name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
TensorProduct.tmul_add | Mathlib.LinearAlgebra.TensorProduct.Defs | [
"Quotient.sound'",
"AddMonoid.toAddSemigroup",
"addConGen",
"TensorProduct.Eqv",
"FreeAddMonoid.of",
"CommSemiring.toSemiring",
"FreeAddMonoid.instAddCancelMonoid",
"AddCancelMonoid.toAddRightCancelMonoid",
"TensorProduct.Eqv.of_add_right",
"Prod.mk",
"AddCommMonoid",
"CommSemiring",
"instHA... | true |
Metric.unitBall.instSemigroupWithZero._proof_2 | Mathlib.Analysis.Normed.Field.UnitBall | [
"NonUnitalSeminormedRing",
"Semigroup.toMul",
"Real",
"HMul.hMul",
"Metric.unitBall.instSemigroup",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"NonUnitalRing.toNonUnitalNonAssocRing",
"Set.Elem",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Metric.ball",
... | false |
_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ico_filter_modEq_eq._simp_1_7 | Mathlib.Data.Int.CardIntervalMod | [
"Int.modEq_iff_dvd",
"Dvd.dvd",
"HSub.hSub",
"Int",
"Int.instDvd",
"instHSub",
"Int.ModEq",
"propext",
"Int.instSub",
"Eq"
] | false |
List.prefix_of_prefix_length_le | Init.Data.List.Sublist | [
"List.brecOn",
"_private.Init.Data.List.Sublist.0.List.prefix_of_prefix_length_le.match_1_1",
"LE.le",
"instLENat",
"List.cons",
"List.append",
"instHAppendOfAppend",
"List",
"Exists.casesOn",
"Nat.le_of_succ_le_succ",
"List.IsPrefix",
"Nat",
"Exists.intro",
"eq_of_heq",
"Eq.ndrec",
"L... | true |
HomotopicalAlgebra.ModelCategory.mk'._proof_3 | Mathlib.AlgebraicTopology.ModelCategory.Basic | [
"inferInstance",
"CategoryTheory.MorphismProperty.HasTwoOutOfThreeProperty",
"HomotopicalAlgebra.CategoryWithWeakEquivalences",
"HomotopicalAlgebra.weakEquivalences",
"CategoryTheory.Category"
] | false |
Lean.instToJsonModuleArtifacts.toJson | Lean.Setup | [
"Lean.Json",
"Lean.Json.mkObj",
"Lean.Json.opt",
"Lean.ModuleArtifacts.olean?",
"Lean.instToJsonFilePath",
"String",
"Lean.ModuleArtifacts.ilean?",
"Lean.ModuleArtifacts",
"Lean.ModuleArtifacts.oleanServer?",
"Lean.ModuleArtifacts.lean?",
"List.cons",
"List",
"Lean.ModuleArtifacts.ir?",
"L... | true |
MvPolynomial.IsHomogeneous.totalDegree | Mathlib.RingTheory.MvPolynomial.Homogeneous | [
"Iff.mpr",
"Finsupp.mem_support_iff",
"Finsupp.instAddZeroClass",
"Finsupp.instFunLike",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Nat.instMulZeroClass",
"Nat.instLattice",
"instHSMul",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"Nat.instOne",
"Finsupp.weight",
... | true |
CircleDeg1Lift.iterate_le_of_map_le_add_int | Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | [
"Int.cast",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.instLE",
"Real",
"instHSMul",
"HMul.hMul",
"Real.instAddMonoid",
"congrArg",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"Preorder.toLE",
"CircleDeg1Lift.instFunLikeReal",
"monotone_id"... | true |
Padic.addValuation | Mathlib.NumberTheory.Padics.PadicNumbers | [
"Int.instAddCommGroup",
"Padic.AddValuation.map_one",
"Nat.Prime",
"Int.instLinearOrder",
"AddValuation.of",
"AddCommGroup.toAddCancelCommMonoid",
"WithTop.linearOrderedAddCommMonoidWithTop",
"Padic.addValuationDef",
"Fact",
"Padic.AddValuation.map_add",
"Int",
"instRingPadic",
"AddValuation... | true |
Ideal.span_union | Mathlib.RingTheory.Ideal.Span | [
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"Submodule.completeLattice",
"CompleteLattice.toConditionallyCompleteLattice",
"Set.instUnion",
"SemilatticeSup.toMax",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Submodule.span_union",
"Max.max",
"NonAssocSemiring.toNonUnitalNonAssocS... | true |
Valuation.map_sub_eq_of_lt_left | Mathlib.RingTheory.Valuation.Basic | [
"Eq.mpr",
"NegZeroClass.toNeg",
"Preorder.toLT",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"sub_eq_add_neg",
"HSub.hSub",
"LinearOrderedCommMonoidWithZero.toLinearOrder",
"SemilatticeInf.toPartialOrder",
