name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 701 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Server.FileWorker.AbsoluteLspSemanticToken.priority | Lean.Server.FileWorker.SemanticHighlighting | [
"Lean.Server.FileWorker.AbsoluteLspSemanticToken",
"Nat"
] | true |
_private.Mathlib.Topology.Bornology.Constructions.0.Bornology.isBounded_pi._simp_1_3 | Mathlib.Topology.Bornology.Constructions | [
"Set.univ",
"Set.univ_pi_nonempty_iff",
"Set.Nonempty",
"propext",
"Set.pi",
"Eq.symm",
"Eq",
"Set"
] | false |
Subfield.mem_mk | Mathlib.Algebra.Field.Subfield.Defs | [
"Subring.toSubsemiring",
"GroupWithZero.toDivisionMonoid",
"Subring.instSetLike",
"DivInvOneMonoid.toInvOneClass",
"Ring.toNonAssocRing",
"Iff.rfl",
"Submonoid.toSubsemigroup",
"DivisionSemiring.toGroupWithZero",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"DivisionRing.toDivisionSemir... | true |
_private.Init.Data.Repr.0.List.repr._sparseCasesOn_1 | Init.Data.Repr | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
RingTheory.Sequence.IsWeaklyRegular.recIterModByRegularWithRing._unary._proof_16 | Mathlib.RingTheory.Regular.RegularSequence | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"List",
"CommRing.toCommSemiring",
"RingTheory.Sequence.IsWeaklyRegular",
"Module",
"PSigma"
] | false |
HasFDerivAtFilter.sub_const | Mathlib.Analysis.Calculus.FDeriv.Add | [
"Iff.mpr",
"NormedSpace",
"hasFDerivAtFilter_sub_const_iff",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"HasFDerivAtFilter",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"Field.toSemifield",
"ContinuousLinearMap",
"SubNegMono... | true |
CochainComplex.Lifting.hasLift | Mathlib.Algebra.Homology.ModelCategory.Lifting | [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"HomologicalComplex.hom_ext",
"CochainComplex.Lifting.cochain₀._proof_1",
"HomologicalComplex.instCategory",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.CommSq.HasLift",
"CochainComplex.HomComplex.instAddC... | true |
_private.Mathlib.Topology.Algebra.AsymptoticCone.0.asymptoticCone_affineSubspace._simp_1_4 | Mathlib.Topology.Algebra.AsymptoticCone | [
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"Field.toSemifield",
"Filter.Frequently",
"TopologicalSpace",
"asymptoticCone",
"Semifield.toDivisionSemiring",
"mem_asymptoticCone_iff",
"AddTorsor",
"propext",
"DivisionSemiring.to... | false |
Lean.SCC.State.noConfusion | Lean.Util.SCC | [
"Lean.SCC.State.noConfusionType",
"HEq.refl",
"Lean.SCC.State",
"Lean.SCC.State.casesOn",
"Std.HashMap",
"List",
"Nat",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Hashable",
"Lean.SCC.Data",
"BEq",
"Eq"
] | false |
CoxeterSystem.length_mul_mod_two | Mathlib.GroupTheory.Coxeter.Length | [
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"Equiv.instEquivLike",
"HMul.hMul",
"ZMod.commRing",
"AddMonoid.toAddSemigroup",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Group",
"Eq.mp",
"id",
... | true |
String.Internal.anyImpl | Init.Data.String.Search | [
"String.Slice.Pattern.CharPred.instToForwardSearcherForallCharBoolDefaultForwardSearcher",
"String",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher.instIteratorLoopIdSearchStep",
"String.Slice",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher",
"String.Slice.Pattern.CharPred... | true |
WeierstrassCurve.IsCharTwoJEqZeroNF.casesOn | Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms | [
"CommRing",
"CommSemiring.toSemiring",
"WeierstrassCurve.a₂",
"WeierstrassCurve",
"CommRing.toCommSemiring",
"WeierstrassCurve.IsCharTwoJEqZeroNF",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"WeierstrassCurve.IsCharTwoJEqZeroNF.mk",
"WeierstrassCurve.IsCharTwoJEqZeroNF.rec",
"MulZeroClass.toZero",
... | false |
GaloisInsertion.l_sInf_u_image | Mathlib.Order.GaloisConnection.Basic | [
"Eq.mpr",
"iInf",
"congrArg",
"PartialOrder.toPreorder",
"sInf_image",
