name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp.eq_1 | Mathlib.Geometry.RingedSpace.OpenImmersion | [
"AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.opensFunctor",
"CategoryTheory.Functor.op",
"AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.invApp._proof_1",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.i... | true |
_private.Mathlib.GroupTheory.Index.0.AddSubgroup.finiteIndex_iInf'.match_1_1 | Mathlib.GroupTheory.Index | [
"Finset",
"Subtype.casesOn",
"Membership.mem",
"Subtype",
"Subtype.mk",
"Finset.instSetLike",
"SetLike.instMembership"
] | false |
MvPolynomial.IsHomogeneous.pderiv | Mathlib.RingTheory.MvPolynomial.EulerIdentity | [
"Derivation",
"Finsupp.instAddZeroClass",
"Eq.mpr",
"MvPolynomial.IsWeightedHomogeneous.pderiv",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semiring.toModule",
"Nat.instOne",
"AddMonoidAlgebra.addAddCommMonoid",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"A... | true |
MeasurableEquiv.curry_symm_apply | Mathlib.MeasureTheory.MeasurableSpace.Embedding | [
"MeasurableEquiv.instEquivLike",
"MeasurableEquiv.symm",
"MeasurableSpace",
"MeasurableEquiv.curry",
"MeasurableSpace.pi",
"Eq.refl",
"Function.uncurry",
"Prod",
"MeasurableEquiv",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
hasStrictDerivAt_of_hasDerivAt_of_continuousAt | Mathlib.Analysis.Calculus.MeanValue | [
"HasFDerivAt",
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"hasStrictFDerivAt_of_hasFDerivAt_of_continuousAt",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformCon... | true |
AlgebraicGeometry.IsNoetherian.casesOn | Mathlib.AlgebraicGeometry.Noetherian | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CommRingCat",
"AlgebraicGeometry.IsLocallyNoetherian",
"CommRingCat.instCategory",
"CompactSpace",
"AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace",
"To... | false |
_private.Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic.0.CategoryTheory.WithTerminal.id.match_1.splitter | Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic | [
"CategoryTheory.WithTerminal.id.match_1",
"CategoryTheory.WithTerminal",
"CategoryTheory.WithTerminal.of",
"Unit",
"CategoryTheory.WithTerminal.star"
] | true |
_private.Mathlib.Analysis.Normed.Unbundled.SeminormFromConst.0.seminormFromConst._simp_6 | Mathlib.Analysis.Normed.Unbundled.SeminormFromConst | [
"zero_le",
"LE.le",
"LE",
"IsBotZeroClass",
"True",
"eq_true",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
VectorField.DifferentiableWithinAt.pullbackWithin | Mathlib.Analysis.Calculus.VectorField | [
"ContinuousLinearMap.comp",
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedAddCommGroup",
"ContinuousLinearEquiv.symm",
"WithTop.charZero",
"CompleteSpace",
"instCharZeroENat",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"instAddMonoidW... | true |
Quiver.Path.vertices.match_1 | Mathlib.Combinatorics.Quiver.Path.Vertices | [
"Unit.unit",
"Quiver.Hom",
"Quiver.Path.nil",
"HEq.refl",
"Quiver.Path",
"Quiver.Path.cons",
"Unit",
"Quiver",
"eq_of_heq",
"Eq.ndrec",
"Quiver.Path.casesOn",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq"
] | false |
AlgebraicTopology.DoldKan.Compatibility.equivalence₂_inverse | Mathlib.AlgebraicTopology.DoldKan.Compatibility | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp",
"AlgebraicTopology.DoldKan.Compatibility.equivalence₂",
"CategoryTheory.Iso",
"CategoryTheory.Equivalence.functor",
"Eq",
"rfl",
"CategoryTheory.Category",
"CategoryTheory.Eq... | true |
NontriviallyNormedField.toNormedField | Mathlib.Analysis.Normed.Field.Basic | [
"NormedField",
"NontriviallyNormedField"
] | true |
Topology.WithLower.ofLower | Mathlib.Topology.Order.LowerUpperTopology | [