"AddZeroCl... | true |
_private.Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology.0.IsValuativeTopology.instIsTopologicalAddGroup.match_1 | Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | [
"Set.instSProd",
"Units.val",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"CommRing",
"Preorder.toLT",
"ValuationClass.toMonoidWithZeroHomClass",
"SProd.sprod",
"WithZero.instMonoidWithZero",
"CommSemiring.toSemiring",
"MonoidWithZeroHomC... | false |
_private.Std.Time.Format.Basic.0.Std.Time.parseQuarterShort | Std.Time.Format.Basic | [
"Pure.pure",
"instOrElseOfAlternative",
"String",
"Std.Time.Month.Quarter",
"HOrElse.hOrElse",
"Int",
"LE.le",
"Applicative.toPure",
"_private.Std.Time.Format.Basic.0.Std.Time.parseQuarterNumber._proof_3",
"String.Pos.Raw",
"Subtype.mk",
"And",
"Unit",
"Std.Internal.Parsec.String.pstring",... | true |
_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.VarInfo._sizeOf_1 | Lean.Compiler.LCNF.ExplicitRC | [
"_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.VarInfo.rec",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Bool",
"instAddNat",
"instSizeOfNat",
"OfNat.ofNat",
"_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.VarInfo",
"Bool._sizeOf_inst"
] | false |
FirstOrder.Language.LHom.sumInl_onFunction | Mathlib.ModelTheory.LanguageMap | [
"Sum",
"Sum.inl",
"FirstOrder.Language.LHom.onFunction",
"Nat",
"FirstOrder.Language.Functions",
"Eq.refl",
"FirstOrder.Language.sum",
"FirstOrder.Language",
"Eq",
"FirstOrder.Language.LHom.sumInl"
] | true |
_private.Init.Data.String.Decode.0.utf8DecodeChar?_eq_assemble₃._proof_2 | Init.Data.String.Decode | [
"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'",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.sub_nonneg_of_le"... | false |
Subarray.start | Init.Data.Array.Subarray | [
"Subarray",
"Std.Slice.internalRepresentation",
"Std.Slice.Internal.SubarrayData.start",
"Std.Slice.Internal.SubarrayData",
"Nat"
] | true |
Std.ExtTreeSet.max_erase_le_max | Std.Data.ExtTreeSet.Lemmas | [
"Std.ExtTreeSet.ne_empty_of_erase_ne_empty",
"Std.ExtTreeMap.maxKey_erase_le_maxKey",
"Std.ExtTreeSet.erase",
"Ordering",
"Std.ExtTreeSet.inner",
"Ne",
"Std.TransCmp",
"Std.ExtTreeSet.min._proof_1",
"Bool.true",
"Unit",
"Std.ExtTreeSet",
"Bool",
"Std.ExtTreeSet.instEmptyCollection",
"Empty... | true |
NormedRing.toNonUnitalNormedRing._proof_4 | Mathlib.Analysis.Normed.Ring.Basic | [
"NormedRing.toRing",
"Ring.toNeg",
"Ring.zsmul_neg'",
"Int",
"Nat.cast",
"Nat",
"instNatCastInt",
"Int.negSucc",
"Nat.succ",
"Eq",
"Ring.zsmul",
"NormedRing",
"Neg.neg"
] | false |
Set.Ico_add_Ioc_subset | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"Set.Ioc",
"add_lt_add_of_le_of_lt",
"Preorder.toLT",
"PartialOrder.toPreorder",
"AddRightStrictMono",
"AddLeftMono",
"Preorder.toLE",
"Membership.mem",
"Exists",
"AddRightMono",
"PartialOrder",
"addLeftMono_of_addLeftStrictMono",
"HasSubset.Subset",
"LE.le",
"Set.Ico",
"And.casesOn",
... | true |
AddUnits.opEquiv._proof_4 | Mathlib.Algebra.Group.Units.Opposite | [
"AddUnits.val",
"AddUnits.val_neg",
"AddMonoid.toAddZeroClass",
"AddOpposite.op_injective",
"AddZeroClass.toAddZero",
"AddOpposite",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"AddMonoid",
"AddOpposite.instAddMonoid",
"AddZero.toAdd",
"Zero.toOfNat0",
"AddOpposite.unop",
"AddUnits.instNe... | false |
CompletelyDistribLattice.MinimalAxioms | Mathlib.Order.CompleteBooleanAlgebra | [
"CompletelyDistribLattice.MinimalAxioms.mk"
] | true |
Equiv.toHomeomorph._proof_3 | Mathlib.Topology.Homeomorph.Defs | [
"Iff.mpr",
"Continuous",
"Equiv.instEquivLike",
"Equiv",
"TopologicalSpace",
"Iff",
"Set.preimage",
"Equiv.toHomeomorph._proof_1",
"IsOpen",
"DFunLike.coe",
"continuous_def",
"Equiv.invFun",
"EquivLike.toFunLike",
"Set"
] | false |
UpperHemicontinuousWithinAt.eq_1 | Mathlib.Topology.Semicontinuity.Defs | [
"Filter.instMembership",
