name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Environment.const2ModIdx | Lean.Environment | [
"Lean.ModuleIdx",
"Lean.Environment.toKernelEnv",
"Std.HashMap",
"Lean.Kernel.Environment.const2ModIdx",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.Environment",
"Lean.instHashableName"
] | true |
Int.floor_eq_self_iff_mem | Mathlib.Algebra.Order.Floor.Ring | [
"Int.cast",
"Eq.mpr",
"Int.floor",
"Int.floor_intCast",
"IsOrderedRing",
"congrArg",
"LinearOrder",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"id",
"Int",
"AddGroupWithOne.toIntCast",
"Set.mem_range._simp_1",
"Iff",
"Exists.casesOn",
"... | true |
DirectSum.GradeZero.commRing._proof_8 | Mathlib.Algebra.DirectSum.Ring | [
"instHSMul",
"AddMonoidHom.instAddMonoidHomClass",
"instAddCommMonoidDirectSum",
"AddCommGroup.toAddCommMonoid",
"DirectSum.GradeZero.ring",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"AddMonoid.toNSMul",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DirectSum.GCommRing.toGRi... | false |
Affine.Simplex.disjoint_interior_closedInterior_faceOpposite | Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | [
"Nontrivial",
"False",
"Nat.instMulZeroClass",
"Affine.Simplex.interior",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Finset.univ",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Affine.Simplex.disjoint_interior_closedInterior_face",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Comp... | true |
_private.Init.Data.Array.Lemmas.0.Array.map_eq_append_iff._simp_1_2 | Init.Data.Array.Lemmas | [
"Array.instAppend",
"Array.filterMap_eq_append_iff",
"Exists",
"instOfNatNat",
"Array",
"instHAppendOfAppend",
"And",
"Array.filterMap",
"Nat",
"propext",
"OfNat.ofNat",
"Eq",
"Array.size",
"HAppend.hAppend",
"Option"
] | false |
Algebra.tensorH1CotangentOfIsLocalization._proof_3 | Mathlib.RingTheory.Etale.Kaehler | [
"RingHom.instRingHomClass",
"CommRing",
"Algebra.Extension.commRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"IsLocalization",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"IsScalarTower.toAlgHom",
"Is... | false |
Polynomial.trailingDegree_le_of_ne_zero | Mathlib.Algebra.Polynomial.Degree.TrailingDegree | [
"Iff.mpr",
"ENat.instNatCast",
"Finset",
"Finset.min_le",
"Membership.mem",
"Polynomial.mem_support_iff",
"Ne",
"LE.le",
"Nat.cast",
"Polynomial",
"Polynomial.coeff",
"instLEENat",
"Finset.instSetLike",
"Nat",
"ENat",
"Polynomial.trailingDegree",
"Semiring",
"Zero.toOfNat0",
"OfN... | true |
NonUnitalRingHom.copy | Mathlib.Algebra.Ring.Hom.Defs | [
"MulHom",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"NonUnitalRingHom.copy._proof_1",
"NonUnitalRingHom.instFunLike",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonUnitalRingHom.toAddMonoidHom",
"Distrib.toMul",
"NonUnitalRingHom.toMulHom",
"NonUnitalRingHom.mk",
"NonUnitalNonAsso... | true |
_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.RotateRight.0.Std.Tactic.BVDecide.BVExpr.bitblast.blastRotateRight.go_get_aux._proof_1_3 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.RotateRight | [
"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",
"Lean.Omega.combo_s... | false |
Lean.Meta.Tactic.TryThis.addExactSuggestions | Lean.Meta.Tactic.TryThis | [
"Pure.pure",
"Lean.MessageData",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Array.push",
"instForInOfForIn'",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"Lean.Meta.Tactic.TryThis.SuggestionStyle",
"String",
... | true |
Commute.geom_sum₂_Ico | Mathlib.Algebra.Field.GeomSum | [
"Eq.mpr",
"False",
"instHDiv",
"HMul.hMul",
"eq_false",
"Ring.toNonAssocRing",
"MulZeroClass.toMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"_private.Mathlib.Algebra.Field.GeomSum.0.Commute.geom_sum₂_Ico._simp_1_1",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.h... | true |
