name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Equiv.partialOrder | Mathlib.Order.Lattice | [
"Preorder.toLT",
"Equiv.instEquivLike",
"Equiv.partialOrder._proof_2",
"Equiv.partialOrder._proof_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Equiv",
"Equiv.injective",
"Function.Injective.partialOrder",
"DFunLike.coe",
"Equiv.preorder",
"Preorder",
"EquivLike.toFunLik... | true |
ContinuousLinearMap.instStarModuleId | Mathlib.Analysis.InnerProductSpace.Adjoint | [
"LinearIsometryEquiv.instEquivLike",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"ContinuousLinearMap.adjointAux._proof_9",
"CompleteSpace",
"SemilinearMapClass.toMulActionSemiHomClass",
"NormedSpace.toIsBoundedSMul",
"Co... | true |
CategoryTheory.WithTerminal.equivComma_inverse_obj_obj | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.WithTerminal.id.match_1",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.WithTerminal.equivComma",
"CategoryTheory.Comma",
"CategoryTheory.WithTerminal",
"CategoryT... | true |
not_irreducible_expand | Mathlib.FieldTheory.Perfect | [
"PerfectRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.Prime",
"not_irreducible_pow",
"frobeniusEquiv",
"congrArg",
"CommSemiring.toSemiring",
"RingEquiv.instEquivLike",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"RingEquiv.instRingEquivClass",
"Fact",
"... | true |
_private.Init.Data.String.Lemmas.Basic.0.String.Pos.startPos_le._simp_1_2 | Init.Data.String.Lemmas.Basic | [
"LE.le",
"instLENat",
"String.Pos.Raw",
"Nat",
"String.instLERaw",
"propext",
"String.Pos.Raw.byteIdx",
"String.Pos.Raw.le_iff",
"Eq"
] | false |
AffineSubspace.toAddTorsor | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic | [
"VSub.mk",
"Submodule",
"AddAction.mk",
"AddTorsor.mk",
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddCommMonoid",
"AffineSubspace.toAddTorsor._proof_2",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AffineSubspace.toAddTorsor._proof_6",
"AddCommGroup",
"Subtype",
"AffineSubspace.toAddTorso... | true |
Primrec.nat_omega_rec | Mathlib.Computability.Primrec.List | [
"Iff.mpr",
"Primrec₂.left",
"Eq.mpr",
"congrArg",
"Primrec.snd",
"Primcodable.ofDenumerable",
"Primrec.comp₂",
"List.map",
"Prod.forall._simp_1",
"Option.some",
"Function.comp",
"Membership.mem",
"Exists",
"Primrec.fst",
"Primrec.nat_omega_rec'",
"id",
"List.map_map",
"Primrec₂.rig... | true |
Turing.TM2Computable.noConfusion | Mathlib.Computability.TuringMachine.Computable | [
"Turing.FinTM2.k₀",
"Turing.TM2ComputableAux.tm",
"HEq.refl",
"List.map",
"Option.some",
"Turing.TM2Computable",
"List",
"Turing.TM2Computable.casesOn",
"eq_of_heq",
"Turing.FinTM2.Γ",
"Eq.ndrec",
"Turing.FinTM2.k₁",
"Turing.TM2Outputs",
"HEq",
"Turing.TM2ComputableAux",
"Turing.TM2Com... | false |
Algebra.TensorProduct.right_algebraMap_apply | Mathlib.RingTheory.TensorProduct.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Algebra.toModule",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddMonoidWithOne.toOne",
"RingHom.instFunLike",
"NonAss... | true |
_private.Mathlib.Analysis.InnerProductSpace.PiL2.0.OrthonormalBasis.sum_sq_norm_inner_right._simp_1_1 | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"Monoid",
"HMul.hMul",
"pow_two",
"Monoid.toMulOneClass",
"MulOne.toMul",
"instOfNatNat",
"Monoid.toPow",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat",
"instHPow",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"instHMul"
] | false |
CentroidHom.instInhabited | Mathlib.Algebra.Ring.CentroidHom | [
"CentroidHom.id",
"Inhabited",
"NonUnitalNonAssocSemiring",
"CentroidHom",
"Inhabited.mk"
] | true |
_private.Mathlib.Logic.Equiv.Defs.0.Equiv.equivCongr_trans._proof_1_1 | Mathlib.Logic.Equiv.Defs | [
"False",
"Equiv.instEquivLike",
"eq_false",
"Equiv.equivCongr",