"Membership.mem",
"TopologicalSpace",
"UpperHemicontinuousWithinAt",
"Eq.refl",
"nhdsSet",
"Eq",
"Filter",
"SemicontinuousWithinAt",
"Set"
] | true |
Submodule.smul_comap_le_comap_smul | Mathlib.RingTheory.Ideal.Operations | [
"Iff.mpr",
"Eq.mpr",
"Submodule",
"instHSMul",
"Semiring.toModule",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Submodule.mem_comap",
"PartialOrder.toPreorder",
"LinearMap.instFunLike",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.mp",
... | true |
WeierstrassCurve.Affine.instDecidableEqPoint.decEq._proof_2 | Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | [
"CommRing",
"WeierstrassCurve.Affine.Nonsingular",
"WeierstrassCurve.Affine",
"Eq",
"rfl"
] | false |
Finsupp.isCentralScalar | Mathlib.Data.Finsupp.SMulWithZero | [
"Finsupp.instFunLike",
"Finsupp.smulZeroClass",
"instHSMul",
"Finsupp.ext",
"SMulZeroClass",
"MulOpposite",
"IsCentralScalar.mk",
"IsCentralScalar",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"Finsupp.instZero",
"DFunLike.coe",
"Finsupp",
"IsCentralScalar.op_smul_eq_smul",
"MulOpposite.op",
... | true |
Lean.Elab.Term.Arg.stx.noConfusion | Lean.Elab.Arg | [
"Lean.Syntax",
"id",
"Lean.Elab.Term.Arg.stx",
"Lean.Elab.Term.Arg.noConfusion",
"Lean.Elab.Term.Arg",
"Eq"
] | false |
mersenne_le_mersenne._gcongr_1 | Mathlib.NumberTheory.LucasLehmer | [
"Iff.mpr",
"mersenne_le_mersenne",
"LE.le",
"instLENat",
"mersenne",
"Nat"
] | false |
_private.Mathlib.GroupTheory.Coxeter.Inversion.0.CoxeterSystem.IsReflection.conj._simp_1_1 | Mathlib.GroupTheory.Coxeter.Inversion | [
"DivInvMonoid.toInv",
"zpow_neg_one",
"DivInvMonoid.toZPow",
"Int.instNegInt",
"Int",
"DivInvMonoid",
"Inv.inv",
"HPow.hPow",
"instOfNat",
"instHPow",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Neg.neg"
] | false |
instIsContMDiffRiemannianBundleOfNatWithTopENat_2 | Mathlib.Geometry.Manifold.VectorBundle.Riemannian | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"WithTop.charZero",
"WithTop.instPartialOrder",
"Real",
"instCompleteLinearOrderENat",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"of_decide_eq_true",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"CompleteLattice.instOmegaCompletePartialOrder",
... | true |
Polynomial.card_roots_sub_C | Mathlib.Algebra.Polynomial.Roots | [
"AddGroup.toSubtractionMonoid",
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.C",
"NegZeroClass.toNeg",
"IsDomain",
"Nat.instMulZeroClass",
"CommRing",
"WithBot",
"Trans.trans",
"Polynomial.roots",
"Preorder.toLT",
"Polynomial.instNeg",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSe... | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.containsKey_of_containsKey_filterMap._simp_1_1 | Std.Data.Internal.List.Associative | [
"Option.some",
"Option.all",
"Bool.true",
"propext",
"Bool",
"Eq",
"Option.all_eq_true",
"Option"
] | false |
CategoryTheory.BasedFunctor._sizeOf_inst | Mathlib.CategoryTheory.FiberedCategory.BasedCategory | [
"CategoryTheory.BasedFunctor",
"CategoryTheory.BasedFunctor._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"CategoryTheory.BasedCategory",
"CategoryTheory.Category"
] | false |
CategoryTheory.Square.rec | Mathlib.CategoryTheory.Square | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Square",
"CategoryTheory.Square.mk",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | false |
AList.insertRec._proof_1 | Mathlib.Data.List.AList | [
"invImage",
"instSizeOfDefault",
"sizeOfWFRel",
"AList._sizeOf_inst",
"Lean.opaqueId",
"AList",
"WellFounded"
] | false |
Equiv.symm_image_subset._simp_1 | Mathlib.Logic.Equiv.Set | [
"Equiv.instEquivLike",
"Equiv",
"HasSubset.Subset",
"propext",
"Set.image",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"Equiv.symm_image_subset",
"EquivLike.toFunLike",
"Set.instHasSubset",
"Set"
] | false |
Padic.mulValuation._proof_1 | Mathlib.NumberTheory.Padics.PadicNumbers | [