CategoryTheory.projectiveDimension_lt_iff | Mathlib.CategoryTheory.Abelian.Projective.Dimension | [
"Iff.mpr",
"WithBot.addMonoidWithOne",
"WithBot.instPreorder",
"Eq.mpr",
"WithBot.zeroLEOneClass",
"WithBot.addLeftMono",
"False",
"Nat.instMulZeroClass",
"csInf_mem",
"sInf_lt_iff",
"WithBot",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"instCompleteLinearOrderENat",
"instCharZeroENat"... | true |
Lean.Parser.Term.termTry | Lean.Parser.Do | [
"Lean.Parser.Term.doSeq",
"Lean.Parser.Term.doCatch",
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.Term.doCatchMatch",
"Lean.Parser.leadingNode",
"Lean.Parser.optional",
"instHAndThenOfAndThen",
"HOrElse.hOrElse",
"instOfNatNat",
"Lean.Parser.symbol",
"Lean.Parser.withAntiquot",
"... | true |
IsGroupLikeElem.antipode._simp_1 | Mathlib.RingTheory.HopfAlgebra.GroupLike | [
"HopfAlgebraStruct.toBialgebra",
"IsGroupLikeElem",
"Bialgebra.toCoalgebra",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"Algebra.toModule",
"HopfAlgebra",
"LinearMap",
"IsGroupLikeElem.antipode",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnita... | false |
ExceptT.bindCont.eq_2 | Init.Control.Lawful.Instances | [
"Pure.pure",
"Monad.toApplicative",
"Except.error",
"Applicative.toPure",
"ExceptT",
"ExceptT.bindCont",
"Eq.refl",
"Except",
"Monad",
"Eq"
] | true |
intervalIntegral.derivWithin_integral_of_tendsto_ae_left._auto_1 | Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Orientation.kahler_map | Mathlib.Analysis.InnerProductSpace.TwoDim | [
"instInnerProductSpaceRealComplex",
"LinearIsometryEquiv.instEquivLike",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Orientation",
"Real.partialOrder",
"Real",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toMod... | true |
Lean.Elab.Tactic.Grind.SimpCacheKey.noConfusionType | Lean.Elab.Tactic.Grind.Basic | [
"Lean.Elab.Tactic.Grind.ExtraTheorem",
"Lean.Elab.Tactic.Grind.SimpCacheKey",
"Array",
"Lean.Name",
"Eq",
"Lean.Elab.Tactic.Grind.SimpCacheKey.casesOn"
] | false |
_private.Mathlib.CategoryTheory.WithTerminal.Cone.0.CategoryTheory.WithTerminal.coneBack_obj_π_app | Mathlib.CategoryTheory.WithTerminal.Cone | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Over.mk",
"CategoryTheory.instCategoryOver",
"CategoryTheory.WithTerminal",
"C... | true |
GrpTypeEquivalenceGrp.inverse._proof_1 | Mathlib.CategoryTheory.Monoidal.Internal.Types.Grp | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"GrpCat.hasForgetToMonCat",
"MonTypeEquivalenceMon.inverse",
"GrpCat",
"MonoidHom.instFunLike",
"inv_mul_cancel",
"DivInvOneMonoid.toInvOneClass",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"MonoidHom",
... | false |
Fin.castSucc_lt_last._simp_2 | Mathlib.Data.Fin.SuccPred | [
"instOfNatNat",
"instHAdd",
"Fin.castSucc_lt_last",
"HAdd.hAdd",
"Nat",
"Fin.last",
"LT.lt",
"True",
"instLTFin",
"eq_true",
"instAddNat",
"Fin.castSucc",
"OfNat.ofNat",
"Fin",
"Eq"
] | false |
Aesop.SaturateM.Context.noConfusionType | Aesop.Saturate | [
"Aesop.SaturateM.Context.casesOn",
"Aesop.SaturateM.Context",
"Aesop.Options'",
"Eq"
] | false |
SSet.innerFibrations | Mathlib.AlgebraicTopology.Quasicategory.InnerFibration | [
"CategoryTheory.MorphismProperty",
"Opposite",
"CategoryTheory.Functor.category",
"SSet",
"CategoryTheory.MorphismProperty.rlp",
"CategoryTheory.types",
"SimplexCategory",
"CategoryTheory.Category.opposite",
"CategoryTheory.Category.toCategoryStruct",
"SimplexCategory.smallCategory",
"SSet.inner... | true |
LinearMap.BilinForm.dualSubmoduleToDual._proof_11 | Mathlib.LinearAlgebra.BilinearForm.DualLattice | [
"Submodule",
"IsDomain",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"LinearMap.BilinForm.dualSubmo... | false |
Nat.eq_sub_of_add_eq' | Init.Data.Nat.Lemmas | [
"_private.Init.Data.Nat.Lemmas.0.Nat.eq_sub_of_add_eq'._proof_1_1",
"HSub.hSub",
"instSubNat",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"Decidable.byContradiction",