"Equiv",
"Topology.WithLower",
"Equiv.refl"
] | true |
_private.Lean.Elab.Deriving.ToExpr.0.Lean.Elab.Deriving.ToExpr.mkToExprBody.mkAlts | Lean.Elab.Deriving.ToExpr | [
"Pure.pure",
"Lean.instMonadEnvOfMonadLift",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.ConstructorVal.toConstantVal",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Syntax.ident",
"Lean.E... | true |
_private.Init.Data.Fin.Lemmas.0.Fin.pred_inj.match_1_1 | Init.Data.Fin.Lemmas | [
"instNeZeroNatHAdd_1",
"Fin.casesOn",
"Fin.mk",
"Fin.instOfNat",
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"LT.lt",
"instAddNat",
"Nat.zero",
"instLTNat",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"Nat.casesOn"
] | false |
Finsupp.mapDomain_apply_eq_sum | Mathlib.Data.Finsupp.Basic | [
"Finsupp.instFunLike",
"instDecidableNot",
"Pi.addCommMonoid",
"congrArg",
"Finset",
"Finsupp.mapDomain",
"AddMonoid.toAddZeroClass",
"Finset.sum_apply",
"Finsupp.support",
"Membership.mem",
"AddZeroClass.toAddZero",
"Finset.sum_const_zero",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
... | true |
_private.Mathlib.MeasureTheory.MeasurableSpace.Constructions.0.measurable_findGreatest._simp_1_2 | Mathlib.MeasureTheory.MeasurableSpace.Constructions | [
"Compl.compl",
"setOf",
"Set.instCompl",
"Eq.symm",
"Eq",
"Not",
"Set.compl_setOf",
"Set"
] | false |
CategoryTheory.Limits.isLimitChangeEmptyCone._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.IsTerminal | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"False.elim",
"Aesop.BuiltinRules.pEmpty_false",
"CategoryTheory.Functor.category",
"id",
"PEmpty",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Functor.map",
"Cate... | false |
Manifold.pathELength_def | Mathlib.Geometry.Manifold.Riemannian.PathELength | [
"instOneTangentSpaceRealModelWithCornersSelf",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
"mfderiv",
"chartedSpaceSelf",
"NormedSpace",
"Real.denselyNormedField",
"Real.instRCLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupTangentSpace",
"ContinuousLinearMap.fun... | true |
Ordinal.IsNormal.le_iff | Mathlib.SetTheory.Ordinal.Arithmetic | [
"Ordinal.instLinearOrder",
"Ordinal.partialOrder",
"Ordinal.IsNormal",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"Iff",
"Ordinal.IsNormal.strictMono",
"StrictMono.le_iff_le",
"Ordinal"
] | true |
IsCoercive.continuousLinearEquivOfBilin_apply | Mathlib.Analysis.InnerProductSpace.LaxMilgram | [
"InnerProductSpace.toNormedSpace",
"Real",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"Semiring.toModule",
"ContinuousLinearMap.topologicalSpace",
"Inner.inner",
"Real.instRCLike",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Is... | true |
_private.Mathlib.GroupTheory.Coxeter.Inversion.0.CoxeterSystem.getD_rightInvSeq_mul_self._proof_1_2 | Mathlib.GroupTheory.Coxeter.Inversion | [
"Lean.RArray.leaf",
"False",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"Eq.mp",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",
"Nat.Linear.ExprCnstr.eq_... | false |
Matrix.det_smul_inv_vecMul_eq_cramer_transpose | Mathlib.LinearAlgebra.Matrix.NonsingularInverse | [
"Eq.mpr",
"Pi.Function.module",
"Matrix.det_smul_inv_mulVec_eq_cramer",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"Pi.addCommMonoid",
"Matrix.det_transpose",
"CommRing.toNonUnitalCommRing",
"Matrix.transpose_transpose",
"M... | true |
MeasureTheory.indicatorConstLp_add | Mathlib.MeasureTheory.Function.LpSpace.Indicator | [
"Eq.mpr",
"MeasureTheory.Measure",
"MeasurableSet",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Set.indicator",
"MeasureTheory.indicatorConstLp",
"MeasureTheory.indicatorConstLp._proof_1",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"Membership.m... | true |