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"Int.instIsStrictOrderedRing",
"Nat.Prime",
"instConditionallyCompleteLinearOrder",
"instZeroPadic",
"congrArg",
"Int.instLinearOrder",
"PartialOrder.toPreorder",
"Classical.propDecidable",
"SemilatticeInf.toPartialOrder",
"Fact",
"Distr... | false |
Quiver.SingleObj.listToPath_pathToList | Mathlib.Combinatorics.Quiver.SingleObj | [
"Eq.mpr",
"Quiver.SingleObj.pathToList",
"Quiver.Hom",
"Quiver.Path.nil",
"congrArg",
"Quiver.SingleObj.ext",
"Quiver.SingleObj",
"Quiver.Path.rec",
"Quiver.SingleObj.inst",
"id",
"Quiver.Path",
"Quiver.Path.cast",
"Quiver.Path.cons",
"Quiver.SingleObj.star",
"Quiver.SingleObj.listToPath... | true |
Ordinal.add_log_le_log_mul | Mathlib.SetTheory.Ordinal.Exponential | [
"Eq.mpr",
"Ordinal.noZeroDivisors",
"Ordinal.log_of_left_le_one",
"Ordinal.instLinearOrder",
"Ordinal.mulRightMono",
"Preorder.toLT",
"le_rfl",
"HMul.hMul",
"Ordinal.partialOrder",
"MulZeroClass.toMul",
"congrArg",
"Ordinal.opow_add",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
... | true |
SimpleGraph.incidenceSetEquivNeighborSet._proof_1 | Mathlib.Combinatorics.SimpleGraph.Basic | [
"SimpleGraph.incidenceSet",
"Membership.mem",
"Set.Elem",
"SimpleGraph",
"Subtype.val",
"Set.instMembership",
"Sym2",
"Subtype.property",
"Set"
] | false |
HahnSeries.cardSupp_congr | Mathlib.RingTheory.HahnSeries.Cardinal | [
"HahnSeries.support",
"Cardinal",
"congrArg",
"Cardinal.mk",
"PartialOrder",
"Set.Elem",
"id",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"HahnSeries",
"Eq",
"HahnSeries.cardSupp",
"Eq.trans",
"Zero",
"Set"
] | true |
_private.Lean.Util.Diff.0.Lean.Diff.matchSuffix._proof_2 | Lean.Util.Diff | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Subarray",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"Lean.Omega.Int.ofNat_sub_sub",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dich... | false |
Std.HashSet.Equiv.diff_right | Std.Data.HashSet.Lemmas | [
"Std.HashSet",
"Std.HashSet.instSDiff",
"Std.HashSet.Equiv.inner",
"LawfulHashable",
"Std.HashSet.Equiv.mk",
"SDiff.sdiff",
"Unit",
"EquivBEq",
"Std.HashSet.inner",
"Std.HashSet.Equiv",
"Hashable",
"BEq",
"Std.HashMap.Equiv.diff_right"
] | true |
Rep.hom_inv_rightUnitor | Mathlib.RepresentationTheory.Rep.Basic | [
"Monoid",
"Representation.Equiv.symm",
"Rep.instMonoidalCategory",
"Rep.V",
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"TensorProduct.addCommMonoid",
"Representation.trivial",
"Re... | true |
_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.applyReplacementFun._proof_2 | Mathlib.Tactic.Translate.Core | [
"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'",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Expr",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.su... | false |
ApplicativeTransformation.mk.inj | Mathlib.Control.Traversable.Basic | [
"Pure.pure",
"ApplicativeTransformation.mk.noConfusion",
"ApplicativeTransformation",
"Seq.seq",
"Applicative.toPure",
"Applicative",
"ApplicativeTransformation.mk",
"Unit",
"eq_of_heq",
"HEq",
"Applicative.toSeq",
"Eq"
] | true |
_private.Batteries.Data.List.Lemmas.0.List.getElem_filter_eq_getElem_getElem_findIdxs_sub._proof_1_36 | Batteries.Data.List.Lemmas | [
"_private.Batteries.Data.List.Lemmas.0.List.getElem_filter_eq_getElem_getElem_findIdxs_sub._proof_1_9",
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"GetElem.getElem",
"List.findIdxs",
"_private.Batteries.Data.List.Lemmas.0.List.getElem_filter_eq_getElem_getElem_findIdxs_sub._pro... | false |
_private.Mathlib.Geometry.Manifold.IntegralCurve.Basic.0.IsMIntegralCurveAt.hasMFDerivAt.match_1_1 | Mathlib.Geometry.Manifold.IntegralCurve.Basic | [
"Filter.instMembership",
"IsMIntegralCurveOn",
"Real",
"NormedSpace",
"Real.denselyNormedField",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"Exists",
"nhds",
"And.casesOn",
"TopologicalSpace",