"Equiv.trans_apply",
"congrArg",
"Equiv.trans",
"HEq.refl",
"Equiv.equivCongr_apply_apply",
"Classical.byContradiction",
"DFunLike.coe.hcongr_6",
"Exists",
"Eq.mp",
"Equiv.symm_trans_apply",
"id",
"Equiv",
"Lean.Grind.fo... | false |
DifferentiableAt.continuousMultilinearMapCompContinuousLinearMap | Mathlib.Analysis.Calculus.FDeriv.ContinuousMultilinearMap | [
"ContinuousLinearMap.comp",
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Pi.addCommMonoid",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"Pi.topologicalSpace",
"ContinuousLinearMap.topologicalSpace... | true |
_private.Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex.0.SSet.Subcomplex.Pairing.RankFunction.Cell.subcomplex_not_le_filtration._simp_1_2 | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | [
"Set.mem_union",
"Membership.mem",
"Set.instUnion",
"propext",
"Or",
"Union.union",
"Eq",
"Set.instMembership",
"Set"
] | false |
OrthonormalBasis.repr_reindex | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"fact_one_le_two_ennreal",
"Equiv.instEquivLike",
"OrthonormalBasis.repr",
"OrthonormalBasis.reindex",
"Inner.inner",
"congrArg",
... | true |
CategoryTheory.PreOneHypercover.Hom.w₁₂._autoParam | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.MessageData.Exprs.noConfusionType | Mathlib.Lean.MessageData.ForExprs | [
"Lean.MessageData",
"Lean.MessageData.Exprs.casesOn",
"Eq",
"Lean.MessageData.Exprs"
] | false |
curveIntegrable_neg_iff | Mathlib.MeasureTheory.Integral.CurveIntegral.Basic | [
"NormedCommRing.toNormedRing",
"SubtractionMonoid.toInvolutiveNeg",
"Pi.instNeg",
"NormedRing.toRing",
"NormedSpace",
"Pi.involutiveNeg",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Eq.mp",
"neg_neg",
"Subt... | true |
ENNReal.div_eq_one_iff | Mathlib.Data.ENNReal.Inv | [
"Eq.mpr",
"MulOne.toOne",
"instHDiv",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"Eq.rec",
"id",
"MulOne.toMul",
"HDiv.hDiv",
"Ne",
"ENNReal.instCommSemiring",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"instMulZeroOneClassOfSemiring",
"MulOneClass.toMulOne",
... | true |
HomotopicalAlgebra.Precylinder.unop._proof_3 | Mathlib.AlgebraicTopology.ModelCategory.PathObject | [
"HomotopicalAlgebra.Precylinder.unop._proof_1",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op_inj",
"HomotopicalAlgebra.Precylinder.I",
"Quiver.Hom.unop",
"HomotopicalAlgebra.Precylinder.π",
"CategoryTheory.CategoryStruct.id",
"HomotopicalAlgebra.Precylinder",
... | false |
Submonoid.multiset_noncommProd_mem | Mathlib.Algebra.Group.Submonoid.BigOperators | [
"Monoid",
"Eq.mpr",
"MulOne.toOne",
"Monoid.toMulOneClass",
"congrArg",
"setOf",
"Multiset.noncommProd_coe",
"Commute",
"Membership.mem",
"Multiset",
"id",
"MulOne.toMul",
"Set.Pairwise",
"Quotient.inductionOn",
"Quotient.mk",
"Multiset.instMembership",
"List",
"Multiset.ofList",
... | true |
Nat.nth_mem_of_ne_zero | Mathlib.Data.Nat.Nth | [
"Nat.nth_mem",
"Nat.lt_card_toFinset_of_nth_ne_zero",
"Ne",
"instOfNatNat",
"Nat",
"Nat.nth",
"OfNat.ofNat"
] | true |
CategoryTheory.Reflective.mk | Mathlib.CategoryTheory.Adjunction.Reflective | [
"CategoryTheory.Functor",
"CategoryTheory.Reflective.mk",
"CategoryTheory.Adjunction",
"CategoryTheory.Functor.Faithful",
"CategoryTheory.Reflective",
"CategoryTheory.Category",
"CategoryTheory.Functor.Full"
] | true |
IsCoinitial.eq_1 | Mathlib.Order.Bounds.Defs | [
"IsCoinitial",
"Membership.mem",
"Exists",
"LE.le",
"LE",
"And",
"Eq.refl",
"Eq",
"Set.instMembership",
"Set"
] | true |
_private.Lean.Meta.DiscrTree.Main.0.Lean.Meta.DiscrTree.getKeyArgs._sparseCasesOn_3 | Lean.Meta.DiscrTree.Main | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
Algebra.rankAtStalk_eq_of_isPushout | Mathlib.RingTheory.Flat.Rank | [