"Membership.mem",
"id",
"GaloisInsertion.l_biInf_u",
"sInf_eq_iInf",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"GaloisInsertion",
"Eq.refl",
"Set.image",
"CompleteSemilattice... | true |
Lean.Meta.Grind.Arith.Cutsat.ToIntInfo.mulThms? | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"Lean.Meta.Grind.Arith.Cutsat.ToIntInfo",
"Lean.Meta.Grind.Arith.Cutsat.ToIntThms",
"Option"
] | true |
_private.Lean.Meta.Basic.0.Lean.Meta.realizeValue.match_9 | Lean.Meta.Basic | [
"Except.ok",
"String",
"Nat.hasNotBit",
"Prod.mk",
"_private.Lean.Meta.Basic.0.Lean.Meta.realizeValue._sparseCasesOn_9",
"Lean.Core.State",
"Except.ctorIdx",
"Except",
"Prod",
"Dynamic",
"Prod.casesOn",
"Lean.Exception"
] | false |
Std.Tactic.BVDecide.BVExpr.bitblast.go_denote_mem_prefix._proof_1 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Expr | [
"Std.Sat.AIG.Decl",
"Std.Tactic.BVDecide.BVExpr.bitblast.go",
"LE.le",
"instLENat",
"Std.Sat.AIG",
"Nat",
"LT.lt",
"Std.Tactic.BVDecide.BVExpr.Cache",
"Std.Tactic.BVDecide.BVExpr.Return.result",
"Std.Tactic.BVDecide.BVExpr",
"instLTNat",
"Std.Tactic.BVDecide.instDecidableEqBVBit",
"Std.Sat.A... | false |
CategoryTheory.Limits.Types.binaryCoproductCocone_ι_app | Mathlib.CategoryTheory.Limits.Types.Coproducts | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"TypeCat.ofHom",
"Sum",
"Sum.inl",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.Discrete.mk",
"Unit",
"CategoryTheory.Discrete.as",
"CategoryTheory.Limits.Cocone.ι",
"... | true |
Lean.Parser.Level.paren.formatter | Lean.Parser.Level | [
"Lean.PrettyPrinter.Formatter",
"Lean.Parser.levelParser.formatter",
"Lean.Parser.withCache.formatter",
"Lean.Parser.leadingNode.formatter",
"instOfNatNat",
"Lean.PrettyPrinter.Formatter.withAntiquot.formatter",
"Lean.Parser.symbol.formatter",
"Bool.true",
"Nat",
"Lean.Parser.withoutPosition.forma... | true |
CategoryTheory.Functor.leftExtensionEquivalenceOfIso₁_inverse_map_right | Mathlib.CategoryTheory.Functor.KanExtension.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.LeftExtension",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Comma.hom",
"CategoryTheory.Iso",
"CategoryTheory.Comma",
"Categ... | true |
_private.Batteries.Recycling.MonadSatisfying.Basic.0.SatisfiesM.bind.match_1_1 | Batteries.Recycling.MonadSatisfying.Basic | [
"HEq.refl",
"Monad.toApplicative",
"Eq.casesOn",
"Subtype",
"Exists.casesOn",
"Exists.intro",
"eq_of_heq",
"Eq.ndrec",
"Applicative.toFunctor",
"Eq.refl",
"HEq",
"SatisfiesM",
"Eq.symm",
"Monad",
"Subtype.val",
"Eq",
"Functor.map"
] | false |
CentroidHom.starCenterIsoCentroid._proof_11 | Mathlib.Algebra.Star.CentroidHom | [
"NonUnitalStarSubsemiring.instNonUnitalSubsemiringClass",
"CentroidHom.starCenterIsoCentroid._proof_2",
"CentroidHom.instStar",
"NonUnitalStarSubsemiring.instStarMemClass",
"Membership.mem",
"Subtype",
"StarAddMonoid.toInvolutiveStar",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"StarRing.toStarAdd... | false |
iteratedDerivWithin_vcomp_three | Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno | [
"Eq.mpr",
"Inhabited.default",
"NormedCommRing.toSeminormedCommRing",
"Fintype.sum_unique",
"instNeZeroNatHAdd_1",
"MulOne.toOne",
"False",
"instHSMul",
"Fintype.elems",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Function.update",
"le_rfl",
"Equiv.instEquivLike"... | true |
List.fillNones.eq_4 | Batteries.Data.List.Basic | [
"List.cons",
"Option.none",
"List",
"Eq.refl",
"List.fillNones",
"Eq",
"Option"
] | true |
_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.updateCell.match_3.eq_1 | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"HSub.hSub",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"Std.DTreeMap.Internal.Impl.Size... | true |
_private.Mathlib.Topology.Algebra.Group.TopologicalAbelianization.0.TopologicalAbelianization.commGroup._simp_5 | Mathlib.Topology.Algebra.Group.TopologicalAbelianization | [