"instAddNat",
"instDecidableEqNat",
"Eq",
"Not"
] | true |
_private.Mathlib.CategoryTheory.Localization.Monoidal.Basic.0.CategoryTheory.Localization.Monoidal._aux_Mathlib_CategoryTheory_Localization_Monoidal_Basic___macroRules__private_Mathlib_CategoryTheory_Localization_Monoidal_Basic_0_CategoryTheory_Localization_Monoidal_termL'_1 | Mathlib.CategoryTheory.Localization.Monoidal.Basic | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr... | false |
Ideal.height_strict_mono_of_isPrime | Mathlib.RingTheory.Ideal.Height | [
"Eq.mpr",
"CommRing",
"Ideal.height_top",
"Preorder.toLT",
"iInf",
"instCompleteLinearOrderENat",
"Ideal.height_lt_top",
"Semiring.toModule",
"instAddMonoidWithOneENat",
"Ideal.minimalPrimes",
"instTopENat",
"congrArg",
"CommSemiring.toSemiring",
"CompletelyDistribLattice.toCompleteLattice... | true |
List.Sublist.bagInter_inter | Mathlib.Data.List.Lattice | [
"Eq.mpr",
"List.inter_cons_of_notMem",
"False",
"Decidable.casesOn",
"eq_false",
"instLawfulBEq",
"congrArg",
"Decidable",
"Membership.mem",
"id",
"List.rec",
"if_pos",
"instBEqOfDecidableEq",
"List.Sublist.refl._simp_1",
"List.cons",
"Inter.inter",
"List",
"List.instInterOfBEq_bat... | true |
Array.findIdx?_isSome | Init.Data.Array.Find | [
"congrArg",
"Array.any_congr",
"Array.casesOn",
"Array.any",
"List.findIdx?",
"instOfNatNat",
"List.findIdx?_toArray",
"List.toArray",
"Array",
"List.any_toArray'",
"List",
"List.size_toArray",
"Nat",
"congr",
"True",
"eq_self",
"Bool",
"of_eq_true",
"List.any",
"Eq.refl",
"A... | true |
Lean.Grind.CommRing.Stepwise.superpose_certC | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly.combineC",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.beq'",
"Int",
"Lean.Grind.CommRing.Poly.mulMonC",
"Nat",
"Bool",
"Lean.Grind.CommRing.Mon"
] | true |
_private.Init.Data.UInt.Lemmas.0.USize.toUInt8_eq._simp_1_1 | Init.Data.UInt.Lemmas | [
"Nat",
"propext",
"UInt8.toNat_inj",
"UInt8.toNat",
"Eq.symm",
"UInt8",
"Eq"
] | false |
CategoryTheory.Limits.biprod.fst_op_opIso_hom_assoc | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Limits.biprod.opIso",
"Eq.mp",
"CategoryTheory.Limits.HasBinaryBip... | true |
_private.Mathlib.Analysis.Calculus.TangentCone.ProperSpace.0.tangentConeAt_nonempty_of_properSpace._simp_1_7 | Mathlib.Analysis.Calculus.TangentCone.ProperSpace | [
"One",
"ZeroLEOneClass",
"LE.le",
"LE",
"zero_le_one",
"True",
"eq_true",
"One.toOfNat1",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
Aesop.Options.ctorIdx | Aesop.Options.Public | [
"Aesop.Options",
"Nat"
] | false |
_private.Lean.Elab.Match.0.Lean.Elab.Term.isPatternVar._sparseCasesOn_4 | Lean.Elab.Match | [
"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 |
CategoryTheory.WithTerminal.down | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.WithTerminal",
"CategoryTheory.WithTerminal.of",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.WithTerminal.instCategory",
"CategoryTheory.Category"
] | true |
Matrix.toBlocks₂₁ | Mathlib.Data.Matrix.Block | [
"Equiv.instEquivLike",
"Matrix",
"Matrix.of",
"Sum",
"Equiv",
"Sum.inl",
"Sum.inr",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Dioph.«termD&_» | Mathlib.NumberTheory.Dioph | [
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
partialOrderOfSO._proof_4 | Mathlib.Order.RelClasses | [
"asymm",
"False.elim",
"asymm_of_isTrans_of_irrefl",
"IsStrictOrder.toIsTrans",
"IsStrictOrder",
"partialOrderOfSO.match_5",
"Or",
"Eq",
"rfl",
"IsStrictOrder.toIrrefl"
] | false |
FourierTransformInv.casesOn | Mathlib.Analysis.Fourier.Notation | [
"FourierTransformInv.rec",
"FourierTransformInv.mk",
"FourierTransformInv"
] | false |
List.iterate.match_1 | Mathlib.Data.List.Defs | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
Aesop.RappId.noConfusion | Aesop.Tree.Data | [
"Aesop.RappId.noConfusionType",