Rat.cast_le_intCast | Mathlib.Data.Rat.Cast.Order | [
"Int.cast",
"Eq.mpr",
"Rat.cast_intCast",
"DivisionRing.toRatCast",
"congrArg",
"LinearOrder",
"Iff.rfl",
"Rat",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Rat.instIntCast",
"i... | true |
_private.Mathlib.ModelTheory.PartialEquiv.0.FirstOrder.Language.isExtensionPair_iff_exists_embedding_closure_singleton_sup._simp_1_3 | Mathlib.ModelTheory.PartialEquiv | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"LE.le",
"sup_le_iff",
"And",
"Max.max",
"propext",
"SemilatticeSup.toPartialOrder",
"Eq",
"SemilatticeSup"
] | false |
ultrafilter_extend_pure | Mathlib.Topology.Compactification.StoneCech | [
"Pure.pure",
"ultrafilter_extend_extends",
"Function.comp",
"TopologicalSpace",
"T2Space",
"Ultrafilter.instPure",
"Ultrafilter.extend",
"congr_fun",
"Ultrafilter",
"Eq"
] | true |
Monoid.PushoutI.NormalWord.consRecOn._proof_2 | Mathlib.GroupTheory.PushoutI | [
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"Group",
"Monoid.CoprodI.Word.toList",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Monoid.PushoutI.NormalWord.head",
"DivInvMonoid.toMonoid",
"Monoid.CoprodI.Word",
... | false |
Nat.lt_add_one | Init.Prelude | [
"Nat.le_refl",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Nat.succ"
] | true |
AddSubgroup.center_le_centralizer | Mathlib.GroupTheory.Subgroup.Centralizer | [
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"LE.le",
"AddSubgroup",
"AddSubgroup.centralizer",
"AddGroup",
"AddGroup.toSubNegMonoid",
"AddZero.toAdd",
"SubNegMonoid.toAddMonoid",
"AddSubgroup.center",
"Se... | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital.0._auto_470 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.Geometry.Manifold.PoincareConjecture.0._aux_Mathlib_Geometry_Manifold_PoincareConjecture___macroRules__private_Mathlib_Geometry_Manifold_PoincareConjecture_0_term𝕊___1 | Mathlib.Geometry.Manifold.PoincareConjecture | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.node5",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.... | false |
HomotopicalAlgebra.ModelCategory.cm4b | Mathlib.AlgebraicTopology.ModelCategory.Basic | [
"CategoryTheory.HasLiftingProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomotopicalAlgebra.ModelCategory.categoryWithFibrations",
"HomotopicalAlgebra.Cofibration",
"HomotopicalAlgebra.ModelCategory.categoryWithCofibrations",
"HomotopicalAlgebra.ModelCategory.categoryWithWeakEquival... | true |
CategoryTheory.Square.toArrowArrowFunctor._proof_1 | Mathlib.CategoryTheory.Square | [
"CategoryTheory.Square.category",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Square.Hom.τ₁",
"CategoryTheory.Square.Hom.comm₁₃",
"CategoryTheory.Square",
"CategoryTheory.Square.f₁₃",
"CategoryTheory.Square.X₃",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Cate... | false |
Fin.castLE_comp_castSucc | Mathlib.Data.Fin.SuccPred | [
"Fin.castLE",
"Nat.le_of_succ_le",
"Function.comp",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Fin.castSucc",
"OfNat.ofNat",
"Fin",
"Eq",
"rfl"
] | true |
String.Slice.dropSuffix?_eq_none_iff._simp_1 | Init.Data.String.Lemmas.Pattern.TakeDrop.Basic | [
"String.Slice.Pattern.BackwardPattern",
"String.Slice",
"String.Slice.dropSuffix?_eq_none_iff",
"String.Slice.Pattern.LawfulBackwardPattern",
"Option.none",
"String.Slice.dropSuffix?",
"propext",
"Bool",
"String.Slice.endsWith",
"Bool.false",
"Eq",
"Option"
] | false |
Filter.mem_add | Mathlib.Order.Filter.Pointwise | [
"Filter.instMembership",
"Filter.instAdd",
"Iff.rfl",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"instHAdd",
"And",
"Set.add",
"Iff",
"HAdd.hAdd",
"Filter",
"Add",
"Set.instHasSubset",
"Set"