"zpow_add",
"HMul.hMul",
"Monoid.toMulOneClass",
"DivInvMonoid.toZPow",
"Group",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Int",
"Group.toDivInvMonoid",
"instHAdd",
"MulOneClass.toMulOne",
"HPow.hPow",
"HAdd.hAdd",
"Int.instAdd",
"ZPow.toPow",
"instHPow",
"Eq.symm",
"Eq",
"instHM... | false |
FreeMagma.instMonad | Mathlib.Algebra.Free | [
"MulHom",
"FreeMagma.lift",
"Unit.unit",
"Equiv.instEquivLike",
"Seq.mk",
"SeqLeft.mk",
"Function.comp",
"Equiv",
"SeqRight.mk",
"Pure.mk",
"Functor.mk",
"FreeMagma.of",
"Applicative.mk",
"Unit",
"MulHom.funLike",
"Function.const",
"Monad.mk",
"FreeMagma.instMul",
"Monad",
"Bin... | true |
NonarchimedeanGroup.cauchySeq_of_tendsto_div_nhds_one | Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean | [
"Filter.instMembership",
"UniformSpace",
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"MulOne.toOne",
"Nat.instLattice",
"OpenSubgroup",
"Nat.recAux",
"Filter.tendsto_def",
"Lattice.toSemilatticeSup",
"instHDiv",
"Cauchy",
"InvOneClass.toOne",
"HMul.hMul",
"CauchySeq",
"DivisionCommMonoid.toDi... | true |
IsLocalizedModule.isInteger_add | Mathlib.Algebra.Module.LocalizedModule.Int | [
"IsLocalizedModule.IsInteger._proof_1",
"CommSemiring.toSemiring",
"LinearMap.range",
"IsLocalizedModule.IsInteger",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"instHAdd",
"HAdd.hAdd",
"AddCommSemigroup.toAddCommMagma",
"Module",
"AddCommMonoid.toAddCommSemigroup",
"RingHom.id",
"Semiri... | true |
SetRel.id_subset_iff | Mathlib.Data.Rel | [
"SetRel.id",
"SetRel",
"Std.Refl.mk",
"Membership.mem",
"Prod.mk",
"LE.le",
"Iff",
"Set.instLE",
"Iff.intro",
"SetRel.id_subset",
"SetRel.IsRefl",
"Prod",
"Set.instMembership",
"rfl"
] | true |
FloatArray.instForInFloatOfMonad | Init.Data.FloatArray.Basic | [
"FloatArray",
"Float",
"FloatArray.forIn",
"ForIn.mk",
"ForIn",
"Monad"
] | true |
forall_self_imp | Init.PropLemmas | [
"Iff",
"Iff.intro"
] | true |
Std.DTreeMap.Internal.Impl.Tree.balanced_impl | Std.Data.DTreeMap.Internal.Operations | [
"Std.DTreeMap.Internal.Impl.Balanced",
"Nat",
"Std.DTreeMap.Internal.Impl.Tree",
"Std.DTreeMap.Internal.Impl.Tree.impl"
] | true |
_private.Mathlib.Algebra.Category.Grp.Basic.0.GrpCat.Hom.mk.injEq | Mathlib.Algebra.Category.Grp.Basic | [
"GrpCat",
"MonoidHom",
"GrpCat.str",
"Eq.propIntro",
"Monoid.toMulOneClass",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"_private.Mathlib.Algebra.Category.Grp.Basic.0.GrpCat.Hom.mk",
"MulOneClass.toMulOne",
"GrpCat.Hom",
"Eq.ndrec",
"Eq.refl",
"GrpCat.carrier",
"Eq",
"_private.Math... | true |
CochainComplex.mappingConeHomOfDegreewiseSplitXIso.eq_1 | Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit | [
"CochainComplex.mappingConeHomOfDegreewiseSplitXIso._proof_2",
"HomologicalComplex.instCategory",
"CochainComplex.HomComplex.instAddCommGroupCochain",
"CochainComplex.cocycleOfDegreewiseSplit._proof_10",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"CochainComplex.mappingCone.in... | true |
RingQuot.definition._proof_5._@.Mathlib.Algebra.RingQuot.2555519587._hygCtx._hyg.2 | Mathlib.Algebra.RingQuot | [
"AlgHom.toMonoidHom'._proof_2",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"RingHom",
"RingQuot.instSemiring",
"RingQuot",
"RingQuot.mkAlgHom",
"congr_arg",
"CommSemiring",
"RingHom.instFunLike",
"RingQuot.instAlgebra",
"RingHomClass.toRingHom",
"RingQuot.mkAlgHom_rel",
"RingQuot.definition.... | false |
WithTop.untopD_natCast | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"WithBot.instNatCast",
"NatCast",
"Nat.cast",
"Nat",
"WithTop.untopD",
"Eq",
"rfl",
"WithTop"
] | true |
CategoryTheory.Limits.CoconeMorphism.hom_inv_id | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.CoconeMorphism.hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso.hom_inv_id",
"CategoryTheory.Iso",
"CategoryTheory.Limits.Cocone.categor... | true |