"Eq.mpr",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Module.rankAtStalk",
"Algebra.algebraMap",
"AlgEquiv.symm",
"Algebra.IsPushout.equiv",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup... | true |
Class.instCompleteLattice._proof_13 | Mathlib.SetTheory.ZFC.Class | [
"LT.mk",
"Class.instCompleteLattice._aux_1",
"ZFSet",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Preorder.mk",
"Class.instCompleteLattice._aux_9",
"Class.instCompleteLattice._proof_6",
"LE.le",
"Class.instCompleteLattice._proof_5",
"Set.instDistribLattice._proof_7",
"LE.mk",
"Class.instCom... | false |
Lean.Server.Test.Runner.Client.Hyp.isInserted? | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.Hyp",
"Bool",
"Option"
] | true |
CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d | Mathlib.CategoryTheory.Preadditive.Injective.Resolution | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.single₀",
"congrArg",
"CategoryTheory.InjectiveResolution.ι",
"AddRightCancelSemigroup.toAddSemigroup",
... | true |
FrameHom | Mathlib.Order.Hom.CompleteLattice | [
"FrameHom.mk",
"CompleteLattice"
] | true |
NormedDivisionRing.ratCast._inherited_default | Mathlib.Analysis.Normed.Field.Basic | [
"Rat.castRec",
"Rat",
"id",
"Int",
"Div.mk",
"Nat",
"NatCast.mk",
"IntCast.mk"
] | false |
Std.DTreeMap.Internal.Impl.balanceₘ.fun_cases_unfolding | Std.Data.DTreeMap.Internal.Balancing | [
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.balanceₘ.match_3.congr_eq_1",
"Std.DTreeMap.Internal.Impl.balanceₘ",
"HMul.hMul",
"_private.Std.Data.DTreeMap.Internal.Balancing.0.Std.DTreeMap.Internal.Impl.balanceₘ.match_1.splitter",
"congrArg",
"Std.DTreeMap.Internal.Impl.rotateR",
"HEq.refl",
"False.elim",
... | true |
_private.Init.Data.String.Lemmas.Pattern.Pred.0.String.Slice.Pattern.Model.CharPred.Decidable.revMatchAt?_eq_revMatchAt?_decide._simp_1_1 | Init.Data.String.Lemmas.Pattern.Pred | [
"String.Slice.Pattern.Model.CharPred.Decidable.instPatternModelForallCharPropOfDecidablePred",
"String.Slice",
"String.Slice.Pattern.Model.CharPred.instPatternModelForallCharBool",
"DecidablePred",
"String.Slice.Pattern.Model.CharPred.Decidable.isLongestRevMatchAt_iff_isLongestRevMatchAt_decide",
"propext... | false |
LieAlgebra.IsExtension.exact | Mathlib.Algebra.Lie.Extension | [
"LieHom",
"CommRing",
"LieHom.range",
"LieRing",
"LieHom.ker",
"LieIdeal.toLieSubalgebra",
"LieAlgebra.IsExtension",
"LieSubalgebra",
"LieAlgebra",
"Eq"
] | true |
MonotoneOn._to_dual_cast_4 | Mathlib.Order.Monotone.Defs | [
"Preorder.toLE",
"Membership.mem",
"LE.le",
"MonotoneOn",
"MonotoneOn._proof_3",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | false |
FirstOrder.Language.Ultraproduct.structure._aux_3 | Mathlib.ModelTheory.Ultraproducts | [
"FirstOrder.Language.Prestructure.rel_equiv",
"instDecidableEqFin",
"Quotient.finChoice",
"FirstOrder.Language.Structure.RelMap",
"autoParam",
"Fin.fintype",
"piSetoid",
"FirstOrder.Language.Structure",
"Filter.Product",
"Quotient",
"Nat",
"FirstOrder.Language.Relations",
"FirstOrder.Languag... | false |
CategoryTheory.Lax.LaxTrans.StrongCore.naturality | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"CategoryTheory.Lax.LaxTrans.app",
"CategoryTheory.LaxFunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory",
"CategoryTheo... | true |
CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux | Mathlib.CategoryTheory.Sites.CoverLifting | [
"CategoryTheory.Functor.op",
"CategoryTheory.Presheaf.IsSheaf.isLimitMultifork",
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.catego... | true |
_private.Mathlib.Condensed.Discrete.LocallyConstant.0.CompHausLike.LocallyConstant.adjunction._proof_2 | Mathlib.Condensed.Discrete.LocallyConstant | [
"CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions",
"CategoryTheory.Functor",
