name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.TransformStep.toStep | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.Simp.Result.mk",
"Lean.Meta.Simp.Step",
"Option.some",
"_private.Lean.Meta.Tactic.Simp.Types.0.Lean.TransformStep.toStep.match_1",
"Lean.Expr",
"Lean.Meta.Simp.Result",
"Bool.true",
"Option.none",
"Unit",
"Lean.Meta.Simp.Step.continue",
"Lean.Meta.Simp.Step.visit",
"Lean.Meta.Simp.S... | true |
_private.Lean.Meta.Constructions.SparseCasesOn.0.Lean.Meta.SparseCasesOnKey.rec | Lean.Meta.Constructions.SparseCasesOn | [
"_private.Lean.Meta.Constructions.SparseCasesOn.0.Lean.Meta.SparseCasesOnKey.mk",
"Array",
"Bool",
"Lean.Name",
"_private.Lean.Meta.Constructions.SparseCasesOn.0.Lean.Meta.SparseCasesOnKey"
] | false |
_private.Mathlib.Algebra.Order.Monovary.0.monovary_iff_forall_smul_nonneg._simp_1_2 | Mathlib.Algebra.Order.Monovary | [
"forall_true_left",
"True",
"propext",
"Eq",
"True.intro"
] | false |
Lean.Parser.many1.formatter | Lean.Parser.Extra | [
"Lean.PrettyPrinter.Formatter",
"Lean.Parser.symbol.formatter",
"Lean.Parser.withAntiquotSpliceAndSuffix.formatter",
"Lean.PrettyPrinter.Formatter.many1NoAntiquot.formatter",
"Lean.Name.mkStr1"
] | true |
_private.Mathlib.Analysis.AbsoluteValue.Equivalence.0.AbsoluteValue.exists_one_lt_lt_one_pi_of_one_lt._simp_1_2 | Mathlib.Analysis.AbsoluteValue.Equivalence | [
"Filter.instMembership",
"Filter.mem_atTop_sets",
"Preorder.toLE",
"Membership.mem",
"Exists",
"GE.ge",
"Filter.atTop",
"IsDirectedOrder",
"propext",
"Nonempty",
"Eq",
"Set.instMembership",
"Filter",
"Preorder",
"Set"
] | false |
ConvexOn.monotoneOn_deriv | Mathlib.Analysis.Convex.Deriv | [
"NormedCommRing.toSeminormedCommRing",
"le_refl",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"Real.denselyNormedField",
"CommSemiring.toSemiring",
"DifferentiableAt",
"ConvexOn.slope_le_deriv",
"deriv",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",... | true |
Std.DTreeMap.minKey!_insertIfNew_of_isEmpty | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.isEmpty",
"Std.DTreeMap.Internal.Impl.minKey!_insertIfNew_of_isEmpty",
"Ord.mk",
"Ordering",
"Std.DTreeMap.inner",
"Std.DTreeMap.insertIfNew",
"Std.TransCmp",
"Bool.true",
"Std.DTreeMap.wf",
"Bool",
"Inhabited",
"Std.DTreeMap.minKey!",
"Eq"
] | true |
Algebra.TensorProduct.tensorQuotientEquiv._proof_9 | Mathlib.RingTheory.TensorProduct.Quotient | [
"CommRing",
"CommSemiring.toSemiring",
"RingHomCompTriple",
"CommRing.toCommSemiring",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
Submodule.Quotient.addCommGroup._proof_3 | Mathlib.LinearAlgebra.Quotient.Defs | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.addCommGroup._aux_1",
"Add.mk",
"AddCommGroup.toAddGroup",
"Submodule.hasQuotient",
"AddCommGroup",
"QuotientAddGroup.Quotient.addGroup._proof_1",
"HasQuotient.Quotient",
"instHAdd",
"HAdd.hAdd",
"Submodule.toAddSubgroup",
"Add... | false |
CategoryTheory.StructuredArrow.map₂_obj_right | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Comma",
"CategoryTheory.discreteCategory",
"PUnit",
"Eq.refl",
"CategoryTheory.Category.toCategoryStru... | true |
Aesop.Goal.setMVars | Aesop.Tree.Data | [
"Aesop.GoalData.forwardRuleMatches",
"Aesop.GoalData",
"Aesop.GoalData.addedInIteration",
"Lean.instBEqMVarId",
"Aesop.GoalData.parent",
"Aesop.GoalData.depth",
"Aesop.GoalData.isIrrelevant",
"Aesop.Goal",
"Aesop.GoalData.origin",
"Lean.MVarId",
"Aesop.GoalData.lastExpandedInIteration",
"Aesop... | true |
Positive.addRightCancelSemigroup._proof_1 | Mathlib.Algebra.Order.Positive.Ring | [
"IsRightCancelAdd",
"Preorder.toLT",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Subtype",
"Positive.instAddSubtypeLtOfNat_mathlib",
"Subtype.coe_injective",
"AddRightCancelMonoid",
"AddZero.toZero",
"AddSemigroup.toAdd",