_private.Mathlib.RingTheory.RingHom.Locally.0.RingHom.locally_iff_exists.match_1_3 | Mathlib.RingTheory.RingHom.Locally | [
"CommRing",
"Semiring.toModule",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"IsLocalization.Away",
"Algebra",
"RingHom",
"Exists",
"Submodule.instTop",
"Ideal",
"RingHom.comp",
"CommRing.toCommSemiring",
"Exists.casesOn",
"Exists.intro",
"Ideal.span",
"Set.range",
"Top.top",
... | false |
Set.himp_def | Mathlib.Order.BooleanAlgebra.Set | [
"Compl.compl",
"himp_eq",
"Set.instUnion",
"Set.instCompl",
"Set.instHImp",
"Set.instBooleanAlgebra",
"Union.union",
"Eq",
"HImp.himp",
"Set"
] | true |
GradedMonoid.smul_mk | Mathlib.Algebra.GradedMonoid | [
"GradedMonoid.instSMul",
"instHSMul",
"SMul",
"GradedMonoid",
"HSMul.hSMul",
"Eq",
"rfl",
"GradedMonoid.mk"
] | true |
Prod.instInvolutiveInv | Mathlib.Algebra.Group.Prod | [
"Prod.instInv",
"InvolutiveInv.mk",
"InvolutiveInv.toInv",
"InvolutiveInv",
"Prod",
"Prod.instInvolutiveInv._proof_1"
] | true |
_private.Mathlib.Geometry.Manifold.GroupLieAlgebra.0.mpullback_mulInvariantVectorField._simp_1_3 | Mathlib.Geometry.Manifold.GroupLieAlgebra | [
"HMul.hMul",
"zpow_mul",
"DivInvMonoid.toZPow",
"DivisionMonoid",
"Int",
"DivisionMonoid.toDivInvMonoid",
"Int.instMul",
"HPow.hPow",
"ZPow.toPow",
"instHPow",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Lean.Meta.Simp.dpreDefault | Lean.Meta.Tactic.Simp.Rewrite | [
"HAndThen.hAndThen",
"instHAndThenOfAndThen",
"Lean.Meta.Simp.instAndThenDSimproc",
"Unit",
"Lean.Meta.Simp.userPreDSimprocs",
"Lean.Meta.Simp.DSimproc",
"Lean.Meta.Simp.SimprocsArray",
"Lean.Meta.Simp.drewritePre"
] | true |
CategoryTheory.Bicategory.whisker_assoc | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.Bicategory.associator",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Cate... | true |
Nat.one_le_cast._simp_1 | Mathlib.Data.Nat.Cast.Order.Basic | [
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddLeftMono",
"Nat.one_le_cast",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"ZeroLEOneClass",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.cast",
"CharZero",
... | false |
MProd.mk._flat_ctor | Init.Prelude | [
"MProd.mk",
"MProd"
] | false |
_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_4 | Mathlib.Data.List.NodupEquivFin | [
"Fin.val_fin_lt",
"Eq.mpr",
"dite_congr",
"Preorder.toLT",
"StrictMono",
"congrArg",
"PartialOrder.toPreorder",
"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_2",
"Lean.Grind.Nat.lt_eq",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"... | false |
Mathlib.Meta.Positivity.int_div_nonneg_of_nonneg_of_pos | Mathlib.Tactic.Positivity.Basic | [
"Int.instDiv",
"instHDiv",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"HDiv.hDiv",
"LT.lt.le",
"Int",
"LE.le",
"Int.instLTInt",
"instOfNat",
"LT.lt",
"instLatticeInt",
"OfNat.ofNat",
"Int.instLEInt",
"Int.ediv_nonneg",
"Lattice.toSemilatticeInf"
] | true |
CategoryTheory.Functor.relativelyRepresentable.pullback₃.p₁ | Mathlib.CategoryTheory.MorphismProperty.Representable | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.Functor.relativelyRepresentable.fst'",
"CategoryTheory.Limits.pullback.fst",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Functor.relativelyRepresentable.pull... | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.Const.alterKey.match_1 | Std.Data.Internal.List.Associative | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.smul_mem | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme | [
"GradedRing.toGradedMonoid",
"SetLike",
"Eq.mpr",
"HomogeneousLocalization.NumDenSameDeg.num",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"DirectSum.decomposeRingEquiv",
"Subtype.mk.congr_simp",
"Nat.instOrderedSub",
"CommRing",
"AlgebraicGeometry.ProjIsoSpecTopC... | true |
CategoryTheory.Functor.final_of_isFiltered_of_pUnit | Mathlib.CategoryTheory.Filtered.Final | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Classical.choice",