"CategoryTheory.Preregular",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompHausLike.HasExplicitFiniteCoproducts",
"CategoryTheory.ConcreteCategory.hom",
"ContinuousMap",
"Ca... | false |
groupCohomology.cocycles₁IsoOfIsTrivial._proof_6 | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | [
"Pi.Function.module",
"Submodule",
"Rep.V",
"CommRing",
"Pi.addCommMonoid",
"Equiv.instEquivLike",
"Rep.IsTrivial",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Additive",
"AddMonoid.toAddZeroClass",
"groupCohomology.instFunLikeSubtypeForal... | false |
Lean.Parser.Term.arrow.formatter | Lean.Parser.Term | [
"Lean.PrettyPrinter.Formatter",
"Lean.PrettyPrinter.Formatter.trailingNode.formatter",
"instOfNatNat",
"Lean.PrettyPrinter.Formatter.checkPrec.formatter",
"Nat",
"Lean.Parser.termParser.formatter",
"Lean.Parser.unicodeSymbol.formatter",
"Lean.PrettyPrinter.Formatter.andthen.formatter",
"OfNat.ofNat"... | true |
isOpen_range_sigmaMk | Mathlib.Topology.Constructions | [
"instTopologicalSpaceSigma",
"TopologicalSpace",
"isOpenMap_sigmaMk",
"IsOpen",
"Sigma.mk",
"Set.range",
"IsOpenMap.isOpen_range",
"Sigma"
] | true |
definition._@.Mathlib.Topology.FiberBundle.Constructions.1875155857._hygCtx._hyg.8 | Mathlib.Topology.FiberBundle.Constructions | [
"Bundle.Pullback",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"SemilatticeInf.toMin",
"TopologicalSpace",
"Bundle.TotalSpace.proj",
"TopologicalSpace.induced",
"Bundle.TotalSpace",
"Bundle.Pullback.lift",
"ConditionallyCompleteLattice.toLattice",
"M... | false |
Matrix.toBilin'_apply | Mathlib.LinearAlgebra.Matrix.BilinearForm | [
"Pi.Function.module",
"Algebra.to_smulCommClass",
"instHSMul",
"Semiring.toModule",
"Pi.addCommMonoid",
"HMul.hMul",
"Finset.univ",
"Matrix.module",
"CommSemiring.toNonUnitalCommSemiring",
"LinearMap.BilinForm",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Matr... | true |
_private.Mathlib.Lean.Meta.CongrTheorems.0.Lean.Meta.mkRichHCongr.withNewEqs | Mathlib.Lean.Meta.CongrTheorems | [
"_private.Mathlib.Lean.Meta.CongrTheorems.0.Lean.Meta.mkRichHCongr.withNewEqs.loop",
"Lean.Expr",
"Lean.Meta.MetaM",
"instOfNatNat",
"List.toArray",
"Array",
"Lean.Meta.CongrArgKind",
"Lean.Meta.FunInfo",
"Nat",
"Bool",
"Prod",
"OfNat.ofNat",
"List.nil",
"Option"
] | true |
_private.Mathlib.Algebra.Lie.Submodule.0.LieSubmodule.instInfSet._simp_2 | Mathlib.Algebra.Lie.Submodule | [
"Set.iInter",
"Membership.mem",
"Set.mem_iInter",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
KaehlerDifferential.isBaseChange | Mathlib.RingTheory.Kaehler.TensorProduct | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"LinearMap.restrictScalars",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"instAddCommGroupKaehlerDifferential... | true |
MeasCat.instLargeCategory._proof_5 | Mathlib.MeasureTheory.Category.MeasCat | [
"Measurable.comp",
"Measurable",
"MeasCat.carrier",
"MeasCat",
"Function.comp",
"Subtype",
"MeasCat.str",
"Subtype.val",
"Subtype.property"
] | false |
Filter.tendsto_neg_atTop_iff._simp_1 | Mathlib.Order.Filter.AtTopBot.Group | [
"NegZeroClass.toNeg",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"PartialOrder",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Filter.atTop",
"Filter.Tendsto",
"propext",
"Filter.atBot",
... | false |
SimplexCategory.δ_one_eq_const | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"instNeZeroNatHAdd_1",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SimplexCategory.instDecidableEqHom",
"SimplexCategory.δ",
"id",
"Fin.instOfNat",
"instOfNatNat",
"Bool.true",
"instHAdd",
"SimplexCategory.const",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Simp... | true |
_private.Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology.0.CochainComplex.HomComplex.CohomologyClass.toHom._simp_1 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | [
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubgroup",
"AddZero.toZero",
"AddGroup",
"AddZeroClass",
"AddGroup.toSubNegMonoid",
"AddSubgroup.instSetLike",
"propext",
"Zero.toOfNat0",
"SubNegMonoid.toAddMonoid",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"... | false |
Matrix.spectrum_toLpLin | Mathlib.Analysis.Matrix.Spectrum | [
"Module.End.instRing",
"NormedCommRing.toNormedRing",
"WithLp",
"Pi.Function.module",
"AlgEquiv.instEquivLike",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"NormedRing.toRing",
"IsScalarTower.right",
"CommRing.toNonUnitalCo... | true |
Lean.Meta.Sym.SymExtension.id | Lean.Meta.Sym.SymM | [
"Nat",
"Lean.Meta.Sym.SymExtension"
] | true |
Units.instIsManifoldModelWithCornersSelf | Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra | [
"Units.val",
"CompleteSpace",
"NormedRing.toRing",
"Units.instTopologicalSpaceUnits",
"PseudoMetricSpace.toUniformSpace",
"Units",
"NormedRing.toNonUnitalNormedRing",
"IsManifold",
"NonUnitalNormedRing.toNormedAddCommGroup",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"instHasSummableGeomSerie... | true |
Lean.Meta.DiscrTree.Key.star | Lean.Meta.DiscrTree.Types | [
"Lean.Meta.DiscrTree.Key.star",
"Lean.Meta.DiscrTree.Key"
] | true |
FirstOrder.Language.BoundedFormula.listEncode.eq_def | Mathlib.ModelTheory.Encoding | [
"FirstOrder.Language.BoundedFormula.imp",
"_private.Mathlib.ModelTheory.Encoding.0.FirstOrder.Language.BoundedFormula.listEncode.match_1.splitter",
"Eq.mpr",
"FirstOrder.Language.BoundedFormula.listEncode.match_1",
"congrArg",
"HEq.refl",
"List.map",
"FirstOrder.Language.BoundedFormula.brecOn",
"Fir... | true |
MvQPF.WEquiv.below.trans | Mathlib.Data.QPF.Multivariate.Constructions.Fix | [
"MvQPF.WEquiv.below.trans",
"instOfNatNat",
"MvQPF.WEquiv.below",
"instHAdd",
"HAdd.hAdd",
"Nat",
"MvQPF.WEquiv.trans",
"instAddNat",
"MvQPF",
"MvQPF.P",
"OfNat.ofNat",
"MvPFunctor.W",
"MvQPF.WEquiv",
"TypeVec"
] | true |
Multiset.nodup_zero | Mathlib.Data.Multiset.ZeroCons | [
"Multiset.Nodup",
"Multiset",
"Ne",
"List.Pairwise.nil",
"Zero.toOfNat0",
"OfNat.ofNat",
"Multiset.instZero"
] | true |
_private.Mathlib.Order.Category.DistLat.0.DistLat.Hom.mk._flat_ctor | Mathlib.Order.Category.DistLat | [
"_private.Mathlib.Order.Category.DistLat.0.DistLat.Hom.mk",
"DistLat.str",
"DistribLattice.toLattice",
"LatticeHom",
"DistLat.Hom",
"DistLat.carrier",
"DistLat"
] | false |
Lean.Server.LoadedILean.refs | Lean.Server.References | [
"Lean.Lsp.ModuleRefs",
"Lean.Server.LoadedILean"
] | true |
EReal.nhds_top | Mathlib.Topology.Instances.EReal.Lemmas | [
"Set.Ioi",
"Preorder.toLT",
"iInf",
"Iff.of_eq",
"congrArg",
"Filter.instInfSet",
"EReal.instTopologicalSpace",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"nhds",
"CoheytingAlgebra.toOrderTop",
"instTopEReal",
"Ne",
"CompleteDistribLattice.toCoframe",
"instCompleteLinearOrder... | true |
_private.Init.Data.String.Lemmas.FindPos.0.String.Slice.posGE._unary.eq_def | Init.Data.String.Lemmas.FindPos | [
"String.instLTRaw",
"String.Slice.pos",
"_private.Init.Data.String.FindPos.0.String.Slice.posGE._unary._proof_4",
"String.Slice.rawEndPos",
"String.Slice",
"PSigma.casesOn",
"_private.Init.Data.String.FindPos.0.String.Slice.posGE._unary._proof_5",
"String.instDecidableIsValidForSlice",
"String.Pos.R... | false |
Std.Time.Database.TZdb | Std.Time.Zoned.Database.TZdb | [
"Std.Time.Database.TZdb.mk"
] | true |
HomologicalComplex.mkHomFromDouble_f₁ | Mathlib.Algebra.Homology.Double | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"HomologicalComplex.double",
"Classical.propDecidable",
"HomologicalComplex.mkHomFromDouble",
"HomologicalComplex",
"Cat... | true |