] | true |
LieSubalgebra.top_coe | Mathlib.Algebra.Lie.Subalgebra | [
"CommRing",
"LieSubalgebra.instSetLike",
"Set.univ",
"LieSubalgebra.instTop",
"LieRing",
"SetLike.coe",
"LieSubalgebra",
"LieAlgebra",
"Top.top",
"Eq",
"rfl",
"Set"
] | true |
Std.Rco.Sliceable.mk._flat_ctor | Init.Data.Slice.Notation | [
"Std.Rco",
"outParam",
"Std.Rco.Sliceable",
"Std.Rco.Sliceable.mk"
] | false |
CuspForm.instAddCommGroup._proof_4 | Mathlib.NumberTheory.ModularForms.Basic | [
"instInnerProductSpaceRealComplex",
"ModularForm.instAddCommGroup._proof_2",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"AddCommGroup.intIsScalarTower",
"Real",
"instHSMul",
"Real.instRCLike",
"Matrix",
"NormedSpace.toModule",
"instDecidableEqFin",
"Complex.instN... | false |
Algebra.FormallyUnramified.elem.congr_simp | Mathlib.RingTheory.Unramified.Finite | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.EssFiniteType",
"Algebra.FormallyUnramified",
"Algebra.FormallyUnramified.elem",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"N... | true |
Finset.Ioc_pred_right_eq_Ioo | Mathlib.Order.Interval.Finset.SuccPred | [
"Eq.mpr",
"Set.Ioc",
"congrArg",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"id",
"Finset.coe_Ioc",
"Finset.coe_Ioo",
"Set.Ioc_pred_right_eq_Ioo",
"Finset.coe_injective",
"SetLike.coe",
"Finset.instSetLike",
"Order.p... | true |
Lean.ClassState.switch | Lean.Class | [
"Lean.SMap.switch",
"Lean.ClassState.outParamMap",
"Lean.ClassState",
"Lean.ClassState.outLevelParamMap",
"Array",
"Nat",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.instHashableName",
"Lean.ClassState.mk"
] | true |
Float.toUSize | Init.Data.Float | [
"Inhabited.default",
"Float",
"Pi.instInhabited",
"instInhabitedUSize",
"USize"
] | true |
Orientation.inner_rightAngleRotation_left | Mathlib.Analysis.InnerProductSpace.TwoDim | [
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Orientation",
"Real.partialOrder",
"Real",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Inner.inner",
"Real.instRCLike",
"congrArg",
"CommSemiring.toSemiring",
"Orientation.rightAngleRotation_def",
"Add... | true |
Lean.HeadIndex.forallE | Lean.HeadIndex | [
"Lean.HeadIndex.forallE",
"Lean.HeadIndex"
] | true |
Lean.Parser.Term.doBreak.parenthesizer | Lean.Parser.Do | [
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Bool.true",
"Lean.Parser.symbol.parenthesizer",
"Nat",
"Lean.PrettyPrinter.Parenthesizer.withAntiquot.pare... | true |
Filter.tendsto_prod_self_iff | Mathlib.Order.Filter.Lift | [
"Filter.instMembership",
"Set.instSProd",
"SProd.sprod",
"congrArg",
"Membership.mem",
"Exists",
"_private.Mathlib.Order.Filter.Lift.0.Filter.tendsto_prod_self_iff._simp_1_3",
"Prod.mk",
"HasSubset.Subset",
"iff_self",
"funext",
"And",
"Iff",
"Set.preimage",
"Filter.Tendsto",
"implies_... | true |
AnalyticAt.congr | Mathlib.Analysis.Analytic.Basic | [
"NormedSpace",
"HasFPowerSeriesAt.congr",
"FormalMultilinearSeries",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"nhds",
"Filter.EventuallyEq",
"HasFPowerSeriesAt._proof_2",
"HasFPowerSeriesAt._proof_1",
"Field.toSemifield"... | true |
CategoryTheory.Cat.FreeRefl.lift'.eq_1 | Mathlib.CategoryTheory.Category.ReflQuiv | [
"CategoryTheory.Functor",
"CategoryTheory.Cat.FreeRefl.instCategory",
"Quiver.Hom",
"CategoryTheory.catToReflQuiver",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.ReflPrefunctor.mk",
"CategoryTheory.Cat.FreeRefl.lift",
"CategoryTheory.Cat.FreeRefl",
"CategoryTheory.ReflQuiver.toQuiver",
"Eq... | true |
forall_or_left._simp_2 | Mathlib.Tactic.Push | [
"propext",
"forall_or_left",
"Or",
"Eq.symm",
"Eq"
] | false |
Units.mul_le_of_le_inv_mul | Mathlib.Algebra.Order.Monoid.Unbundled.Units | [
"Monoid",
"Units.val",