"ModelWithCorners",
"And",
"Exists.casesOn",
"And.intro",
"TangentSpace",
"Exist... | false |
Representation.apply_eq_of_coe_eq | Mathlib.RepresentationTheory.Basic | [
"LinearMap.id",
"Eq.mpr",
"_private.Mathlib.RepresentationTheory.Basic.0.Representation.apply_eq_of_coe_eq._simp_1_2",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"Representation",
"MonoidHom.instFunLike",
"inv_mul_cancel",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Representation.IsTriv... | true |
Topology.RelCWComplex.iUnion_skeleton_eq_complex | Mathlib.Topology.CWComplex.Classical.Basic | [
"Iff.mpr",
"Topology.RelCWComplex",
"Eq.mpr",
"ENat.instNatCast",
"Set.iUnion_subset_iff",
"congrArg",
"CommSemiring.toSemiring",
"Set.subset_iUnion_of_subset",
"Topology.RelCWComplex.openCell",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Set.instUnion",
"id",
"subset_antisymm",
"HasSubse... | true |
Matrix.rank_mul_eq_left_of_isUnit_det | Mathlib.LinearAlgebra.Matrix.Rank | [
"Iff.mpr",
"Eq.mpr",
"Pi.Function.module",
"LinearMap.range_comp_of_range_eq_top",
"Submodule",
"RingHomSurjective.ids",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemir... | true |
_private.Mathlib.Topology.Algebra.Valued.NormedValued.0.Valued.toNormedField._simp_21 | Mathlib.Topology.Algebra.Valued.NormedValued | [
"Real",
"HMul.hMul",
"NNReal",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Real.instMul",
"NNReal.instSemiring",
"NonUnitalNonAssocSemiring.toDistrib",
"NNReal.coe_mul",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Eq",
"NNReal.toReal",
"instHMul"
] | false |
RingHom.map_rat_algebraMap | Mathlib.Algebra.Algebra.Rat | [
"CommSemiring.toSemiring",
"Rat",
"Algebra",
"RingHom.ext_iff",
"RingHom",
"Rat.commSemiring",
"Rat.subsingleton_ringHom",
"algebraMap",
"RingHom.comp",
"RingHom.instFunLike",
"Iff.mp",
"Semiring",
"Subsingleton.elim",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe"
] | true |
DirectLimit.instDivisionRing._proof_18 | Mathlib.Algebra.Colimit.DirectLimit | [
"Semiring.toNatCast",
"instHDiv",
"Preorder.toLE",
"DivisionRing.toDivisionSemiring",
"inferInstance",
"HDiv.hDiv",
"NNRat",
"LE.le",
"DivisionSemiring.nnratCast_def",
"DirectLimit.instDivisionSemiring",
"NNRat.num",
"Nat.cast",
"DirectLimit",
"DivisionSemiring.toNNRatCast",
"DivisionSem... | false |
_private.Mathlib.RingTheory.HahnSeries.Multiplication.0.HahnModule.coeff_smul_right._simp_1_1 | Mathlib.RingTheory.HahnSeries.Multiplication | [
"And",
"propext",
"not_and",
"Eq",
"Not"
] | false |
_private.Lean.Meta.MethodSpecs.0.Lean.getMethodSpecsInfo._sparseCasesOn_1 | Lean.Meta.MethodSpecs | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
_private.Mathlib.GroupTheory.Perm.Support.0.Equiv.Perm.disjoint_swap_swap._proof_1_1 | Mathlib.GroupTheory.Perm.Support | [
"Lean.Grind.eq_false_of_not_eq_true",
"List.pairwise_cons_cons",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Equiv.instEquivLike",
"eq_false",
"List.Pairwise",
"Lean.Grind.iff_eq",
"Lean.Grind.not_or",
"List.nodup_iff_pairwise_ne",
"Classical.byContradiction",
"Equiv.swap",
"Membership.m... | false |
_private.Mathlib.Analysis.ODE.Gronwall.0.le_gronwallBound_of_liminf_deriv_right_le._simp_1_1 | Mathlib.Analysis.ODE.Gronwall | [
"Set.Ici",
"Membership.mem",
"True",
"eq_true",
"Eq",
"Set.instMembership",
"Preorder",
"Set.self_mem_Ici",
"Set"
] | false |
Nat.getElem!_toList_roo_eq_zero | Init.Data.Range.Polymorphic.NatLemmas | [
"Inhabited.default",
"congrArg",
"Option.getD",
"List.instGetElem?NatLtLength",
"instInhabitedNat",
"Nat.getElem?_toList_roo_eq_none",
"Std.PRange.instIsAlwaysFiniteNat_1",
"instOfNatNat",
"LE.le",
"instLENat",
"List.getElem!_eq_getElem?_getD",
"Option.none",
"List",
"instHAdd",
"HAdd.hA... | true |
LieIdeal.mem_comap._simp_1 | Mathlib.Algebra.Lie.Ideal | [
"LieHom",
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"CommRing",
"LieRing.toAddCommGroup",