Lean.Parser.ParserInfo.collectTokens | Lean.Parser.Types | [
"Lean.Parser.Token",
"List",
"Lean.Parser.ParserInfo"
] | true |
Lean.Meta.State._sizeOf_inst | Lean.Meta.Basic | [
"Lean.Meta.State._sizeOf_1",
"Lean.Meta.State",
"SizeOf.mk",
"SizeOf"
] | false |
CategoryTheory.Presieve.FamilyOfElements.Compatible.to_sieveCompatible | Mathlib.CategoryTheory.Sites.IsSheafFor | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Presieve.FamilyOfElements.SieveCompatible",
"CategoryTheory.Sieve",
"CategoryTheory.types",
"Iff.mp",
"CategoryTheory.Category.opposite",
"CategoryTheory.Presieve.FamilyOfElements",
"CategoryTheory.Presieve.compat... | true |
isInteger_of_is_root_of_monic | Mathlib.RingTheory.Polynomial.RationalRoot | [
"IsLocalization.IsInteger",
"NonAssocSemiring.toAddCommMonoidWithOne",
"IsDomain",
"CommRing",
"Dvd.dvd",
"CommSemiring.toSemiring",
"IsFractionRing",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"semigroupDvd",
"IsFractionRing.den",
"Algebra",
"CommSemiring.toCommMonoidWithZ... | true |
AddUnits.instAddCommGroupAddUnits | Mathlib.Algebra.Group.Units.Defs | [
"AddCommGroup",
"AddCommMonoid",
"AddCommGroup.mk",
"AddCommMonoid.toAddMonoid",
"AddUnits.instAddCommGroupAddUnits._proof_1",
"AddUnits.instAddGroup",
"AddUnits"
] | true |
_private.Mathlib.LinearAlgebra.CliffordAlgebra.Even.0.CliffordAlgebra.even.lift.fFold._proof_8 | Mathlib.LinearAlgebra.CliffordAlgebra.Even | [
"Distrib.leftDistribClass",
"Submodule",
"CommRing",
"CliffordAlgebra.EvenHom",
"IsScalarTower.right",
"AddMonoid.toAddSemigroup",
"Ring.toNonAssocRing",
"_private.Mathlib.LinearAlgebra.CliffordAlgebra.Even.0.CliffordAlgebra.even.lift.S._proof_2",
"LinearMap.ext",
"CommSemiring.toSemiring",
"Dis... | false |
Std.DTreeMap.Internal.Impl.get?.eq_1 | Std.Data.DTreeMap.Internal.Model | [
"Ord",
"Std.DTreeMap.Internal.Impl.get?",
"Option.none",
"Std.DTreeMap.Internal.Impl.leaf",
"Eq.refl",
"Eq",
"Std.LawfulEqOrd",
"Option"
] | true |
_private.Mathlib.Topology.Algebra.Group.Matrix.0.Matrix.SpecialLinearGroup.range_toGL.match_1_2 | Mathlib.Topology.Algebra.Group.Matrix | [
"Units.val",
"CommRing",
"Matrix.SpecialLinearGroup",
"CommSemiring.toSemiring",
"Matrix",
"AddGroupWithOne.toAddMonoidWithOne",
"Exists",
"AddMonoidWithOne.toOne",
"CommRing.toCommSemiring",
"Exists.casesOn",
"Fintype",
"Semiring.toMonoid",
"Exists.intro",
"One.toOfNat1",
"Matrix.Genera... | false |
Group.nilpotent_of_surjective | Mathlib.GroupTheory.Nilpotent | [
"Iff.mpr",
"Eq.mpr",
"MonoidHom.range",
"Trans.trans",
"MonoidHom.instFunLike",
"eq_top_iff",
"MonoidHom",
"Subgroup.map",
"Monoid.toMulOneClass",
"congrArg",
"eq_isEquiv",
"PartialOrder.toPreorder",
"MonoidHom.range_eq_map",
"Subgroup.upperCentralSeries",
"Group",
"Preorder.toLE",
"... | true |
Real.exists_seq_rat_strictAnti_tendsto | Mathlib.Topology.Instances.Real.Lemmas | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Real.instArchimedean",
"DivisionRing.toRatCast",
"StrictMono.monotone",
"MulZeroClass.toMul",
"instNoMaxOrderOfNontrivial",
"TopologicalSpace.PseudoMetrizableSpace.firstCountableTopology",
"Real.instRatCast",
"Rat",
"PartialOrder.toPreord... | true |
PadicInt.intCast_eq | Mathlib.NumberTheory.Padics.PadicIntegers | [
"Int.cast",
"Nat.Prime",
"PadicInt",
"congrArg",
"Fact",
"PadicInt.instCommRing",
"Int",
"AddGroupWithOne.toIntCast",
"iff_self",
"Int.cast_inj._simp_1",
"Iff",
"Nat",
"True",
"of_eq_true",
"congrFun'",
"CommRing.toRing",
"Eq",
"Ring.toAddGroupWithOne",
"Eq.trans",
"PadicInt.in... | true |
List.le_apply_get_maxOn?_of_mem | Init.Data.List.MinMaxOn | [
"Eq.mpr",
"List.minOn?",
"congrArg",
"List.isSome_minOn?_of_mem",
"Std.OppositeOrderInstances.instIsLinearPreorderOpposite",
"Membership.mem",
"inferInstance",
"Eq.mp",
"List.maxOn?_eq_minOn?",
"Option.get.congr_simp",