"HMul.hMul",
"Monoid.toMulOneClass",
"Units",
"MulLeftMono",
"MulOne.toMul",
"LE.le",
"LE",
"MulOneClass.toMulOne",
"Inv.inv",
"Iff.mp",
"Units.le_inv_mul_iff",
"Units.instInv",
"instHMul"
] | true |
RCLike.abs_re_le_norm | Mathlib.Analysis.RCLike.Basic | [
"Real.instIsOrderedRing",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real.partialOrder",
"Real.instLE",
"Real",
"HMul.hMul",
"Real.lattice",
"AddMonoid.toAddSemigroup",
"Real.instAddMonoid",
"AddGroupWithOne.toAddGroup",
"abs",
"congrArg",... | true |
Subtype.preirreducibleSpace | Mathlib.Topology.Irreducible | [
"IsPreirreducible",
"Set.univ",
"Subtype.casesOn",
"Membership.mem",
"Set.Elem",
"Subtype",
"Set.instInter",
"Subtype.mk",
"Inter.inter",
"And.casesOn",
"PreirreducibleSpace.mk",
"TopologicalSpace",
"And",
"Set.Nonempty",
"Exists.casesOn",
"Set.preimage",
"And.intro",
"Exists.intro... | true |
Int8.ofBitVec_int64ToBitVec | Init.Data.SInt.Lemmas | [
"Int64.toInt8",
"Int8",
"Int64",
"instOfNatNat",
"Int8.ofBitVec",
"Nat",
"BitVec.signExtend",
"Int64.toBitVec",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
CategoryTheory.Functor.FullyFaithful.over._proof_3 | Mathlib.CategoryTheory.Comma.Over.Basic | [
"CategoryTheory.Functor.FullyFaithful.map_injective",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Over.homMk.congr_simp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Over.mk",
"CategoryTheory.instCategoryO... | false |
Std.Internal.List.Const.getValue!_map_of_getKey?_eq_some | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"congrArg",
"List.map",
"Option.some",
"Std.Internal.List.Const.getValue?_map_of_getKey?_eq_some",
"Option.get!",
"Sigma.fst",
"List",
"Option.map",
"EquivBEq",
"Std.Internal.List.getValue?",
"True",
"eq_self",
"of_eq_true",
"Inhabited",
"congrFun'",
... | true |
EisensteinSeries.summable_left_one_div_linear_sub_one_div_linear | Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | [
"Int.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"UpperHalfPlane.coe",
"IsTopologicalRing.toIsTopologicalSemiring",
"Finset.summable_compl_iff",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Finset",
"Comple... | true |
Std.ExtDTreeMap.Const.get?_diff | Std.Data.ExtDTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.ExtDTreeMap.inductionOn₂",
"Membership.mem",
"Std.ExtDTreeMap.instDecidableMem",
"Ordering",
"Std.TransCmp",
"Std.ExtDTreeMap.instSDiffOfTransCmp",
"Std.ExtDTreeMap.Const.get?",
"SDiff.sdiff",
"Option.none",
"Std.DTreeMap.Const.get?_diff",
"Std.ExtDTreeMap",
"Eq",
"Std... | true |
_private.Mathlib.Analysis.Calculus.LogDeriv.0.logDeriv_div._simp_1_1 | Mathlib.Analysis.Calculus.LogDeriv | [
"False",
"eq_false",
"instOfNatNat",
"two_ne_zero",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
AddChar.zmod._proof_2 | Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality | [
"Real",
"AddCircle.toCircle_add",
"HMul.hMul",
"Monoid.toMulOneClass",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"AddCircle",
"Real.instAddCommGroup",
"Group.toDivInvMonoid",
"Real.instOne",
"instHAdd",
"MulOneClass.toMulOne",
"HA... | false |
MeasureTheory.Measure.euclideanHausdorffMeasure_zero_or_top | Mathlib.Geometry.Euclidean.Volume.Measure | [
"MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"ENNReal.instModuleNNReal",
"NNReal.instCommSemiring",
"Real.partialOrder",
"Real",
"ENNReal.ofNNReal",
"instHSMul",
"MeasureTheory.Measure",
... | true |
iSupIndep_of_dfinsuppSumAddHom_injective | Mathlib.LinearAlgebra.DFinsupp | [
"AddSubmonoid.subtype",
"Eq.mpr",
"Submodule",
"AddSubmonoid.toNatSubmodule",
"AddSubmonoid.instCompleteLattice",
"iSupIndep",
"congrArg",
"Submodule.completeLattice",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Function.comp",