"Nat",
"Aesop.RappId",
"Eq.ndrec",
"Eq.refl",
"Aesop.RappId.casesOn",
"Eq"
] | false |
isOpen_compl_iff._simp_1 | Mathlib.Topology.Basic | [
"Compl.compl",
"Set.instCompl",
"IsClosed",
"TopologicalSpace",
"propext",
"IsOpen",
"Eq",
"isOpen_compl_iff",
"Set"
] | false |
_private.Mathlib.Analysis.Convex.Side.0.AffineSubspace.sSameSide_self_iff.match_1_1 | Mathlib.Analysis.Convex.Side | [
"CommRing",
"CommSemiring.toSemiring",
"AffineSubspace.SSameSide",
"AddCommGroup.toAddCommMonoid",
"IsStrictOrderedRing",
"AddCommGroup.toAddGroup",
"Membership.mem",
"PartialOrder",
"AddCommGroup",
"And.casesOn",
"AffineSubspace.instSetLike",
"And",
"CommRing.toCommSemiring",
"And.intro",... | false |
Pi.normedCommGroup._proof_1 | Mathlib.Analysis.Normed.Group.Constructions | [
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"CommMagma.toMul",
"NormedCommGroup",
"CommSemigroup.toCommMagma",
"mul_comm",
"Pi.commSemigroup",
"NormedCommGroup.toCommGroup",
"Eq",
"CommGroup.toCommMonoid",
"instHMul"
] | false |
kroneckerTMulLinearEquiv._proof_2 | Mathlib.RingTheory.MatrixAlgebra | [
"LinearMap.id",
"Pi.Function.module",
"IsScalarTower.to_smulCommClass'",
"Matrix.liftLinear_single",
"Pi.addCommMonoid",
"Matrix.module",
"Matrix.isScalarTower",
"instDecidableEqProd",
"LinearMap.ext",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Matrix",
"IsSc... | false |
Function.Injective.invOfMemRange_surjective | Mathlib.Data.Fintype.Inv | [
"Set.mem_range_self",
"Function.Injective.right_inv_of_invOfMemRange",
"Function.Injective.invOfMemRange",
"congrArg",
"Membership.mem",
"Set.Elem",
"Subtype.mk",
"Fintype",
"True",
"eq_self",
"Exists.intro",
"of_eq_true",
"congrFun'",
"Set.range",
"Function.Injective",
"Eq",
"Set.in... | true |
SSet.const_app | Mathlib.AlgebraicTopology.SimplicialSet.Basic | [
"SSet.const",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"Quiver.Hom.op",
"TypeCat.instFunLikeFun",
"TypeCat.ofHom",
"instOfNatNat",
"SSet",
"CategoryTheory.Functor.map",
"instHAdd",
"SimplexCategory.const",
"TypeCat.Fun",
"... | true |
AlgHom.fieldRange._proof_1 | Mathlib.FieldTheory.IntermediateField.Basic | [
"AlgHom.algHomClass",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemiring",
"AlgHomClass.toRingHomClass",
"Semiring.toNonAssocSemiring",
"Field",
"RingHomClass"
] | false |
Polynomial.card_support_eraseLead_add_one | Mathlib.Algebra.Polynomial.EraseLead | [
"Eq.mpr",
"Polynomial.eraseLead_support",
"congrArg",
"Finset",
"HSub.hSub",
"id",
"Finset.card_erase_of_mem",
"instSubNat",
"Ne",
"instOfNatNat",
"Polynomial.eraseLead",
"Polynomial",
"Nat.casesAuxOn",
"instHAdd",
"instHSub",
"Polynomial.card_support_eq_zero",
"HAdd.hAdd",
"Nat",
... | true |
Lean.Meta.Grind.propagateNotDown._regBuiltin.Lean.Meta.Grind.propagateNotDown.declare_1._@.Lean.Meta.Tactic.Grind.Propagate.3610191934._hygCtx._hyg.8 | Lean.Meta.Tactic.Grind.Propagate | [
"Lean.Meta.Grind.registerBuiltinDownwardPropagator",
"IO",
"Lean.Meta.Grind.propagateNotDown",
"Unit",
"Lean.Name.mkStr1"
] | false |
AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singleton | Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite | [
"Iff.mpr",
"AlgebraicGeometry.PresheafedSpace.Hom",
"Set.ext",
"Eq.mpr",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.locallyOfFinitePresentation_of_isOpenImmersion",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme.Hom.toLRSHom",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrie... | true |
Algebra.SubmersivePresentation.ofSubsingleton._proof_2 | Mathlib.RingTheory.Extension.Presentation.Submersive | [
"Algebra.Generators.ker",
"RingHom.ker_eq_top_of_subsingleton",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Algebra.Extension.commRing",
"Algebra.Generators.Ring",
"Semiring.toModule",
"AlgHom.algHomClass",
"MvPolynomial.aeval",
"Algebra.algebraMap",
"congrArg",