"id",
"LE.le",
"LE",
"_private.Init.Data.List.MinMaxOn.0.List.le_apply_... | true |
SetLike.GradeZero.instRing._proof_9 | Mathlib.Algebra.DirectSum.Internal | [
"SetLike",
"AddGroupWithOne.intCast_negSucc._autoParam",
"Semiring.toNatCast",
"NegZeroClass.toNeg",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"SetLike.GradeZero.instRing._aux_6",
"SetLike.GradeZero.subring",
"AddMonoid.toAddZeroClass",
"SubringClass.toRing._pro... | false |
OrderIso.sumLexAssoc_apply_inl_inr | Mathlib.Data.Sum.Order | [
"OrderIso.sumLexAssoc",
"Sum.Lex.LE",
"Equiv.instEquivLike",
"Lex",
"Sum",
"Equiv",
"OrderIso",
"Sum.inl",
"LE",
"instFunLikeOrderIso",
"Sum.inr",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike",
"toLex"
] | true |
GrpCat.SurjectiveOfEpiAuxs.g_apply_fromCoset | Mathlib.Algebra.Category.Grp.EpiMono | [
"GrpCat.SurjectiveOfEpiAuxs.g",
"MonoidHom.range",
"instHSMul",
"GrpCat",
"MonoidHom.instFunLike",
"instSMulOfMul",
"Equiv.instEquivLike",
"GrpCat.SurjectiveOfEpiAuxs.XWithInfinity.fromCoset",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"GrpCat.str",
"Monoid.toMulOne... | true |
integral_log | Mathlib.Analysis.SpecialFunctions.Integrals.Basic | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Real",
"Mathlib.Meta.NormNum.instAddMonoidWithOne",
"Mathlib.Tactic.... | true |
CategoryTheory.FreeMonoidalCategory.Hom.ctorElim | Mathlib.CategoryTheory.Monoidal.Free.Basic | [
"CategoryTheory.FreeMonoidalCategory.Hom.α_inv",
"CategoryTheory.FreeMonoidalCategory.Hom.whiskerLeft",
"CategoryTheory.FreeMonoidalCategory.Hom.ctorIdx",
"CategoryTheory.FreeMonoidalCategory.Hom.id",
"CategoryTheory.FreeMonoidalCategory.Hom.l_hom",
"CategoryTheory.FreeMonoidalCategory.Hom.casesOn",
"Ca... | false |
Aesop.PremiseIndex._sizeOf_inst | Aesop.Forward.PremiseIndex | [
"Aesop.PremiseIndex._sizeOf_1",
"Aesop.PremiseIndex",
"SizeOf.mk",
"SizeOf"
] | false |
ModuleCat.exteriorPower.functor | Mathlib.Algebra.Category.ModuleCat.ExteriorPower | [
"CategoryTheory.Functor",
"CommRing",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat.exteriorPower.functor._proof_4",
"ModuleCat",
"CategoryTheory.Functor.mk",
"ModuleCat.exteriorPower",
"Nat",
"ModuleCat.moduleCategory",
"ModuleCat.exteriorPower.map",
"CategoryTheory.Categ... | true |
sSupIndep_iff | Mathlib.Order.SupIndep | [
"Iff.mpr",
"sSupIndep",
"Eq.mpr",
"Iff.of_eq",
"iSupIndep",
"congrArg",
"iSup",
"iSup_subtype",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"Set.Elem",
"Set.instSingletonSe... | true |
Aesop.GoalState.ctorIdx | Aesop.Tree.Data | [
"Aesop.GoalState",
"Aesop.GoalState.casesOn",
"Nat"
] | false |
unexpandMkArray0 | Init.NotationExtra | [
"Pure.pure",
"Lean.Syntax.node",
"_private.Init.NotationExtra.0.unexpandArrayEmpty.match_1",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"EStateM.instMonad",
"Array.mkArray0",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad",
... | true |
Lean.Elab.Tactic.evalWithReducible | Lean.Elab.Tactic.ElabTerm | [
"instMonadControlTOfPure",
"Lean.Meta.State",
"Lean.Elab.Tactic.Context",
"Lean.Syntax",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instOfNatNat",
"Lean.Elab.Tactic.instMonadTacticM",
"Applicative.toPure",
"instMonadControlStateRefT'",
"GetElem.getElem",
"Unit",
"Lean.Core.CoreM",
"Lean.Elab.Tact... | true |
Submonoid.mem_closure_pair | Mathlib.Algebra.Group.Submonoid.Membership | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"CompleteLattice.toLattice",
"Submonoid.mem_sup",
"Monoid.toMulOneClass",
"congrArg",
"_private.Mathlib.Algebra.Group.Submonoid.Membership.0.Submonoid.mem_closure_pair._simp_1_1",
"Membership.mem",
"Set.singleton_union",
"Exists",
"Set.instUni... | true |
BooleanRing.sup_comm | Mathlib.Algebra.Ring.BooleanRing | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.mul_congr",