"Membership.mem",
"CompleteLattic... | true |
Std.DHashMap.mem_diff_iff._simp_1 | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.instSDiff",
"Membership.mem",
"Std.DHashMap.instMembership",
"LawfulHashable",
"Std.DHashMap.mem_diff_iff",
"SDiff.sdiff",
"And",
"EquivBEq",
"propext",
"Hashable",
"BEq",
"Eq",
"Not",
"Std.DHashMap"
] | false |
Equiv.altCongrHom._proof_2 | Mathlib.GroupTheory.SpecificGroups.Alternating | [
"MulEquiv.instEquivLike",
"MonoidHom.instFunLike",
"Subgroup.mem_comap._simp_2",
"Equiv.instEquivLike",
"MonoidHom",
"Subgroup.map",
"Monoid.toMulOneClass",
"congrArg",
"_private.Mathlib.GroupTheory.SpecificGroups.Alternating.0.Equiv.altCongrHom._simp_1",
"Equiv.Perm.sign",
"MulEquiv.instMulEqui... | false |
_private.Std.Sat.AIG.RefVec.0.Std.Sat.AIG.RefVec.countKnown.go.match_1.splitter._sparseCasesOn_2 | Std.Sat.AIG.RefVec | [
"Std.Sat.AIG.Decl",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Nat.land",
"Nat",
"Bool",
"Eq.refl",
"Std.Sat.AIG.Decl.gate",
"Std.Sat.AIG.Decl.rec",
"Std.Sat.AIG.Decl.atom",
"Std.Sat.AIG.Decl.false",
"Std.Sat.AIG.Decl.ctorIdx",
"OfNat.ofNat",
"Bool.fa... | false |
StarMulEquiv.symm_apply_apply | Mathlib.Algebra.Star.MonoidHom | [
"StarMulEquiv",
"StarMulEquiv.toMulEquiv",
"Mul",
"StarMulEquiv.instEquivLike",
"Star",
"Eq",
"DFunLike.coe",
"StarMulEquiv.symm",
"MulEquiv.symm_apply_apply",
"EquivLike.toFunLike"
] | true |
CategoryTheory.ShortComplex.SnakeInput.comp_f₀_assoc | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.SnakeInput.comp_f₀",
"CategoryTheory.ShortComplex.SnakeInput.L₀",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.Snak... | true |
ContDiff.hasStrictFDerivAt | Mathlib.Analysis.Calculus.ContDiff.RCLike | [
"NormedSpace",
"CommSemiring.toSemiring",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContDiff",
"Ne",
"fderiv",
"ContDiffAt.hasStrictFDerivAt",
"RCLike.toDenselyNormedField",
"RCLike",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"HasStrictFDerivAt",
"ENat",
"instCommSem... | true |
Subgroup.coe_zpowers | Mathlib.Algebra.Group.Subgroup.ZPowers.Basic | [
"DivInvMonoid.toZPow",
"Group",
"Subgroup",
"Int",
"Group.toDivInvMonoid",
"SetLike.coe",
"HPow.hPow",
"Subgroup.zpowers",
"instHPow",
"Set.range",
"Eq",
"Subgroup.instSetLike",
"rfl",
"Set"
] | true |
Std.Internal.IsCut | Std.Data.Internal.Cut | [
"Ordering",
"Std.Internal.IsCut.mk"
] | true |
UniqueFactorizationMonoid.primeFactors | Mathlib.RingTheory.Radical.Basic | [
"UniqueFactorizationMonoid.normalizedFactors",
"Multiset.toFinset",
"Finset",
"NormalizationMonoid",
"Classical.propDecidable",
"UniqueFactorizationMonoid",
"CommMonoidWithZero",
"Eq"
] | true |
InvolutiveNeg.mk._flat_ctor | Mathlib.Algebra.Group.Defs | [
"Neg.mk",
"InvolutiveNeg",
"InvolutiveNeg.mk",
"Eq"
] | false |
_private.Init.Data.Nat.Basic.0.Nat.sub_eq_zero_of_le.match_1_1 | Init.Data.Nat.Basic | [
"Exists",
"instHAdd",
"Exists.casesOn",
"HAdd.hAdd",
"Nat",
"Exists.intro",
"instAddNat",
"Eq"
] | false |
MeasureTheory.instPseudoMetrizableSpaceProbabilityMeasureOfSeparableSpace | Mathlib.MeasureTheory.Measure.LevyProkhorovMetric | [
"Homeomorph.isInducing",
"TopologicalSpace.PseudoMetrizableSpace",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.LevyProkhorov",
"PseudoEMetricSpace.pseudoMetrizableSpace",
"Topology.IsInducing.pseudoMetrizableSpace",
"MeasureTheory.ProbabilityMeasure",
"MeasureTheory.ProbabilityMeasure.instTopol... | true |
_private.Mathlib.Algebra.Lie.CartanExists.0.LieAlgebra.engel_isBot_of_isMin.lieCharpoly._proof_2 | Mathlib.Algebra.Lie.CartanExists | [
"CommRing",
"CommSemiring.toSemiring",
"RingHomInvPair",
"CommRing.toCommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
