat",
"Std.DHashMap.size_filterMap_eq_size_iff",
"Std.ExtDHashMap",
"... | true |
Std.DTreeMap.Internal.Impl.Const.size_filter!_eq_size_iff | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"congrArg",
"Std.DTreeMap.Internal.Impl.getKey",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.filter",
"Eq.mp",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.Const.get",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Bool.true",
"Iff",
"Std... | true |
measurableVAdd_iterateAddAct._simp_1 | Mathlib.MeasureTheory.Group.Arithmetic | [
"IterateAddAct.instAddCommMonoid",
"AddMonoid.toAddSemigroup",
"Measurable",
"measurableVAdd_iterateAddAct",
"IterateAddAct",
"IterateAddAct.instMeasurableSpace",
"MeasurableSpace",
"AddAction.toAddSemigroupAction",
"AddSemigroupAction.toVAdd",
"IterateAddAct.instAddAction",
"propext",
"AddCom... | false |
CochainComplex.mappingCone.mapOfHomotopy._proof_3 | Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Int.instNegInt",
"Int",
"Int.instAddMonoid",
"AddZero.toZero",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"AddZero.toAdd",
"Zero.toOfNat0",
"add_zero",
"OfNat.ofNat",
"Eq",
"Neg.neg"
] | false |
CategoryTheory.Functor.CoconeTypes.IsColimit.equiv_symm_ι_apply | Mathlib.CategoryTheory.Limits.Types.ColimitType | [
"CategoryTheory.Functor",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
"CategoryTheory.Functor.ColimitType",
"Equiv",
"CategoryTheory.Functor.CoconeTypes.ι",
"CategoryTheory.Functor.CoconeTypes.pt",
"CategoryTheory.Functor.CoconeTypes.IsColimit",
"CategoryTheory.Functor.CoconeTypes... | true |
CoalgEquiv.noConfusionType | Mathlib.RingTheory.Coalgebra.Equiv | [
"CoalgebraStruct",
"Function.LeftInverse",
"CoalgHom.toLinearMap",
"CommSemiring.toSemiring",
"CoalgHom",
"CoalgEquiv.casesOn",
"LinearMap.toAddHom",
"AddCommMonoid",
"CommSemiring",
"Function.RightInverse",
"HEq",
"AddCommSemigroup.toAddCommMagma",
"Module",
"CoalgEquiv",
"AddCommMonoid... | false |
_private.Mathlib.Analysis.Normed.Algebra.GelfandMazur.0.NormedAlgebra.Real.norm_φ_eq_norm_φ_of_isMinOn._proof_1_2 | Mathlib.Analysis.Normed.Algebra.GelfandMazur | [
"Lean.RArray.leaf",
"False",
"Preorder.toLT",
"HMul.hMul",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Nat.not_le_eq",
"Lean.Grind.Nat.lt_eq",
"Nat.Linear.Expr.mulL",
"Eq.mp",
"Nat.ToInt.natCast_ofNat",
"Nat.Linear.ExprCnstr.eq_of_toNormPoly_... | false |
_private.Init.Data.Fin.Lemmas.0.Fin.eq_zero_or_eq_succ.match_1_1 | Init.Data.Fin.Lemmas | [
"Unit.unit",
"instNeZeroNatHAdd_1",
"Fin.casesOn",
"Fin.ofNat._proof_1",
"Fin.mk",
"instOfNatNat",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"LT.lt",
"instAddNat",
"Nat.zero",
"instLTNat",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"Nat.casesOn"
] | false |
tsum_geometric_two | Mathlib.Analysis.SpecificLimits.Basic | [
"Real",
"instHDiv",
"Real.instDivInvMonoid",
"EMetricSpace.metrizableSpace",
"Nat.instAtLeastTwoHAddOfNat",
"PseudoMetricSpace.toUniformSpace",
"HDiv.hDiv",
"instOfNatNat",
"hasSum_geometric_two",
"SummationFilter.instNeBotUnconditional",
"Monoid.toPow",
"Real.instOne",
"Real.instMonoid",
... | true |
_private.Init.Data.List.Count.0.List.countP_filterMap._simp_1_1 | Init.Data.List.Count | [
"Option.guard",
"List",
"List.filter",
"Bool",
"List.filterMap",
"Eq.symm",
"Eq",
"List.filterMap_eq_filter"
] | false |