"Membership.mem",
"LieRing",
"LieIdeal.comap",
"propext",
"LieIdeal",
"LieIdeal.mem_comap",
"LieAlgebra",
"LieHom.instFunLike",
"Eq",
"DFunLike.coe",
"lieRingSelfModule",
"SetLike.instM... | false |
PadicInt.zmodRepr_eq_zero_iff_dvd | Mathlib.NumberTheory.Padics.RingHoms | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"Eq.mpr",
"Real",
"Nat.Prime",
"Dvd.dvd",
"NormedRing.toRing",
"PadicInt",
"PadicInt.zmodRepr",
"congrArg",
"sub_zero",
"PadicInt.norm_lt_one_iff_dvd",
"AddMonoid.toAddZeroClass",
"semigroupDvd",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hS... | true |
Aesop.ScopeName.global | Aesop.Rule.Name | [
"Aesop.ScopeName",
"Aesop.ScopeName.global"
] | true |
nnnormHom_apply | Mathlib.Analysis.Normed.Ring.Basic | [
"NormOneClass",
"SeminormedRing.toNorm",
"Ring.toNonAssocRing",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"AddGroupWithOne.toAddMonoidWithOne",
"MonoidWithZeroHom.funLike",
"SeminormedRing.toRing",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NNReal",
"NonAssocSemiring.toMulZeroOn... | true |
Real.pow_div_factorial_le_exp | Mathlib.Analysis.Complex.Exponential | [
"Iff.mpr",
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real.instLE",
"Real",
"Trans.trans",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsOrderedRing.toPosMulMono",
"CommRing.toNonUnitalCommRing",
"pow_nonneg",
"IsOrderedRing.toZeroLEOneClass",
"MulZe... | true |
_private.Mathlib.LinearAlgebra.Matrix.Determinant.Basic.0.Matrix.det_fromBlocks_zero₂₁._simp_1_8 | Mathlib.LinearAlgebra.Matrix.Determinant.Basic | [
"Exists",
"forall_exists_index",
"propext",
"Exists.intro",
"Eq"
] | false |
Lean.Elab.Tactic.ElimTargetView.ctorIdx | Lean.Elab.Tactic.Induction | [
"Lean.Elab.Tactic.ElimTargetView",
"Nat"
] | false |
Bialgebra.toCoalgebra | Mathlib.RingTheory.Bialgebra.Basic | [
"Coalgebra",
"Algebra.toModule",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Bialgebra",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"Bialgebra.toAlgebra",
"Semiring.toNonAssocSemiring"
] | true |
Finset.prod_inv_index | Mathlib.Algebra.Group.Pointwise.Finset.BigOperators | [
"Function.Injective.injOn",
"Finset",
"InvolutiveInv.toInv",
"InvolutiveInv",
"Finset.prod",
"Inv.inv",
"SetLike.coe",
"Finset.instSetLike",
"inv_injective",
"Eq",
"CommMonoid",
"Finset.prod_image",
"DecidableEq",
"Finset.inv"
] | true |
Neg.rec | Init.Prelude | [
"Neg.mk",
"Neg"
] | false |
MeasureTheory.SimpleFunc.instCommRing._proof_7 | Mathlib.MeasureTheory.Function.SimpleFunc | [
"MeasureTheory.SimpleFunc.instAdd",
"AddGroupWithOne.intCast_negSucc._autoParam",
"Semiring.toNatCast",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"MeasureTheory.SimpleFunc.instIntCast",
"CommRing",
"Function.Injective.addGroupWithOne",
"NonUnitalCommRing.toNo... | false |
CategoryTheory.effectiveEpiFamilyStructOfComp._proof_3 | Mathlib.CategoryTheory.EffectiveEpi.Comp | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"id",
"CategoryTheory.CategoryStruct.comp",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | false |
Std.Tactic.BVDecide.BVExpr.bitblast.blastArithShiftRightConst.go_denote_eq._proof_2 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.ShiftRight | [
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.ShiftRight.0.Std.Tactic.BVDecide.BVExpr.bitblast.blastArithShiftRightConst.go_denote_eq._proof_1",
"instHSub",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"Nat.decLt",
"instLTNat",
... | false |
Lean.Meta.SynthInstance.Instance.ctorIdx | Lean.Meta.SynthInstance | [
"Lean.Meta.SynthInstance.Instance",
"Nat"
] | false |
FreeMonoid.freeMonoidCongr_of | Mathlib.Algebra.FreeMonoid.Basic | [
"CancelMonoid.toRightCancelMonoid",
"FreeMonoid",
"MulEquiv.instEquivLike",
"Equiv.instEquivLike",
"Monoid.toMulOneClass",
"FreeMonoid.instCancelMonoid",
"Equiv",
"MulOne.toMul",
"MulOneClass.toMulOne",
"FreeMonoid.of",