"CommSe... | false |
Std.CloseableChannel.instDecidableEqError._proof_2 | Std.Sync.Channel | [
"Std.CloseableChannel.Error.ctorIdx",
"False",
"Std.CloseableChannel.Error",
"absurd",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Not"
] | false |
CompleteDistribLattice.MinimalAxioms.mk.sizeOf_spec | Mathlib.Order.CompleteBooleanAlgebra | [
"Lattice.toSemilatticeSup",
"iInf",
"CompleteLattice.toLattice",
"iSup",
"CompleteDistribLattice.MinimalAxioms",
"CompleteDistribLattice.MinimalAxioms._sizeOf_inst",
"PartialOrder.toPreorder",
"instSizeOfDefault",
"Preorder.toLE",
"Membership.mem",
"SemilatticeSup.toMax",
"CompleteLattice.toIn... | true |
ProfiniteAddGrp.instPreservesLimitsProfiniteForget₂ContinuousAddMonoidHomCarrierToTopTotallyDisconnectedSpaceToProfiniteContinuousMap | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"CategoryTheory.Functor",
"ContinuousAddMonoidHom",
"ContinuousMap",
"CategoryTheory.Limits.PreservesLimitsOfSize.mk",
"CategoryTheory.Functor.comp",
"ProfiniteAddGrp",
"Profinite.limitConeIsLimit",
"TotallyDisconnectedSpace",
"ContinuousAddMonoidHom.instFunLike",
"ProfiniteAddGrp.instHasForget₂Co... | true |
Mathlib.Tactic.AtomM.Recurse.Config.contextual._default | Mathlib.Util.AtomM.Recurse | [
"id",
"Bool",
"Bool.false"
] | false |
separableClosure.adjoin_eq_of_isAlgebraic | Mathlib.FieldTheory.PurelyInseparable.Basic | [
"IntermediateField.lift",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"IntermediateField.isScalarTower",
"CompleteLattice.toLattice",
"congrArg",
"CommSemiring.toSemiring",
"Interm... | true |
IrreducibleSpace.rec | Mathlib.Topology.Irreducible | [
"TopologicalSpace",
"Nonempty",
"IrreducibleSpace",
"IrreducibleSpace.mk",
"PreirreducibleSpace"
] | false |
AddMonoidHom.compLeftContinuous.congr_simp | Mathlib.Topology.ContinuousMap.StoneWeierstrass | [
"Continuous",
"ContinuousMap",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.compLeftContinuous",
"Eq.rec",
"AddZeroClass.toAddZero",
"ContinuousMap.instAddZeroClassOfContinuousAdd",
"TopologicalSpace",
"AddMonoid",
"Eq.ndrec",
"AddZero.toAdd",
"Eq.refl",
"ContinuousAdd",
"AddMonoidHom",
"Ad... | true |
Std.ExtDTreeMap.Const.getKey?_filter | Std.Data.ExtDTreeMap.Lemmas | [
"Option.pfilter",
"Std.ExtDTreeMap.getKey?",
"Std.DTreeMap",
"Std.ExtDTreeMap.mem_of_getKey?_eq_some",
"Option.some",
"Ordering",
"Std.TransCmp",
"Std.ExtDTreeMap.inductionOn",
"Std.DTreeMap.Const.getKey?_filter",
"Std.ExtDTreeMap",
"Bool",
"Std.ExtDTreeMap.filter",
"Std.ExtDTreeMap.Const.ge... | true |
CategoryTheory.GrothendieckTopology.toPretopology._proof_4 | Mathlib.CategoryTheory.Sites.Pretopology | [
"CategoryTheory.GrothendieckTopology.superset_covering",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.GrothendieckTopology.transitive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"congrArg",
"setOf",
"Membership.mem",
"Exists",
"id",
"Cat... | false |
AntitoneOn.sup | Mathlib.Order.Lattice | [
"sup_le_sup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeSup.toMax",
"LE.le",
"Pi.instMaxForall_mathlib",
"Max.max",
"AntitoneOn",
"SemilatticeSup.toPartialOrder",
"SemilatticeSup",
"Set.instMembership",
"Preorder",
"Set"
] | true |
_private.Mathlib.Algebra.Order.Antidiag.Nat.0.Nat.card_pair_lcm_eq.f._proof_1 | Mathlib.Algebra.Order.Antidiag.Nat | [
"Zero.ofOfNat0",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"NeZero",
"OfNat.ofNat"
] | false |
CategoryTheory.Mon.instCartesianMonoidalCategory._proof_3 | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"Eq.mpr",
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.MonObj.instIsMonHomToUnit",
"CategoryTheory.Limits.IsTerminal.ofUniqueHom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrA... | false |
StrictMonoOn.continuousWithinAt_right_of_image_mem_nhdsWithin | Mathlib.Topology.Order.MonotoneContinuity | [
"Filter.instMembership",