HomologicalComplex.extendSingleIso_hom_f | Mathlib.Algebra.Homology.Embedding.Extend | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"HomologicalComplex.mkHomToSingle",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HomologicalComplex.extendSingleIso",
"HomologicalComple... | true |
CategoryTheory.MonoidalCoherence.noConfusionType | Mathlib.Tactic.CategoryTheory.MonoidalComp | [
"CategoryTheory.MonoidalCoherence",
"CategoryTheory.Iso",
"CategoryTheory.MonoidalCoherence.casesOn",
"HEq",
"CategoryTheory.Category"
] | false |
Lean.Meta.Grind.TGrindStep | Lean.Meta.Tactic.Grind.Action | [
"Lean.TSyntax",
"Lean.Name.mkStr5",
"List.cons",
"Lean.SyntaxNodeKind",
"List.nil"
] | true |
HasCompl.ctorIdx | Mathlib.Order.Notation | [
"HasCompl",
"Nat"
] | false |
PiLp.normedSpace | Mathlib.Analysis.Normed.Lp.PiLp | [
"SeminormedAddCommGroup",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Pi.module",
"NormedField.toField",
"Fact",
"PiLp",
"PiLp.seminormedAddCommGroup",
"LE.le",
"Field.toSemifield",
"NormedField",
"Semifield.toDivisionSemiring",
"Fintype",
"SeminormedAddCommGr... | true |
isLowerSet_iInter | Mathlib.Order.UpperLower.Basic | [
"Iff.mpr",
"Set.forall_mem_range",
"Set.iInter",
"Membership.mem",
"isLowerSet_sInter",
"LE",
"IsLowerSet",
"Set.range",
"Set.instMembership",
"Set"
] | true |
String.Slice.subslice.congr_simp | Init.Data.String.Subslice | [
"String.Slice.Subslice",
"String.instLEPos_1",
"String.Slice",
"Eq.rec",
"LE.le",
"String.Slice.subslice",
"Eq.ndrec",
"Eq.refl",
"String.Slice.Pos",
"Eq"
] | true |
MvPolynomial.counit_C | Mathlib.Algebra.MvPolynomial.Counit | [
"Finsupp.instAddZeroClass",
"Int.cast",
"Nat.instMulZeroClass",
"CommRing",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"MvPolynomial.ACounit_C",
"Nat.instAddMonoid",
"RingHom",
"Int",
"AddGroupWithOne.toIntCast",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"Nat",
"Ring.... | true |
affineIndependent_iff_linearIndependent_vsub | Mathlib.LinearAlgebra.AffineSpace.Independent | [
"Iff.mpr",
"Eq.mpr",
"Pi.Function.module",
"instDecidableNot",
"NegZeroClass.toNeg",
"Finset.weightedVSubOfPoint_apply",
"Finset.weightedVSubOfPoint_insert",
"instHSMul",
"Semiring.toModule",
"Pi.addCommMonoid",
"AffineIndependent",
"Finset.sum_subtype_of_mem",
"Ring.toNonAssocRing",
"Clas... | true |
CategoryTheory.LocalizerMorphism.functorialRightResolutions.ι._proof_1 | Mathlib.CategoryTheory.Localization.DerivabilityStructure.OfFunctorialResolutions | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor.full_whiskeringRight_obj",
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.LocalizerMorphism.functor",
"CategoryTheory.Functor.whiskeringRight",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.F... | false |
Equiv.Perm.cycleFactorsFinset_eq_finset | Mathlib.GroupTheory.Perm.Cycle.Factors | [
"Finset.noncommProd_toFinset",
"MulOne.toOne",
"Equiv.Perm.instOne",
"List.Pairwise",
"Function.onFun",
"Iff.of_eq",
"Monoid.toMulOneClass",
"Equiv.Perm.Disjoint.commute",
"congrArg",
"Finset",
"List.map",
"List.coe_toFinset",
"Equiv.Perm.cycleFactorsFinset",
"setOf",
"Fintype.decidableE... | true |
Finset.min.eq_1 | Mathlib.Data.Finset.Max | [
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Finset.min",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"WithTop.some",
"WithTop.instOrderTop",
"Eq.refl",
"WithTop.semilatticeInf",
"Finset.inf",
"Eq",
"instDistribLatticeOfLinearOrder",
"Lattice.toS... | true |
CategoryTheory.Limits.pullback.instIsIsoDiagonalOfMono | Mathlib.CategoryTheory.Limits.Shapes.Diagonal | [