"MulEquiv",
"RightCancelMonoid.toMonoid",
"FreeMonoid.freeMonoidCongr",
... | true |
Equiv.ofUnique._proof_2 | Mathlib.Logic.Equiv.Defs | [
"Inhabited.default",
"Unique",
"Pi.instInhabited",
"Unique.instSubsingleton",
"Unique.instInhabited",
"Subsingleton.elim",
"Eq"
] | false |
String.toList_map | Init.Data.String.Lemmas.Modify | [
"String.toList_mapAux",
"congrArg",
"String",
"List.map",
"String.startPos",
"String.toList_empty",
"instHAppendOfAppend",
"List",
"String.mapAux",
"String.toList",
"True",
"eq_self",
"of_eq_true",
"String.map",
"congrFun'",
"Char",
"String.splits_startPos",
"List.instAppend",
"E... | true |
Finset.compl_eq_univ_iff._simp_1 | Mathlib.Data.Finset.BooleanAlgebra | [
"Finset.univ",
"Compl.compl",
"Finset",
"BooleanAlgebra.toCompl",
"Finset.instEmptyCollection",
"Fintype",
"Finset.compl_eq_univ_iff",
"propext",
"Finset.booleanAlgebra",
"EmptyCollection.emptyCollection",
"Eq",
"DecidableEq"
] | false |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula.0.WeierstrassCurve.Projective.addZ_smul._simp_1_4 | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula | [
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Algebra.toSMul",
"Algebra.id",
"Fin.instOfNat",
"Function.hasSMul",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"instOfNatNat",
"CommRin... | false |
Lean.Attribute.Builtin.getPrio | Lean.Attributes | [
"Lean.getAttrParamOptPrio",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.indentD",
"Lean.Core.instMonadRefCoreM",
"Lean.AttrM",
"String",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.MessageData.instAppend",
"Lean.throwErrorAt",
... | true |
Lean.Meta.CaseValuesSubgoal._sizeOf_inst | Lean.Meta.Match.CaseValues | [
"Lean.Meta.CaseValuesSubgoal._sizeOf_1",
"Lean.Meta.CaseValuesSubgoal",
"SizeOf.mk",
"SizeOf"
] | false |
AddMonoidHom.instDomMulActModule._proof_2 | Mathlib.Algebra.Module.Hom | [
"DomMulAct",
"instHSMul",
"AddMonoidHom.instDomMulActModule._proof_4",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"AddZeroClass.toAddZero",
"DomMulAct.instMonoidOfMulOpposite",
"AddMonoidHom.instAddCommMonoid",
"AddMonoidHom.ext",
"AddCommMonoid",
"AddZero.toZero",
... | false |
CategoryTheory.Limits.colimitCurrySwapCompColimIsoColimitCurryCompColim_ι_ι_hom | Mathlib.CategoryTheory.Limits.Fubini | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.instHasColimitProd",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.colim",
... | true |
Squarefree.dvd_of_squarefree_of_mul_dvd_mul_left | Mathlib.Algebra.Squarefree.Basic | [
"CommMonoidWithZero.toCommMonoid",
"Dvd.dvd",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"MulZeroClass.toMul",
"semigroupDvd",
"SemigroupWithZero.toSemigroup",
"Eq.rec",
"CommMagma.toMul",
"CommMonoidWithZero.toMonoidWithZero",
"IsCancelMulZero",
"DecompositionMonoid",
"MonoidWithZero.toSemi... | true |
Std.DTreeMap.Const.get?_eq_some_iff_exists_compare_eq_eq_and_mem_toList | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap.Const.toList",
"Std.DTreeMap",
"Ord.mk",
"Option.some",
"Membership.mem",
"Exists",
"Ordering",
"Ordering.eq",
"Std.DTreeMap.Const.get?",
"Prod.mk",
"Std.DTreeMap.inner",
"Std.TransCmp",
"List",
"And",
"Iff",
"List.instMembership",
"Std.DTreeMap.wf",
"Std.DTreeMap.Int... | true |
Relation.map_apply | Mathlib.Logic.Relation | [
"Iff.rfl",
"Exists",
"And",
"Iff",
"Eq",
"Relation.Map"
] | true |
List.Vector.traverse_def | Mathlib.Data.Vector.Basic | [
"List.Vector.traverse",
"List.Vector",
"Subtype.casesOn",
"Eq.rec",
"Seq.seq",
"Applicative",
"Subtype.mk",
"List",
"Unit",
"Nat",
"Applicative.toFunctor",
"Eq.refl",
"Applicative.toSeq",
"Nat.succ",
"Eq",
"List.length",
"Functor.map",
"List.Vector.cons"
] | true |
CovBy.lt_iff_le_right | Mathlib.Order.Cover | [
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"CovBy",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"DistribLattice.toLattice",