"StrictMonoOn.continuousWithinAt_right_of_closure_image_mem_nhdsWithin",
"OrderTopology",
"Preorder.toLT",
"ContinuousWithinAt",
"Set.Ici",
"subset_closure",
"LinearOrder",
"nhdsWithin",
"PartialOrder.toPreorder",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"D... | true |
Int.Linear.Poly.eval? | Lean.Meta.Tactic.Grind.Arith.Cutsat.Util | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Rat.instOfNat",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Util.0.Int.Linear.Poly.eval?.go",
"Lean.Meta.Grind.Arith.Cutsat.State.assignment",
"Lean.Meta.Grind.Goal",
"StateRefT'.instAlternativeOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"Rat",
"Lean.M... | true |
Sylow.inhabited | Mathlib.GroupTheory.Sylow | [
"Sylow",
"Group",
"Sylow.nonempty",
"Nat",
"Inhabited",
"Classical.inhabited_of_nonempty"
] | true |
_private.Mathlib.Data.Ordmap.Invariants.0.Ordnode.node4L.match_1.eq_2 | Mathlib.Data.Ordmap.Invariants | [
"Ordnode",
"Ordnode.node4L.match_1",
"Ordnode.node",
"Nat",
"Ordnode.nil",
"Eq.refl",
"Eq"
] | true |
_private.Lean.Meta.Tactic.Simp.Rewrite.0.Lean.Meta.Simp.discharge?'.match_3 | Lean.Meta.Tactic.Simp.Rewrite | [
"Unit.unit",
"Except.ok",
"Lean.Meta.Simp.DischargeResult.failedAssign",
"Lean.Meta.Simp.DischargeResult.maxDepth",
"Except.error",
"Unit",
"Lean.Meta.Simp.DischargeResult.notProved",
"Lean.Meta.Simp.DischargeResult",
"Except.casesOn",
"Except",
"Lean.Meta.Simp.DischargeResult.casesOn",
"Lean.... | false |
ModularForm.E₆ | Mathlib.NumberTheory.ModularForms.EisensteinSeries.Basic | [
"ModularForm",
"MonoidHom.range",
"Real",
"Matrix.SpecialLinearGroup",
"Matrix",
"instDecidableEqFin",
"ModularForm.E",
"Real.semiring",
"Matrix.SpecialLinearGroup.instGroup",
"Real.instRing",
"instOfNatNat",
"Int",
"Units.instGroup",
"Real.commRing",
"Fin.fintype",
"Int.instCommRing",... | true |
BitVec.slt_trichotomy | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"congrArg",
"BitVec",
"id",
"Int",
"Int.lt_trichotomy",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.slt_trichotomy._simp_1_1",
"Int.instLTInt",
"Bool.true",
"BitVec.slt",
"Nat",
"congr",
"LT.lt",
"Bool",
"BitVec.toInt",
"Or",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.slt_tr... | true |
Set.union_diff_self | Mathlib.Order.BooleanAlgebra.Set | [
"Set.instUnion",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
"SDiff.sdiff",
"Set.instBooleanAlgebra",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra",
"Union.union",
"sup_sdiff_self",
"Eq",
"Set.instSDiff",
"Set"
] | true |
Matrix.mul_transvection_apply_same | Mathlib.LinearAlgebra.Matrix.Transvection | [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Matrix.mul_single_apply_same",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Matrix.add",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"Matrix.instHMulOfFintypeOfMulOfAd... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RatAddSound.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.mem_of_necessary_assignment._simp_1_4 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RatAddSound | [
"Exists",
"not_exists",
"propext",
"Eq",
"Not"
] | false |
AddCommGroup.modEq_iff_eq_add_zsmul | Mathlib.Algebra.Group.ModEq | [
"Eq.mpr",
"AddCommGroup.ModEq",
"instHSMul",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Exists",
"_private.Mathlib.Algebra.Group.ModEq.0.AddCommGroup.modEq_iff_eq_add_zsmul._simp_1_1",
"AddZeroClass.toAddZero",
"AddCommGroup... | true |
CommMonCat.fullyFaithfulForgetToMonCat.eq_1 | Mathlib.Algebra.Category.MonCat.Basic | [
"MonoidHom.instFunLike",
"CommMonCat.instConcreteCategoryMonoidHomCarrier",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CommMonCat.fullyFaithfulForgetToMonCat._proof_1",
"CommMonCat.fullyFaithfulForgetToMonCat._proof_2",
"MonCat.Hom.hom",
"CommMonC... | true |