"CategoryTheory.Discrete.instSubsingletonDiscreteHom",
"Exists",
"CategoryTheory.IsFiltered.toIsFilteredOrEmpty",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Functor.final_of_exists_of_isFil... | true |
Ordinal.opow_right_inj | Mathlib.SetTheory.Ordinal.Exponential | [
"Ordinal.instLinearOrder",
"Preorder.toLT",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"Function.Injective.eq_iff",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Ordinal.isNormal_opow",
"Ordinal.one",
"StrictMono.injective",
"Iff",
"HPow.hPow",
"LT.lt",
"One.toOfNat... | true |
RBTree.RBNode.Path.Balanced.redL | Batteries.Recycling.RBTree.Alter | [
"RBTree.RBColor.red",
"RBTree.RBColor.black",
"RBTree.RBNode.Path.Balanced",
"RBTree.RBNode.Path.left",
"RBTree.RBNode.Path.Balanced.redL",
"RBTree.RBColor",
"RBTree.RBNode",
"Nat",
"RBTree.RBNode.Balanced",
"RBTree.RBNode.Path"
] | true |
Group.instResiduallyFiniteOfFinite | Mathlib.GroupTheory.ResiduallyFinite | [
"Iff.mpr",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Group.residuallyFinite_iff_forall_finiteIndex",
"Subgroup.FiniteIndex",
"Finite",
"Group.ResiduallyFinite",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Subgroup",
"Bot.bot",
"Sub... | true |
CategoryTheory.orderDualEquivalence._proof_5 | Mathlib.CategoryTheory.Category.Preorder | [
"OrderDual.toDual",
"CategoryTheory.Functor",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.orderDualEquivalence._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"OrderDual.ofDual",
"Quiver.Hom",
"CategoryTheory.orderDualEquivalence._proof_2",
"Quiver.Hom.op",
"CategoryTheory.Functor.mk... | false |
LinearMap.IsNonneg.casesOn | Mathlib.LinearAlgebra.SesquilinearForm.Basic | [
"Algebra.to_smulCommClass",
"Semiring.toModule",
"LinearMap.IsNonneg.rec",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"RingHom",
"Algebra.id",
"LinearMap.IsNonneg",
"LE.le",
"LinearMap.module",
"LinearMap",
"LE",
"AddCommMonoid",
"CommSemiring",
"LinearMap.IsNonneg.mk",
"Linea... | false |
CategoryTheory.CommShift₂Setup.z_zero₂._autoParam | Mathlib.CategoryTheory.Shift.CommShiftTwo | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.Meta.RefinedDiscrTree.Key.opaque | Mathlib.Lean.Meta.RefinedDiscrTree.Basic | [
"Lean.Meta.RefinedDiscrTree.Key",
"Lean.Meta.RefinedDiscrTree.Key.opaque"
] | true |
CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.ι_map_associator_hom_eq_associator_hom | Mathlib.CategoryTheory.Monoidal.DayConvolution | [
"CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.convolution₂'",
"CategoryTheory.MonoidalCategory.DayConvolution.convolution",
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Opposite",
"Equiv... | true |
_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.computeDistance._unary._proof_9 | Init.Data.String.Pattern.String | [
"Eq.mpr",
"String.instLTRaw",
"congrArg",
"String.Slice.byteIdx_rawEndPos",
"String.Slice.rawEndPos",
"String.Slice",
"id",
"String.Slice.utf8ByteSize",
"LE.le",
"instLENat",
"String.Pos.Raw",
"Array",
"_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buil... | false |
Lean.Elab.HeaderProcessedSnapshot.bodyStx | Lean.Elab.DefView | [
"Lean.Syntax",
"Lean.Elab.HeaderProcessedSnapshot"
] | true |
CategoryTheory.CostructuredArrow.ιCompGrothendieckProj | Mathlib.CategoryTheory.Comma.StructuredArrow.Functor | [
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.Grothendieck.ι",
"CategoryTheory.Functor.category",
"CategoryTheory.CostructuredArrow.grothendieckProj",
"CategoryTheory.Functor.comp",
"CategoryTheory.Grothendieck",
"CategoryTheory.Cat.str",
"CategoryTheory.Functor.id",
"Ca... | true |
RingEquiv.toSemilinearEquiv._proof_3 | Mathlib.Algebra.Module.Equiv.Defs | [
"RingEquiv.toSemilinearEquiv._proof_1",
"RingEquiv.instEquivLike",
"RingEquiv.instRingEquivClass",
"Distrib.toAdd",
"RingHomInvPair.symm",
"RingHomInvPair",