"LE.le",
"Iff",
"LT.lt",
"Iff.mp",
"SemilatticeSup.toPartialOrder",
"covBy_iff_lt_iff_le_right",
"instDistribLatticeOfLinearOrder"
] | true |
CategoryTheory.CategoryOfElements.map_map_coe | Mathlib.CategoryTheory.Elements | [
"CategoryTheory.categoryOfElements",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"Sigma.fst",
"CategoryTheory.Functor.map",
"CategoryTheory.CategoryOfElements.map",
"CategoryTheory.types",
... | true |
MonoidHom.snd._proof_1 | Mathlib.Algebra.Group.Prod | [
"MulOne.toOne",
"Prod.instMulOneClass",
"MulOneClass.toMulOne",
"One.toOfNat1",
"MulOneClass",
"Prod",
"OfNat.ofNat",
"Eq",
"Prod.snd",
"rfl"
] | false |
CategoryTheory.Subgroupoid.IsNormal.mk._flat_ctor | Mathlib.CategoryTheory.Groupoid.Subgroupoid | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Groupoid.inv",
"Membership.mem",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Groupoid",
"CategoryTheory.Subgroupoid.IsNormal.mk",
"CategoryTheory.Subgroupoid.arrows",
"CategoryTheory.Subgroupoid",
"CategoryTheory.Subgr... | false |
Std.HashMap.unitOfList_cons | Std.Data.HashMap.Lemmas | [
"Unit.unit",
"_private.Std.Data.HashMap.Lemmas.0.Std.HashMap.ext",
"instForInOfForIn'",
"inferInstance",
"Std.HashMap",
"Std.HashMap.instEmptyCollection",
"Id",
"Membership",
"List.cons",
"List",
"Unit",
"List.instMembership",
"Std.HashMap.unitOfList",
"Std.HashMap.insertIfNew",
"Id.inst... | true |
MeasureTheory.AEStronglyMeasurable.iUnion | Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable | [
"TopologicalSpace.PseudoMetrizableSpace",
"MeasureTheory.Measure",
"MeasureTheory.AEStronglyMeasurable.sum_measure",
"MeasureTheory.Measure.restrict",
"MeasurableSpace",
"TopologicalSpace",
"MeasureTheory.AEStronglyMeasurable.mono_measure",
"Countable",
"MeasureTheory.Measure.sum",
"Set.iUnion",
... | true |
Lean.Widget.HighlightedMsgEmbed.rec_2 | Lean.Server.FileWorker.WidgetRequests | [
"Lean.Widget.StrictOrLazy",
"Lean.Widget.TaggedText.tag",
"Lean.Server.WithRpcRef",
"String",
"Lean.Widget.HighlightedMsgEmbed.expr",
"Lean.Widget.StrictOrLazy.lazy",
"Lean.Widget.WidgetInstance",
"Lean.Widget.HighlightedMsgEmbed.trace",
"Lean.Widget.StrictOrLazy.strict",
"Lean.Widget.TaggedText",... | false |
_private.Mathlib.Topology.UniformSpace.ProdApproximation.0.ContinuousMap.exists_finite_sum_smul_approximation_of_mem_uniformity._simp_1_4 | Mathlib.Topology.UniformSpace.ProdApproximation | [
"HasSubset.Subset",
"subset_refl",
"Std.Refl",
"True",
"eq_true",
"HasSubset",
"Eq"
] | false |
ENNReal.coe_ne_coe | Mathlib.Data.ENNReal.Basic | [
"ENNReal.ofNNReal",
"ENNReal.coe_inj",
"Iff.not",
"NNReal",
"Ne",
"Iff",
"ENNReal",
"Eq"
] | true |
Module.Basis.finTwoProd | Mathlib.LinearAlgebra.Basis.Fin | [
"Pi.Function.module",
"Module.Basis.ofEquivFun",
"LinearEquiv.symm",
"Semiring.toModule",
"Pi.addCommMonoid",
"LinearEquiv.finTwoArrow",
"Module.Basis.finTwoProd._proof_1",
"instOfNatNat",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Module.Basis",
"NonAssocSemiring.toNonUnitalNonAssocSemiring"... | true |
MeasureTheory.eLpNormEssSup_indicator_const_le | Mathlib.MeasureTheory.Function.LpSeminorm.Indicator | [
"ENNReal.instCanonicallyOrderedAdd",
"zero_le",
"Eq.mpr",
"MeasureTheory.Measure",
"congrArg",
"Set.indicator",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"ESeminormedAddMonoid",
"Classical.propDecidable",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"MeasureTheory.eLpNormEssSup_co... | true |
_private.Mathlib.Algebra.Group.Basic.0.zsmul_zero.match_1_1 | Mathlib.Algebra.Group.Basic | [
"Int.casesOn",
"Int.ofNat",
"Int",
"Nat",
"Int.negSucc"
] | false |
CategoryTheory.Lax.OplaxTrans.ctorIdx | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax | [
"CategoryTheory.Lax.OplaxTrans",
"CategoryTheory.Bicategory",
"Nat",
"CategoryTheory.LaxFunctor"
] | false |
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