NonUnitalNonAssocSemiring.mem_center_iff | Mathlib.Algebra.Ring.CentroidHom | [
"AddMonoid.End.mulLeft",
"Subsemiring.instSetLike",
"HMul.hMul",
"NonUnitalSubsemiring.center",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddMonoid.End.mulRight",
"Commute",
"CentroidHom.centerToCentroid",
"RingHom",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.mp",
"id",
"Subtype",
... | true |
equicontinuousWithinAt_empty._simp_1 | Mathlib.Topology.UniformSpace.Equicontinuity | [
"UniformSpace",
"EquicontinuousWithinAt",
"equicontinuousWithinAt_empty",
"IsEmpty",
"TopologicalSpace",
"True",
"eq_true",
"Eq",
"Set"
] | false |
_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.analyze.go | Lean.Elab.Extra | [
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.analyze.go._f",
"IO.RealWorld",
"Unit",
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.Tree.brecOn",
"StateRefT'",
"Lean.Elab.Term.TermElabM",
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.Tree",
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.AnalyzeResult"
... | true |
Lean.Meta.Grind.AC.EqCnstr.casesOn | Lean.Meta.Tactic.Grind.AC.Types | [
"Lean.Meta.Grind.AC.EqCnstr",
"Lean.Grind.AC.Expr",
"Lean.Expr",
"Lean.Meta.Grind.AC.EqCnstrProof",
"PUnit",
"Nat",
"Bool",
"PUnit.unit",
"Lean.Grind.AC.Var",
"Lean.Grind.AC.Seq",
"Lean.Meta.Grind.AC.EqCnstr.rec",
"Lean.Meta.Grind.AC.EqCnstr.mk"
] | false |
IccRightChart._proof_1 | Mathlib.Geometry.Manifold.Instances.Real | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Real.partialOrder",
"Real.instLE",
"Real",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
"and_self",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Real.instSemilatticeSup",
"Real.instSub",
"AddMonoid.toAddZeroClass",
"PartialOrder.toP... | false |
Set.inl_compl_union_inr_compl | Mathlib.Order.BooleanAlgebra.Set | [
"Compl.compl",
"Set.instUnion",
"Sum",
"Sum.inl",
"Set.instCompl",
"Sum.inr",
"Set.image",
"_private.Mathlib.Order.BooleanAlgebra.Set.0.Set.inl_compl_union_inr_compl._proof_1_1",
"Union.union",
"Eq",
"Set"
] | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity.0.ContinuousOn.cfc_fun._simp_1_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity | [
"UniformSpace",
"Equiv.instEquivLike",
"UniformOnFun.tendsto_iff_tendstoUniformlyOn",
"Function.comp",
"Membership.mem",
"nhds",
"Equiv",
"UniformOnFun.topologicalSpace",
"UniformOnFun.toFun",
"TendstoUniformlyOn",
"Filter.Tendsto",
"propext",
"UniformOnFun",
"Eq",
"Set.instMembership",
... | false |
LocallyConstant.mk | Mathlib.Topology.LocallyConstant.Basic | [
"LocallyConstant.mk",
"IsLocallyConstant",
"LocallyConstant",
"TopologicalSpace"
] | true |
CategoryTheory.Functor.instMonoidalActionMapAction | Mathlib.CategoryTheory.Action.Monoidal | [
"Monoid",
"CategoryTheory.Functor",
"CategoryTheory.Functor.instMonoidalActionMapAction._proof_4",
"CategoryTheory.Functor.Monoidal.mk",
"CategoryTheory.Functor.instMonoidalActionMapAction._proof_3",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.instMonoidalActionMapAction._proof_2",
"Cat... | true |
Homeomorph.neg._proof_1 | Mathlib.Topology.Algebra.Group.Basic | [
"Continuous.neg",
"Continuous",
"Equiv.neg",
"continuous_id'",
"Equiv.toFun",
"ContinuousNeg",
"TopologicalSpace",
"InvolutiveNeg",
"InvolutiveNeg.toNeg"
] | false |
SimpleGraph.UnitDistEmbedding.noConfusion | Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic | [
"Real",
"HEq.refl",
"SimpleGraph.Adj",
"Function.Embedding",
"SimpleGraph",
"SimpleGraph.UnitDistEmbedding",
"Real.instOne",
"MetricSpace",
"SimpleGraph.UnitDistEmbedding.noConfusionType",
"eq_of_heq",
"Eq.ndrec",
"One.toOfNat1",
"HEq",
"MetricSpace.toPseudoMetricSpace",
"SimpleGraph.Uni... | false |
IsOrderedModule.of_smul_one_mono | Mathlib.Algebra.Order.Module.Defs | [
"Eq.mpr",
"MulOne.toOne",
"instHSMul",
"instSMulOfMul",
"HMul.hMul",
"congrArg",
"SMulWithZero.toSMulZeroClass",