"Eq.mpr",
"CategoryTheory.IsIso",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.IsIso.inv_isIso",
"inferInstance",
"id",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.Limits.pullback.diagonal_fst",
"CategoryTheory.Limits.pullb... | true |
AddSubsemigroup.closure.eq_1 | Mathlib.Algebra.Group.Subsemigroup.Basic | [
"AddSubsemigroup.instSetLike",
"setOf",
"AddSubsemigroup.closure",
"HasSubset.Subset",
"AddSubsemigroup.instInfSet",
"SetLike.coe",
"AddSubsemigroup",
"Eq.refl",
"Eq",
"InfSet.sInf",
"Add",
"Set.instHasSubset",
"Set"
] | true |
CategoryTheory.NonemptyParallelPairPresentationAux.presentation._proof_1 | Mathlib.CategoryTheory.Limits.Indization.ParallelPair | [
"CategoryTheory.Limits.IndObjectPresentation.I",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.IndObjectPresentation.instFinalICostructuredArrowFunctorOppositeTypeYonedaToCostructuredArrow",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"Cate... | false |
Aesop.RuleStats.successful | Aesop.Stats.Basic | [
"Aesop.RuleStats",
"Bool"
] | true |
InnerProductSpace.ringOfCoalgebra | Mathlib.Analysis.InnerProductSpace.Coalgebra | [
"NormedCommRing.toNormedRing",
"Ring.mk",
"InnerProductSpace.toNormedSpace",
"InnerProductSpace.ringOfCoalgebra._proof_21",
"Coalgebra.toCoalgebraStruct",
"InnerProductSpace.ringOfCoalgebra._proof_15",
"NormedRing.toRing",
"One.mk",
"AddMonoid.toAddSemigroup",
"Coalgebra",
"InnerProductSpace.rin... | true |
_private.Mathlib.Probability.ProductMeasure.0.MeasureTheory.Measure.infinitePi_map_piCurry_symm._simp_1_2 | Mathlib.Probability.ProductMeasure | [
"Sigma.exists",
"Exists",
"propext",
"Sigma.mk",
"Eq",
"Sigma"
] | false |
Aesop.EMap.casesOn | Aesop.EMap | [
"Aesop.EMap.rec",
"Lean.PArray",
"Lean.Expr",
"Nat",
"Lean.Meta.DiscrTree",
"Aesop.EMap",
"Prod",
"Option",
"Aesop.EMap.mk"
] | false |
_private.Mathlib.Topology.Constructions.0.isOpenMap_sigma._simp_1_2 | Mathlib.Topology.Constructions | [
"Sigma.forall",
"propext",
"Sigma.mk",
"Eq",
"Sigma"
] | false |
AddSemigrp.ofHom_id | Mathlib.Algebra.Category.Semigrp.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"AddSemigrp.of",
"AddSemigroup",
"AddSemigroup.toAdd",
"AddSemigrp.ofHom",
"AddHom.id",
"CategoryTheory.Category.toCategoryStruct",
"AddSemigrp.instCategory",
"AddSemigrp",
"Eq",
"rfl"
] | true |
Filter.lift'_inf_principal_eq | Mathlib.Order.Filter.Lift | [
"Filter.instMembership",
"iInf",
"CompleteLattice.toLattice",
"Iff.of_eq",
"congrArg",
"Filter.inhabitedMem",
"Filter.instInfSet",
"Filter.instCompleteLatticeFilter",
"Function.comp",
"Membership.mem",
"Subtype",
"iInf_subtype'",
"SemilatticeInf.toMin",
"Set.instInter",
"Filter.instInf",... | true |
ContinuousMapZero.toContinuousMapHom | Mathlib.Topology.ContinuousMap.ContinuousMapZero | [
"DistribMulActionHom.mk",
"NonUnitalAlgHom.mk",
"MonoidHom.instFunLike",
"Semiring.toModule",
"MonoidHom",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsTopologicalSemiring",
"ContinuousStar",
"SeparatelyContinuousMul.to_continuousSMul",
"ContinuousMap... | true |
_private.Mathlib.Geometry.Euclidean.Triangle.0.EuclideanGeometry.sin_angle_div_dist_eq_sin_angle_div_dist._simp_1_3 | Mathlib.Geometry.Euclidean.Triangle | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
_private.Mathlib.Data.Ordmap.Ordset.0.Ordnode.mem.match_1.eq_1 | Mathlib.Data.Ordmap.Ordset | [
"Ordering.gt",
"Unit.unit",
"Ordering",
"Ordering.eq",
"Ordnode.mem.match_1",
"Unit",