"RingEquiv.toSemilinearEquiv._proof_2",
"instDistribOfSemiring",
"Distrib.toMul",
"RingHomClass.toRingHom",
"RingHomInvPair.of_ringEquiv",
... | false |
_private.Mathlib.RingTheory.MvPowerSeries.Basic.0.MvPowerSeries.coeff_prod._simp_1_2 | Mathlib.RingTheory.MvPowerSeries.Basic | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
MonoidHom.transfer._proof_1 | Mathlib.GroupTheory.Transfer | [
"Eq.mpr",
"Inhabited.default",
"MulOne.toOne",
"instHSMul",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"Subgroup.FiniteIndex",
"Subgroup.leftTransversals.diff_self",
"Subgroup.leftTransversals.... | false |
_private.Std.Data.Internal.List.Associative.0.Option.getD.match_1.eq_1 | Std.Data.Internal.List.Associative | [
"Option.getD.match_1",
"Option.some",
"Option.none",
"Unit",
"Eq.refl",
"Eq",
"Option"
] | true |
AdicCompletion.liftRingHom._proof_6 | Mathlib.RingTheory.AdicCompletion.Algebra | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"RingHom.instRingHomClass",
"Subtype.mk.congr_simp",
"AdicCompletion.liftRingHom._proof_2",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"instHSMul",
"RingHomClass.toAddMonoidHomClass",
"Semiring.toModule",
"HMul.hMul",
"Is... | false |
List.forall_map_iff | Mathlib.Data.List.Basic | [
"congrArg",
"List.map",
"Function.comp",
"List.rec",
"List.cons",
"iff_self",
"List",
"And",
"List.Forall.eq_1",
"Iff",
"List.Forall",
"List.forall_cons._simp_1",
"congr",
"True",
"propext",
"of_eq_true",
"congrFun'",
"Eq.trans",
"List.nil"
] | true |
Aesop.NormalizationState.isProvenByNormalization | Aesop.Tree.Data | [
"Lean.Meta.SavedState",
"_private.Aesop.Tree.Data.0.Aesop.NormalizationState.isNormal.match_1",
"Lean.MVarId",
"Aesop.NormalizationState",
"Aesop.DisplayRuleName",
"Array",
"Bool.true",
"Unit",
"Bool",
"Prod",
"Bool.false",
"Aesop.Script.LazyStep",
"Option"
] | true |
Measurable.measurableSet_preimage_iff_preimage_val | Mathlib.MeasureTheory.Constructions.Polish.Basic | [
"Set.mem_range_self",
"StandardBorelSpace",
"MeasurableSet",
"Measurable.subtype_mk",
"Measurable",
"Membership.mem",
"Measurable.measurableSet_preimage_iff_of_surjective",
"Set.Elem",
"MeasurableSpace",
"Set.rangeFactorization_surjective",
"Iff",
"MeasurableSpace.CountablySeparated",
"Set.p... | true |
CategoryTheory.Limits.createsColimitsOfSizeOfOp | Mathlib.CategoryTheory.Limits.Preserves.Creates.Opposites | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CreatesColimitsOfSize.mk",
"CategoryTheory.CreatesLimitsOfSize.CreatesLimitsOfShape",
"CategoryTheory.CreatesLimitsOfSize",
"CategoryTheory.CreatesColimitsOfSize",
"CategoryTheory.Limits.createsColimitsOfShapeOfOp",
"... | true |
Std.Async.System.GroupId.rec | Std.Async.System | [
"Std.Async.System.GroupId",
"Nat",
"Std.Async.System.GroupId.mk"
] | false |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat.0.Nat.reducePow._regBuiltin.Nat.reducePow.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat.879423217._hygCtx._hyg.21 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat | [
"IO",
"Bool.true",
"Unit",
"Sum.inr",
"Lean.Meta.Simp.DSimproc",
"Nat.reducePow",
"Lean.Name.mkStr2",
"Lean.Meta.Simp.addSimprocBuiltinAttr",
"Lean.Meta.Simp.Simproc"
] | false |
SSet.Edge.InvStruct.ofEq | Mathlib.AlgebraicTopology.SimplicialSet.CompStruct | [
"Opposite",
"SSet.Edge.InvStruct.homInvId",
"SSet.Edge.InvStruct.invHomId",
"SSet.Edge.InvStruct.ofEq._proof_3",
"instOfNatNat",
"SSet",
"SSet.Edge.InvStruct.inv",
"SSet.Edge.InvStruct.mk",
"SSet.Edge.InvStruct.ofEq._proof_4",
"SSet.Edge.InvStruct.ofEq._proof_2",
"SimplexCategory.mk",
"Opposit... | true |
ProbabilityTheory.IdentDistrib.variance_eq | Mathlib.Probability.IdentDistrib | [
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"congrArg",
"ProbabilityTheory.variance.eq_1",
"id",
"ProbabilityTheory.variance",
"MeasurableSpace",
"Real.measurableSpace",
"ENNReal.toReal",
"ProbabilityTheory.IdentDistrib",