"IsScalarTower",
"Monotone",
"PosSMulMono.mk",
"Preorder.toLE",
"IsOrderedModule",
"Eq.mp",
"id",
"MulOne.toMul",
"LE.le",
"MulPosMono",
"MulOneClass.toMulOne",
"mul_l... | true |
alternatingGroup.isCoatom_stabilizer_of_ncard_lt_ncard_compl | Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups | [
"Iff.mpr",
"Equiv.Perm.applyMulAction",
"Eq.mpr",
"MulAction.IsBlock.subsingleton_of_ssubset_compl_of_stabilizer_alternatingGroup_le",
"lt_of_le_of_lt",
"False",
"Preorder.toLT",
"alternatingGroup.stabilizer_ne_top",
"MulAction.IsBlock.compl_subset_of_stabilizer_le_of_not_subset_of_not_subset_compl"... | true |
toAlgHom_comp_sectionOfRetractionKerToTensorAux | Mathlib.RingTheory.Smooth.Kaehler | [
"Derivation",
"LinearMap.id",
"RingHom.instRingHomClass",
"sectionOfRetractionKerToTensorAux",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"RingHomClass.toAddMonoidHomClass",
"Semiring.toModule",
"map_sub",
"CommRing.toNonUnitalCommRing",
"instAddCo... | true |
_private.Mathlib.Data.Finset.Slice.0.Set.sized_iUnion._simp_1_2 | Mathlib.Data.Finset.Slice | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
Bimod.comp | Mathlib.CategoryTheory.Monoidal.Bimod | [
"CategoryTheory.MonoidalCategory",
"Bimod.X",
"Bimod.comp._proof_4",
"Bimod.Hom.mk",
"Bimod.Hom.hom",
"CategoryTheory.Mon",
"Bimod",
"Bimod.comp._proof_2",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Bimod.Hom",
"CategoryTheory.Category"
] | true |
List.head_append_right | Init.Data.List.Lemmas | [
"List.head_append_right._proof_1",
"List.head",
"Eq.mpr",
"List.head_append._proof_2",
"List.head_append",
"congrArg",
"dif_pos",
"id",
"instDecidableEqBool",
"Ne",
"dite",
"Bool.true",
"instHAppendOfAppend",
"List",
"List.isEmpty",
"True",
"eq_self",
"Bool",
"of_eq_true",
"Eq.... | true |
CategoryTheory.CommShift₂Setup._sizeOf_inst | Mathlib.CategoryTheory.Shift.CommShiftTwo | [
"AddCommMonoid",
"SizeOf.mk",
"AddCommMonoid.toAddMonoid",
"CategoryTheory.CommShift₂Setup._sizeOf_1",
"SizeOf",
"CategoryTheory.HasShift",
"CategoryTheory.CommShift₂Setup",
"CategoryTheory.Category"
] | false |
GrpCat.fullyFaithfulForget₂ToMonCat._proof_2 | Mathlib.Algebra.Category.Grp.Basic | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"GrpCat.hasForgetToMonCat",
"GrpCat",
"MonoidHom.instFunLike",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"GrpCat.str",
"Monoid.toMulOneClass",
"MonCat.Hom.hom",
"id",
"MonCat",
"DivInvMonoid.toMonoid",
"MonCat.instCa... | false |
QuadraticMap.isOrtho_comm | Mathlib.LinearAlgebra.QuadraticForm.Basic | [
"Eq.mpr",
"congrArg",
"CommSemiring.toSemiring",
"id",
"QuadraticMap.instFunLike",
"add_comm",
"AddCommMonoid",
"iff_self",
"CommSemiring",
"instHAdd",
"Iff",
"HAdd.hAdd",
"congr",
"True",
"of_eq_true",
"AddCommSemigroup.toAddCommMagma",
"Module",
"AddCommMonoid.toAddCommSemigroup"... | true |
Subgroup.finite_quotient_of_finiteIndex | Mathlib.GroupTheory.Index | [
"Subgroup.FiniteIndex",
"Finite",
"Fintype.finite",
"Group",
"QuotientGroup.instHasQuotientSubgroup",
"Subgroup",
"HasQuotient.Quotient",
"Subgroup.fintypeQuotientOfFiniteIndex"
] | true |
Matroid.IsCocircuit.delete_isCocircuit | Mathlib.Combinatorics.Matroid.Minor.Contract | [
"Eq.mpr",
"congrArg",
"HasSSubset.SSubset",
"Matroid.IsCircuit.contract_isCircuit",
"Set.instHasSSubset",
"Matroid.dual",
"id",
"Matroid.isCocircuit_def",
"SDiff.sdiff",
"Matroid.IsCircuit",
"propext",
"Matroid.IsCocircuit",
"Matroid.IsCocircuit.isCircuit",
"Eq",
"Matroid",
"Matroid.co... | true |
_private.Mathlib.Order.Interval.Finset.Basic.0.Finset.Iic_top._simp_1_1 | Mathlib.Order.Interval.Finset.Basic | [
"Finset",
"Finset.mem_Iic",
"Preorder.toLE",
"Membership.mem",
"LocallyFiniteOrderBot",
"LE.le",
"Finset.instSetLike",
"propext",
"Finset.Iic",
"Eq",
"SetLike.instMembership",
"Preorder"
] | false |
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