"Ordering.lt",
"Eq.refl",
"Eq"
] | true |
Std.TreeMap.getKeyD_maxKey | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.inner",
"Ordering",
"Std.TransCmp",
"Std.TreeMap.isEmpty",
"Std.TreeMap.maxKey",
"Std.DTreeMap.getKeyD_maxKey",
"Bool",
"Std.TreeMap.getKeyD",
"Bool.false",
"Eq",
"Std.TreeMap"
] | true |
AddMonCat.HasLimits.limitConeIsLimit._proof_1 | Mathlib.Algebra.Category.MonCat.Limits | [
"CategoryTheory.instFaithfulForget",
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonCat.str",
"AddMonCat",
"AddMonCat.instCategory",
"CategoryTheory.types",
"CategoryTheory.forget",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"... | false |
_private.Mathlib.RingTheory.DividedPowers.Basic.0.DividedPowers.dpow_sum'._simp_1_1 | Mathlib.RingTheory.DividedPowers.Basic | [
"eq_comm",
"propext",
"Eq"
] | false |
MonadCont.Label._sizeOf_1 | Mathlib.Control.Monad.Cont | [
"MonadCont.Label",
"MonadCont.Label.rec",
"instOfNatNat",
"Nat",
"SizeOf",
"OfNat.ofNat"
] | false |
CuspForm.copy._proof_1 | Mathlib.NumberTheory.ModularForms.Basic | [
"SlashInvariantForm",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"SlashInvariantForm.slash_action_eq'",
"Real",
"chartedSpaceSelf",
"Complex.instNormedAddCommGroup",
"outParam",
"Matrix",
"UpperHalfPlane.instChartedSpaceComplex",
"instDecidableEqFin",
"Complex.in... | false |
Mathlib.Meta.NormNum.IsNat.rpow_eq_pow | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Eq.mpr",
"Real.instPow",
"Mathlib.Meta.NormNum.IsNat",
"Real",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"id",
"AddMonoidWithOne.toNatCast",
"Real.instRing",
"Nat.cast",
"Monoid.toPow",
"Real.instMonoid",
"HPow.hPow",
"Nat",
"Eq.refl",
"instHPow",
"Mathlib.Meta.NormNum.IsNat... | true |
CategoryTheory.MonoidalCoherence.whiskerLeft | Mathlib.Tactic.CategoryTheory.MonoidalComp | [
"CategoryTheory.MonoidalCoherence.iso",
"CategoryTheory.MonoidalCoherence.mk",
"CategoryTheory.MonoidalCategory.whiskerLeftIso",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCoherence",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.MonoidalCategory.toMonoidalCategorySt... | true |
_private.Init.Data.List.Find.0.List.findIdx?_flatten._simp_1_1 | Init.Data.List.Find | [
"Membership.mem",
"Exists",
"Bool.true",
"List",
"And",
"List.instMembership",
"propext",
"Bool",
"List.any",
"List.any_eq_true",
"Eq"
] | false |
ContinuousLinearMap.isBigOWith_sub | Mathlib.Analysis.Normed.Operator.Asymptotics | [
"Norm.norm",
"SeminormedAddCommGroup",
"NormedSpace",
"Asymptotics.IsBigOWith",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"RingHom",
"RingHomIsometric",
"NormedField.toFie... | true |
ENNReal.ofReal_lt_coe_iff | Mathlib.Data.ENNReal.Real | [
"Eq.mpr",
"Real.instLE",
"Real",
"ENNReal.ofNNReal",
"Preorder.toLT",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"ENNReal.coe_toReal",
"Iff.rfl",
"PartialOrder.toPreorder",
"ENNReal.ofReal_lt_iff_lt_toReal",
"Real.instLT",
"id",
"NNReal",
"LE.le",
"Iff",
"ENNReal.toReal",
"LT... | true |
AddValuation.IsEquiv.comap | Mathlib.RingTheory.Valuation.Basic | [
"RingHom",
"AddValuation.comap",
"Multiplicative",
"AddValuation",
"LinearOrderedAddCommMonoidWithTop",
"AddValuation.IsEquiv",
"OrderDual",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Ring",
"Valuation.IsEquiv.comap",
"instLinearOrderedCommMonoidWithZeroMultiplicativeOrderDual"
] | true |
List.prod_hom₂ | Mathlib.Algebra.BigOperators.Group.List.Basic | [
"Monoid",