OreLocalization.instCommMonoidWithZero | Mathlib.RingTheory.OreLocalization.Basic | [
"CommMonoidWithZero.toCommMonoid",
"OreLocalization.OreSet",
"OreLocalization",
"inferInstance",
"CommMonoidWithZero.toMonoidWithZero",
"MulZeroOneClass.toMulOneClass",
"OreLocalization.instCommMonoid",
"OreLocalization.instCommMonoidWithZero._proof_3",
"MonoidWithZero",
"MonoidWithZero.toMulZeroO... | true |
Set.hasDistribNeg._proof_3 | Mathlib.Algebra.Ring.Pointwise.Set | [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"_private.Mathlib.Algebra.Ring.Pointwise.Set.0.Set.hasDistribNeg._simp_1",
"Mul",
"id",
"Set.involutiveNeg",
"congr",
"HasDistribNeg",
"Set.image",
"HasDistribNeg.toInvolutiveNeg",
"Set.mul",
"InvolutiveNeg.toNeg",
"Eq",
"Set.image_image2_right_comm",
... | false |
Lean.Elab.CommandContextInfo.openDecls._default | Lean.Elab.InfoTree.Types | [
"id",
"List",
"Lean.OpenDecl",
"List.nil"
] | false |
Derivation.liftKaehlerDifferential_unique_iff | Mathlib.RingTheory.Kaehler.Basic | [
"Derivation",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"instAddCommGroupKaehlerDifferential",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"HEq.r... | true |
Finset.min'_lt_max'_of_card._proof_2 | Mathlib.Data.Finset.Max | [
"Finset",
"instOfNatNat",
"_private.Mathlib.Data.Finset.Max.0.Finset.min'_lt_max'_of_card._proof_1",
"Nat",
"LT.lt",
"Finset.card",
"instLTNat",
"OfNat.ofNat"
] | false |
_private.Mathlib.Probability.Independence.CharacteristicFunction.0.ProbabilityTheory.iIndepFun.charFunDual_map_finsetSum_eq_prod._proof_1_2 | Mathlib.Probability.Independence.CharacteristicFunction | [
"Lean.Grind.eq_false_of_not_eq_true",
"False",
"Pi.addCommMonoid",
"AddCommGroup.toAddCommMonoid",
"Finset",
"False.elim",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.mp",
"And.casesOn",
"Lean.Grind.forall_and",
"AddZero.toZero",
"And",
"Finset.instSetLike... | false |
HasSSubset.rec | Init.Core | [
"HasSSubset",
"HasSSubset.mk"
] | false |
add_self_neg_iff | Mathlib.Algebra.Order.Monoid.Defs | [
"Eq.mpr",
"Preorder.toLT",
"Mathlib.Tactic.Contrapose.contrapose_iff₁",
"congrArg",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"AddZeroClass.toAddZero",
"DistribLattice.toLattice",
"id",
"LE.le",
"AddCommMonoid",
... | true |
Std.ExtDHashMap.Const.get?_eq_none_of_contains_eq_false | Std.Data.ExtDHashMap.Lemmas | [
"Std.DHashMap.Const.get?_eq_none_of_contains_eq_false",
"Std.ExtDHashMap.contains",
"Std.ExtDHashMap.inductionOn",
"LawfulHashable",
"Option.none",
"EquivBEq",
"Std.ExtDHashMap",
"Bool",
"Hashable",
"Bool.false",
"BEq",
"Eq",
"Std.ExtDHashMap.Const.get?",
"Std.DHashMap",
"Option"
] | true |
BitVec.cpop_cons | Init.Data.BitVec.Lemmas | [
"instPowNat",
"Eq.mpr",
"BitVec.setWidth",
"Bool.toNat_lt",
"congrArg",
"BitVec.toNat_cpop_le",
"Bool.toNat",
"BitVec.instAdd",
"BitVec",
"id",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"BitVec.toNat",
"LE.le",
"BitVec.ofNat",
"instLENat",
"Nat.mod_eq_of_lt",
"Nat.cast",
"_pri... | true |
AddMonoidHom.addSubmonoidMap._proof_4 | Mathlib.Algebra.Group.Submonoid.Operations | [
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"Subtype",
"AddSubmonoid",
"AddSubmonoid.toAddZeroClass",
"instHAdd",
"And",
"AddZeroClass",
"SetLike.coe",
"HAdd.hAdd",
"And.intro",
"Exists.intro",
"AddZero.toAdd",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"Subtype.val",
"A... | false |
Std.Net.instInhabitedIPAddr | Std.Net.Addr | [
"Std.Net.IPAddr",
"Std.Net.instInhabitedIPAddr.default",
"Inhabited",
"Inhabited.mk"
] | true |
CategoryTheory.FinitaryPreExtensive.isUniversal_finiteCoproducts_Fin | Mathlib.CategoryTheory.Extensive | [
"instNeZeroNatHAdd_1",