"ENNReal",
"Eq.refl",
"ProbabilityTheory.IdentDistrib.evariance_eq",
... | true |
_private.Mathlib.Algebra.MonoidAlgebra.Module.0.MonoidAlgebra.submoduleOfSMulMem._simp_1 | Mathlib.Algebra.MonoidAlgebra.Module | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"MonoidHom.instFunLike",
"MonoidAlgebra.instAddMonoid",
"MonoidHom",
"instDistribSMul",
"AddMonoid.toAddZeroClass",
"MonoidAlgebra.smulZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"NonAssocSemiring.toMulZeroOneClass"... | false |
ProofWidgets.instHtmlEvalHtml | ProofWidgets.Component.HtmlDisplay | [
"Pure.pure",
"ProofWidgets.Html",
"ProofWidgets.HtmlEval.mk",
"IO.RealWorld",
"EIO",
"instMonadEIO",
"Applicative.toPure",
"Lean.Elab.Command.State",
"StateRefT'",
"StateRefT'.instMonad",
"ProofWidgets.HtmlEval",
"Lean.Elab.Command.CommandElabM",
"ReaderT.instApplicativeOfMonad",
"Lean.Exc... | true |
NormedAddGroupHom.Equalizer.liftEquiv._proof_3 | Mathlib.Analysis.Normed.Group.Hom | [
"Subtype.mk.congr_simp",
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"congrArg",
"AddSubgroup.seminormedAddCommGroup",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Subtype",
"NormedAddGroupHom.comp",
"Subtype.mk",
"AddSubgroup",
"NormedAddGroupHom.Equalizer.ι_comp_lift",
"SeminormedAddCo... | false |
Lean.ppConstNameWithInfos | Lean.Util.PPExt | [
"Pure.pure",
"Std.instToFormatString",
"Std.Format.instAppend",
"Lean.PPFns.ppConstNameWithInfos",
"Lean.PPContext.opts",
"Monad.toApplicative",
"String",
"Lean.ppExt",
"Std.Format.line",
"IO.Error.instToString",
"instDecidableEqBool",
"instToFormatOfToString",
"_private.Lean.Util.PPExt.0.Le... | true |
_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.computeDistance.eq_def | Init.Data.String.Pattern.String | [
"_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.computeDistance._proof_5",
"HSub.hSub",
"String.Slice",
"_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.computeDistance._proof_7",
"instDecidableEqUInt8",
"id",... | true |
lt_tsub_iff_left | Mathlib.Algebra.Order.Sub.Defs | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"OrderedSub",
"tsub_le_iff_left",
"instHAdd",
"Iff",
"instHSub",
"HAdd.hAdd",
"LT.lt",
"AddCommSemigroup.toAddCommMagma",
"AddCommSemigr... | true |
Lean.Server.FileWorker.AbsoluteLspSemanticToken.rec | Lean.Server.FileWorker.SemanticHighlighting | [
"Lean.Server.FileWorker.AbsoluteLspSemanticToken",
"Lean.Lsp.SemanticTokenType",
"Lean.Server.FileWorker.AbsoluteLspSemanticToken.mk",
"Nat",
"Lean.Lsp.Position"
] | false |
_private.Mathlib.Data.Nat.Cast.SetInterval.0.Nat.image_cast_int_Ico._simp_1_1 | Mathlib.Data.Nat.Cast.SetInterval | [
"Set.Ici",
"Set.ordConnected_Ici",
"True",
"eq_true",
"Set.OrdConnected",
"Eq",
"Preorder"
] | false |
Finset.mulDistribMulAction._proof_1 | Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset | [
"Monoid",
"instHSMul",
"Finset",
"Finset.smulFinset",
"Finset.coe_smul_finset",
"SetLike.coe",
"Finset.instSetLike",
"Monoid.toSemigroup",
"MulDistribMulAction.toMulAction",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"MulDistribMulAction",
"Eq",
"Set.smulSet"... | false |
Set.PairwiseDisjoint.subset_of_biUnion_subset_biUnion | Mathlib.Data.Set.Pairwise.Lattice | [
"Iff.mpr",
"Eq.mpr",
"Function.onFun",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Set.PairwiseDisjoint",
"PartialOrder.toPreorder",
"Set.subset_union_right",
"Set.mem_iUnion₂_of_mem",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrd... | true |
negPart_eq_neg_inf_zero | Mathlib.Algebra.Order.Group.PosPart | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Lattice",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"Lattice.toSemilatticeSup",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddLeftMono",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"AddRightMono",
"A... | true |