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"List.foldr_hom₂",
"Monoid.toMulOneClass",
"congrArg",
"List.map",
"id",
"MulOne.toMul",
"List",
"MulOneClass.toMulOne",
"congr",
"True",
"eq_self",
"of_eq_true",
"One.toOfNat1",
"Eq.refl",
"congrFun'",
"implies_true",
"List.fo... | true |
Set.Disjoint.set_pi | Mathlib.Data.Set.Prod | [
"Iff.mpr",
"Set.disjoint_left",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"Set.instDistribLattice",
"BooleanAlgebra.toBiheyti... | true |
_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.image_maximalIdeal._simp_1_1 | Mathlib.RingTheory.Valuation.ValuationSubring | [
"Set.mem_image",
"Membership.mem",
"Exists",
"And",
"propext",
"Set.image",
"Eq",
"Set.instMembership",
"Set"
] | false |
CategoryTheory.Bicategory.Adj.whiskerRight_τl | Mathlib.CategoryTheory.Bicategory.Adjunction.Adj | [
"CategoryTheory.Bicategory.Adj.instCategoryStructHom",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Bicategory.Adj.Hom.l",
"Quiver.Hom",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory.Adj.Hom₂.τl",
"CategoryTheory.Bicateg... | true |
FreeAbelianGroup.ring._proof_11 | Mathlib.GroupTheory.FreeAbelianGroup | [
"Monoid",
"FreeAbelianGroup.nonUnitalRing",
"HMul.hMul",
"AddMonoid.toZero",
"NonUnitalNonAssocSemiring.toMul",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonUnitalNonAssocSemiring.zero_mul",
"Monoid.toSemigroup",
"NonUnitalRing.toNonUnitalSemiri... | false |
Lean.Meta.Sym.ProofInstArgInfo.noConfusionType | Lean.Meta.Sym.SymM | [
"Lean.Meta.Sym.ProofInstArgInfo.casesOn",
"Lean.Meta.Sym.ProofInstArgInfo",
"Bool",
"Eq"
] | false |
CategoryTheory.AddMonObj.ofRepresentableBy._proof_3 | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Equiv.apply_symm_apply",
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"AddMonoidHom.instAddMonoidHomClass",
"Opposite",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"AddMonCat.addMonoidObj",
"... | false |
Finset.count_coe_finsuppAntidiagEquiv_apply | Mathlib.Algebra.Order.Antidiag.FinsuppEquiv | [
"Finsupp.instFunLike",
"Equiv.instEquivLike",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Finset.finsuppAntidiag",
"Membership.mem",
"AddZeroClass.toAddZero",
"Multiset.count",
"Equiv",
"Subtype",
"Finsupp.count_toMultiset",
"AddZero.toZero",
"Finset.Nat.instHasAntidiagonal",
"Fin... | true |
WeierstrassCurve.Affine.Point.toClass | Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | [
"FractionRing.field",
"MonoidHom.instFunLike",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"WeierstrassCurve.Affine.Point.instAddZeroClass",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"WeierstrassCurve.Affine.CoordinateRing.XYIdeal'._proof_4",
"OreLocalization.instAlgebra",
"ins... | true |
Algebra.Generators.naive._proof_3 | Mathlib.RingTheory.Extension.Generators | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"AddMonoidAlgebra.commRing",
"CommSemiring.toSemiring",
"Finsupp.instAddMonoid",
"Nat.instAddMonoid",
"Ideal.IsTwoSided",
"Ideal",
"Finsupp.instAddCommMonoid",
"Ideal.instIsTwoSided_1",
"CommRing.toCommSemiring",
"Nat",
"MvPo... | false |
Lean.Widget.InteractiveHypothesisBundle.isRemoved? | Lean.Widget.InteractiveGoal | [
"Bool",
"Lean.Widget.InteractiveHypothesisBundle",
"Option"
] | true |
InfClosed.prod | Mathlib.Order.SupClosed | [
"Set.instSProd",
"SProd.sprod",
"Membership.mem",
"SemilatticeInf.toMin",
"Prod.instSemilatticeInf",
"Prod.fst",
"SemilatticeInf",
"And.right",