"HMul.hMul",
"Nat.rawCast",
"congrArg",
"CommSemiring.toSemiring",
"BooleanRing.sup",
"Mathlib.Meta.NormNum.IsNat.of_raw",
"BooleanRing.toCommRing",
"Mathlib.T... | true |
CategoryTheory.SmallObject.functorMapTgt.eq_1 | Mathlib.CategoryTheory.SmallObject.Construction | [
"CategoryTheory.SmallObject.FunctorObjIndex.i",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.SmallObject.FunctorObjIndex",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"CategoryTheory.Di... | true |
IsLocalDiffeomorphAt.mfderivToContinuousLinearEquiv._proof_2 | Mathlib.Geometry.Manifold.LocalDiffeomorph | [
"ContinuousLinearMap.comp",
"Eq.mpr",
"Function.LeftInverse",
"mfderiv_comp",
"mfderiv",
"NormedSpace",
"IsLocalDiffeomorphAt.localInverse_mdifferentiableAt",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupTangentSpace",
"ContinuousLinearMap.funLike",
... | false |
Action.Functor.mapActionPreservesLimitsOfShapeOfPreserves | Mathlib.CategoryTheory.Action.Limits | [
"Monoid",
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.Limits.PreservesLimitsOfShape.preservesLimit",
"CategoryTheory.Limits.HasLimitsOfShape",
"Action.Functor.mapActionPreservesLimit_of_preserves",
"CategoryTheory.Functor.comp",
"inferInstance",
"CategoryTheory.... | true |
Lean.Compiler.InlineAttributeKind.alwaysInline.sizeOf_spec | Lean.Compiler.InlineAttrs | [
"Lean.Compiler.InlineAttributeKind.alwaysInline",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Compiler.InlineAttributeKind",
"Lean.Compiler.InlineAttributeKind._sizeOf_inst"
] | true |
AddSubgroup.normalizer_addCommutator_ge_right | Mathlib.GroupTheory.Commutator.Basic | [
"Eq.mpr",
"AddSubgroup.addCommutator_comm",
"congrArg",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"AddSubgroup.addCommutator",
"Bracket.bracket",
"Preorder.toLE",
"AddSubgroup.normalizer",
"id",
"LE.le",
"AddSubgroup",
"AddGroup",
"SetLike.coe",
"AddSubgroup.instSetLike"... | true |
Topology.IsCoinducing.continuous | Mathlib.Topology.Maps.Basic | [
"Eq.mpr",
"Continuous",
"congrArg",
"Continuous.mk",
"Topology.IsCoinducing",
"id",
"Topology.IsCoinducing.isOpen_preimage",
"TopologicalSpace",
"Set.preimage",
"propext",
"IsOpen",
"Eq",
"Set"
] | true |
partialFunToPointed._proof_4 | Mathlib.CategoryTheory.Category.PartialFun | [
"Option.elim'",
"Classical.propDecidable",
"CategoryTheory.CategoryStruct.id",
"Pointed.point",
"Option.none",
"Pointed.mk",
"PartialFun.largeCategory",
"Part.Dom",
"CategoryTheory.Category.toCategoryStruct",
"PartialFun",
"Pointed.X",
"Eq",
"Part.toOption",
"rfl",
"Option"
] | false |
NatPow.casesOn | Init.Prelude | [
"NatPow",
"NatPow.rec",
"Nat",
"NatPow.mk"
] | false |
Std.DHashMap.Const.mem_unitOfList._simp_1 | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.Const.unitOfList",
"List.contains",
"Membership.mem",
"Std.DHashMap.instMembership",
"Std.DHashMap.Const.mem_unitOfList",
"LawfulHashable",
"Bool.true",
"List",
"Unit",
"EquivBEq",
"propext",
"Bool",
"Hashable",
"BEq",
"Eq",
"Std.DHashMap"
] | false |
CategoryTheory.Bicategory.eqToHom_whiskerRight | Mathlib.CategoryTheory.Bicategory.Strict.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HEq.refl",
"CategoryTheory.eqToHom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.whiskerRight",
"Eq.casesOn",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.Bicateg... | true |
Filter.Germ.instLinearOrder | Mathlib.Order.Filter.FilterProduct | [
"Preorder.toLT",
"Lattice.toLinearOrder",
"LinearOrder",
"PartialOrder.toPreorder",
"Classical.propDecidable",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Filter.Germ.instLinearOrder._proof_1",
"LE.le",
"Filter.Germ",
"LT.lt",
"Filter.Germ.instLattice",
"... | true |
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