Std.DTreeMap.Raw.Const.get!_insertMany_list_of_contains_eq_false | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.Const.get!",
"instForInOfForIn'",
"List.map",
"List.contains",
"Ord.mk",
"Std.DTreeMap.Raw.Const.insertMany",
"Ordering",
"inferInstance",
"Std.TransCmp",
"Id",
"Membership",
"Prod.fst",
"Std.DTreeMap.Internal.Impl.Const.get!_insertMany!_list_of_contains_eq_false",
"List"... | true |
Lat.Hom._sizeOf_inst | Mathlib.Order.Category.Lat | [
"Lat.Hom",
"SizeOf.mk",
"SizeOf",
"Lat.Hom._sizeOf_1",
"Lat"
] | false |
Matroid.mapEquiv | Mathlib.Combinatorics.Matroid.Map | [
"Matroid.mapEmbedding",
"Equiv",
"Equiv.toEmbedding",
"Matroid"
] | true |
IsPGroup.commGroupOfCardEqPrimeSq._proof_1 | Mathlib.GroupTheory.PGroup | [
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Subgroup.instNormalCenter",
"QuotientGroup.instHasQuotientSubgroup",
"Eq.le",
"DivInvMonoid.toMonoid",
"Subgroup",
"Subgroup.center",
"LE.le",
"Group.toDivInvMonoid",
"MonoidHom.ker",
"HasQuotient.Quotient",
"Q... | false |
CategoryTheory.Discrete.addMonoidalFunctorComp.eq_1 | Mathlib.CategoryTheory.Monoidal.Discrete | [
"CategoryTheory.Functor",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"AddZeroClass.toAddZero",
"CategoryTheory.Iso.refl",
"CategoryTheory.Discrete.addMonoidalFunctorComp",
"CategoryTheory.Iso",
"CategoryTheory.discreteCategory",
"AddMonoid",
"Eq... | true |
Mathlib.Tactic.Algebra.BaseType.mk.injEq | Mathlib.Tactic.Algebra.Basic | [
"Eq.propIntro",
"Lean.Expr.const",
"Mathlib.Tactic.Algebra.BaseType.mk",
"Mathlib.Tactic.Ring.ExSum",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Mathlib.Tactic.Algebra.BaseType",
"Lean.Expr.lam",
"Qq.Quoted.unsafeMk",
"Eq.ndrec",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Eq.r... | true |
Sep.sep | Init.Core | [
"outParam",
"Sep"
] | true |
ProbabilityTheory.IsRatCondKernelCDF.mk | Mathlib.Probability.Kernel.Disintegration.CDFToKernel | [
"MeasureTheory.ae",
"Set.instSProd",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"MeasureTheory.Measure",
"MeasurableSet",
"Real.instRCLike",
"SProd.sprod",
"ProbabilityTheory.IsRatCondKernelCDF",
"Filter.Eventually",
"Real.instRatCast",
"Rat",
"Measur... | true |
CategoryTheory.Hom.instVAddHom | Mathlib.CategoryTheory.Monoidal.Cartesian.Mod | [
"CategoryTheory.AddModObj",
"CategoryTheory.AddModObj.vadd",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"VAdd",
"CategoryTheory.CartesianMonoidalCategory.lift",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"VAdd.mk",
"C... | true |
ProbabilityTheory.IndepFun.mul_hasPDF' | Mathlib.Probability.Density | [
"Eq.mpr",
"MeasureTheory.Measure",
"MeasureTheory.instSFiniteOfSigmaFinite",
"HMul.hMul",
"MeasureTheory.HasPDF.aemeasurable'",
"DivInvOneMonoid.toInvOneClass",
"AEMeasurable",
"Monoid.toMulOneClass",
"congrArg",
"MeasureTheory.SigmaFinite",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid... | true |
CategoryTheory.ProjectiveResolution.rec | Mathlib.CategoryTheory.Preadditive.Projective.Resolution | [
"CategoryTheory.Limits.HasZeroMorphisms",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.HasHomology",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"HomologicalComp... | false |
Nat.SOM.Expr.ctorElim | Init.Data.Nat.SOM | [
"Nat.SOM.Expr.add",
"Nat.SOM.Expr.ctorElimType",
"Nat.SOM.Expr.num",
"Nat.SOM.Expr.ctorIdx",
"Nat.SOM.Expr.casesOn",
"Nat.Linear.Var",
"Nat.SOM.Expr",
"Nat",
"Nat.SOM.Expr.mul",
"Eq.ndrec",
"PULift.down",
"Eq",
"Nat.SOM.Expr.var"
] | false |
_private.Mathlib.Algebra.Order.Group.Unbundled.Int.0.Int.abs_ediv_le_abs.match_1_1 | Mathlib.Algebra.Order.Group.Unbundled.Int | [
"HEq.refl",
"Exists",
"Eq.casesOn",
"Int.instNegInt",
"Int",
"Nat.cast",
"Or.casesOn",
"Exists.casesOn",
"Nat",
"Exists.intro",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Or.inl",
"Or",
"instNatCastInt",
"Eq.symm",
"Eq",
"Neg.neg",
"Or.inr"
] | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.