"And.left",
"And.intro",
"InfClosed",
"Prod",
"Set.instMembership",
"Prod.snd",
"Min.min",
"Set"
] | true |
Bimod.regular_actRight | Mathlib.CategoryTheory.Monoidal.Bimod | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"Bimod.regular",
"CategoryTheory.Mon",
"CategoryTheory.Mon.X",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"Bimod.actRight",
"Eq.refl",
"CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct",
"C... | true |
Std.DTreeMap.Internal.Impl.minKey_le_of_contains | Std.Data.DTreeMap.Internal.Lemmas | [
"Iff.mpr",
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.isEmpty_eq_isEmpty",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"Std.DTreeMap.Internal.Impl.contains_eq_containsKey",
"beqOfOrd",
"Std.DTreeMap.Internal.Impl.Ordered.distinctKeys",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.WF.ordered",
"Exists... | true |
MeasureTheory.indicatorConstLp.eq_1 | Mathlib.MeasureTheory.Function.LpSpace.Indicator | [
"MeasureTheory.Measure",
"MeasurableSet",
"Set.indicator",
"MeasureTheory.indicatorConstLp",
"MeasureTheory.indicatorConstLp._proof_1",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Subtype",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.to... | true |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.natAbs_emod._proof_1_3 | Init.Data.Int.DivMod.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",
"id",
"instDecida... | false |
CategoryTheory.isCofilteredOrEmpty_of_semilatticeInf | Mathlib.CategoryTheory.Filtered.Basic | [
"trivial",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ULift.ext",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"inf_le_right",
"SemilatticeInf.toPartialOrder",
"CategoryTheory.CategoryStruct.id",
"PLift",
"Preorder.smallCategory",
"CategoryTheory.IsCofilteredOrEmpty",
... | true |
CommGrpCat.instConcreteCategoryMonoidHomCarrier._proof_3 | Mathlib.Algebra.Category.Grp.Basic | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"CommGrpCat.instCategory",
"CommGrpCat.Hom.hom'",
"CategoryTheory.CategoryStruct.id",
"CommGrpCat.str",
"id",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"CommGrpCat.carrier",
"CommGrpCat",
"Eq.refl"... | false |
CategoryTheory.CommGrp.instCategory._aux_3 | Mathlib.CategoryTheory.Monoidal.CommGrp_ | [
"CategoryTheory.CommGrp.toGrp",
"Quiver.mk",
"CategoryTheory.CommGrp.instCategory._aux_1",
"Quiver.Hom",
"CategoryTheory.Grp.instCategory",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheo... | false |
CauSeq.Completion.instInhabitedCauchy | Mathlib.Algebra.Order.CauSeq.Completion | [
"LinearOrder",
"CauSeq.Completion.Cauchy",
"IsStrictOrderedRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"CauSeq.Completion.instZeroCauchy",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"IsAbsoluteValue",
"DivisionSemiring.toSemiring",
"Inhabited",
"Zero.toOfNat0"... | true |
Lean.Meta.Grind.EMatchTheoremKind.bwd.noConfusion | Lean.Meta.Tactic.Grind.Extension | [
"Lean.Meta.Grind.EMatchTheoremKind.noConfusion",
"Lean.Meta.Grind.EMatchTheoremKind.bwd",
"id",
"Lean.Meta.Grind.EMatchTheoremKind",
"Bool",
"Eq"
] | false |
ContinuousLinearMap.bddAbove_rayleighQuotient | Mathlib.Analysis.InnerProductSpace.Rayleigh | [
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"Real.instLE",
"Real",
"Real.lattice",
"abs",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"Eq.rec",
"_private.Mathlib.Analysis.InnerProductSpace.Rayleigh.0... | true |