"CategoryTheory.Limits.BinaryCofan.inr",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"Nat.recAux",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"ULift.casesOn",
"CategoryTheory.Functor.hext",
"CategoryTheory.isVanKampenColimit_of_isEmpty",
"CategoryT... | true |
MulPosReflectLE.toSMulPosReflectLE | Mathlib.Algebra.Order.Module.Defs | [
"instHSMul",
"Preorder.toLT",
"instSMulOfMul",
"SMulPosReflectLE.mk",
"le_of_mul_le_mul_right",
"Preorder.toLE",
"Mul",
"LE.le",
"MulPosReflectLE",
"LT.lt",
"Zero.toOfNat0",
"HSMul.hSMul",
"OfNat.ofNat",
"SMulPosReflectLE",
"Preorder",
"Zero"
] | true |
tendsto_Ioo_atTop._simp_1 | Mathlib.Topology.Order.AtTopBotIxx | [
"OrderTopology",
"Preorder.toLT",
"Order.IsSuccPrelimit",
"LinearOrder",
"nhdsWithin",
"PartialOrder.toPreorder",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Set.Elem",
"DistribLattice.toLattice",
"autoParam",
"Filter.atTop",
"TopologicalSpace",
"tendsto_Ioo_atTop._auto_1",
"Filt... | false |
Lean.Elab.instNonemptyIncrementalState | Lean.Elab.Frontend | [
"Classical.ofNonempty",
"Lean.Elab.Frontend.instNonemptyState",
"Nonempty.intro",
"Lean.Elab.IncrementalState",
"Lean.Elab.IncrementalState.mk",
"Lean.Parser.InputContext",
"Lean.Elab.Frontend.State",
"Lean.Parser.instInhabitedInputContext",
"instNonemptyOfInhabited",
"Lean.Language.Lean.instNonem... | true |
Field.powerBasisOfFiniteOfSeparable | Mathlib.FieldTheory.PrimitiveElement | [
"Field.powerBasisOfFiniteOfSeparable._proof_1",
"PowerBasis",
"Lattice.toSemilatticeSup",
"instSMulOfMul",
"Field.exists_primitive_element",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"IntermediateField",
"IntermediateField.toField",
"PartialOrder.toPreorder",
"Algebra",
"Preorder... | true |
SimpleGraph.instDecidableConnected._proof_1 | Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite | [
"Eq.mpr",
"Finset.univ",
"congrArg",
"Iff.rfl",
"SimpleGraph.Preconnected",
"id",
"SimpleGraph.Connected",
"SimpleGraph",
"And",
"Iff",
"Fintype",
"propext",
"Finset.Nonempty",
"Nonempty",
"SimpleGraph.connected_iff",
"Finset.univ_nonempty_iff",
"Eq.symm",
"Eq"
] | false |
Filter.EventuallyEq.isLocalMinOn_iff | Mathlib.Topology.Order.LocalExtr | [
"nhdsWithin",
"IsLocalMinOn",
"Membership.mem",
"Filter.EventuallyEq",
"TopologicalSpace",
"Iff",
"Filter.EventuallyEq.eq_of_nhdsWithin",
"Filter.EventuallyEq.isMinFilter_iff",
"Set.instMembership",
"Preorder",
"Set"
] | true |
Mathlib.Tactic.Abel.subst_into_smulg | Mathlib.Tactic.Abel | [
"congrArg",
"AddCommGroup",
"Int",
"congr",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans",
"Mathlib.Tactic.Abel.smulg"
] | true |
ProofWidgets.HtmlDisplayProps.recOn | ProofWidgets.Component.HtmlDisplay | [
"ProofWidgets.Html",
"ProofWidgets.HtmlDisplayProps.mk",
"ProofWidgets.HtmlDisplayProps",
"ProofWidgets.HtmlDisplayProps.rec"
] | false |
Manifold._aux_Mathlib_Geometry_Manifold_VectorBundle_ContMDiffSection___unexpand_ContMDiffSection_1 | Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | [
"Pure.pure",
"cond",
"Lean.Syntax.node",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.m... | false |
_private.Mathlib.NumberTheory.Cyclotomic.Basic.0.IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_nth_roots._simp_1_2 | Mathlib.NumberTheory.Cyclotomic.Basic | [
"Exists",
"exists_eq_left",
"And",
"propext",
"Eq"
] | false |
CategoryTheory.Functor.HasPointwiseRightDerivedFunctorAt.recOn | Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.MorphismProperty.Q",
"CategoryTheory.Functor.HasPointwiseRightDerivedFunctorAt.mk",
"CategoryTheory.MorphismProperty.Localization",
"CategoryTheory.Functor.HasPointwiseRightDerivedFunctorAt.rec",
"CategoryTheory.Category.toCate... | false |
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