HomotopicalAlgebra.PathObject.IsVeryGood.rec | Mathlib.AlgebraicTopology.ModelCategory.PathObject | [
"HomotopicalAlgebra.PathObject",
"HomotopicalAlgebra.Cofibration",
"HomotopicalAlgebra.PathObject.toPrepathObject",
"HomotopicalAlgebra.PrepathObject.P",
"CategoryTheory.Limits.HasBinaryProduct",
"HomotopicalAlgebra.PathObject.IsVeryGood.mk",
"HomotopicalAlgebra.CategoryWithWeakEquivalences",
"Homotop... | false |
UniformSpaceCat._sizeOf_inst | Mathlib.Topology.Category.UniformSpace | [
"SizeOf.mk",
"SizeOf",
"UniformSpaceCat",
"UniformSpaceCat._sizeOf_1"
] | false |
Cardinal.preAleph_le_aleph | Mathlib.SetTheory.Cardinal.Aleph | [
"Iff.mpr",
"Ordinal.instLinearOrder",
"Cardinal.aleph",
"Ordinal.omega0",
"Ordinal.partialOrder",
"Cardinal",
"OrderEmbedding.addLeft",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"OrderIso",
"RelEmbedding.toEmbedding",
"LE.le",
... | true |
WeierstrassCurve.Projective.X_eq_of_equiv | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Units.val",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Units.instMulAction",
"CommRing",
"instHSMul",
"Mathlib.Tactic.Ring.Common.mul_congr",
"HMul.hMul",
"Nat.rawCast",
"_private.Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic.0.Wei... | true |
_private.Mathlib.LinearAlgebra.Multilinear.DFinsupp.0.MultilinearMap.dfinsuppFamily._simp_3 | Mathlib.LinearAlgebra.Multilinear.DFinsupp | [
"Finset.mem_univ",
"Finset.univ",
"Finset",
"Membership.mem",
"Fintype",
"Finset.instSetLike",
"True",
"eq_true",
"Eq",
"SetLike.instMembership"
] | false |
Lean.Compiler.LCNF.FixedParams.State.noConfusionType | Lean.Compiler.LCNF.FixedParams | [
"instHashableProd",
"Lean.Compiler.LCNF.FixedParams.AbsValue",
"Lean.Compiler.LCNF.FixedParams.instBEqAbsValue",
"Std.HashSet",
"Array.instBEq",
"Lean.Compiler.LCNF.FixedParams.State",
"Array",
"Lean.Compiler.LCNF.FixedParams.instHashableAbsValue",
"instBEqProd",
"Bool",
"Lean.Name",
"Prod",
... | false |
Std.ExtDHashMap.eq_empty_iff_size_eq_zero | Std.Data.ExtDHashMap.Lemmas | [
"Std.DHashMap.isEmpty_eq_size_eq_zero",
"Std.ExtDHashMap.isEmpty",
"beq_iff_eq",
"Std.ExtDHashMap.instEmptyCollection",
"Std.DHashMap.size",
"Bool.eq_iff_iff",
"Std.ExtDHashMap.isEmpty_iff",
"Std.ExtDHashMap.inductionOn",
"instOfNatNat",
"Std.ExtDHashMap.mk",
"instBEqOfDecidableEq",
"LawfulHas... | true |
Sum.getRight | Init.Data.Sum.Basic | [
"Sum.isRight",
"Sum",
"Sum.getRight.match_1",
"Bool.true",
"Sum.inr",
"Bool",
"Eq"
] | true |
CategoryTheory.preadditiveCoyonedaObj._proof_2 | Mathlib.CategoryTheory.Preadditive.Yoneda.Basic | [
"AddHom.mk.congr_simp",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"instHSMul",
"CategoryTheory.moduleEndLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddHom",
"AddMonoid.toAddZeroCla... | false |
_private.Mathlib.Algebra.MvPolynomial.Division.0.MvPolynomial.X_dvd_monomial._simp_1_3 | Mathlib.Algebra.MvPolynomial.Division | [
"Ne",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat",
"propext",
"Nat.one_le_iff_ne_zero",
"OfNat.ofNat",
"Eq"
] | false |
CategoryTheory.Localization.Preadditive.neg'_add'_self | Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive | [
"CategoryTheory.MorphismProperty.LeftFraction.hs",
"CategoryTheory.MorphismProperty.LeftFraction₂.add",
"CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"NegZeroClass.toNeg",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
... | true |
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