"AddLeftStrictMono",
"Function.... | false |
Lean.Meta.Grind.Goal | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.Goal.mk"
] | true |
Std.TreeSet.Raw.compare_get?_self | Std.Data.TreeSet.Raw.Lemmas | [
"instDecidableEqOrdering",
"Std.TreeSet.Raw.WF.out",
"Ordering",
"Ordering.eq",
"Std.TransCmp",
"Option.all",
"Bool.true",
"Std.TreeSet.Raw",
"Unit",
"Bool",
"Std.TreeSet.Raw.inner",
"Decidable.decide",
"Eq",
"Std.TreeSet.Raw.get?",
"Std.TreeMap.Raw.compare_getKey?_self",
"Std.TreeSet.... | true |
_private.Mathlib.RingTheory.HahnSeries.Multiplication.0.HahnSeries.map_mul._simp_1_3 | Mathlib.RingTheory.HahnSeries.Multiplication | [
"HahnSeries.support",
"Membership.mem",
"PartialOrder",
"Ne",
"propext",
"HahnSeries.coeff",
"Zero.toOfNat0",
"OfNat.ofNat",
"HahnSeries",
"Eq",
"Set.instMembership",
"HahnSeries.mem_support",
"Zero",
"Set"
] | false |
_private.Lean.DocString.Parser.0.Lean.Doc.Parser.bullet.go | Lean.DocString.Parser | [
"List.brecOn",
"_private.Lean.DocString.Parser.0.Lean.Doc.Parser.unorderedListIndicator",
"HOrElse.hOrElse",
"_private.Lean.DocString.Parser.0.Lean.Doc.Parser.bullet.match_1",
"List.cons",
"List",
"Unit",
"Lean.Parser.ParserState.mkError",
"List.below",
"Lean.Parser.ParserContext",
"Lean.Parser.... | true |
MeasureTheory.le_eLpNorm_of_bddBelow | Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity | [
"ENNReal.instCanonicallyOrderedAdd",
"MeasureTheory.ae",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NNReal.instCommSemiring",
"ENNReal.rpow_mul",
"MulOne.toOne",
"Real",
"ENNReal.ofNNReal",
"DivInvMonoid.toInv",
"instHSMul",
"MeasureTheory.Measure",
"instHDiv",
"Semiring.toModule",
"in... | true |
groupHomology.boundaries₂ | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"groupHomology.d₃₂",
"Submodule",
"Rep.V",
"CommRing",
"Finsupp.module",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Group",
"Rep.hV1",
"LinearMap.range",
"DivInvMonoid.toMonoid",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"Subtr... | true |
Asymptotics.IsLittleOTVS.fun_add | Mathlib.Analysis.Asymptotics.TVS | [
"NormedCommRing.toSeminormedCommRing",
"ContinuousSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Asymptotics.IsLittleOTVS",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"AddZeroClass.toAddZero",
"AddC... | true |
AddMonoidHom.independent_range_of_coprime_order | Mathlib.GroupTheory.NoncommPiCoprod | [
"Fintype.card_pi",
"Nat.gcd",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Nat.Coprime",
"instDecidableNot",
"AddSubgroup.instCompleteLattice",
"False",
"AddMonoidHom.noncommPiCoprod_range",
"instHSMul",
"Dvd.dvd",
"HMul.hMul",
"Pi.addGroup",
"Finset.univ",
"iSupIndep",
"congrArg",
"iS... | true |
LinearOrderedAddCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete | Mathlib.GroupTheory.ArchimedeanDensely | [
"Left.neg_pos_iff._simp_1",
"Mathlib.Tactic.Push.not_forall_eq",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Mathlib.Tactic.Push.not_exists._simp_1",
"Nontrivial",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"False",
"Subtype.mk.congr_simp",
"OrderAdd... | true |
ContinuousLinearMap.toSpanSingletonLE._proof_2 | Mathlib.Topology.Algebra.Module.LinearMap | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"ContinuousSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"ContinuousLinearMap.funLike",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddCommM... | false |
_private.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs.0.AffineSubspace.mem_direction_iff_eq_vsub_left.match_1_1 | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | [
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"AddTorsor.toVSub",
"VSub.vsub",
"And.casesOn",
"AffineSubspace.instSetLike",
"And",
"Exists.casesOn",
"SetLike.coe",
"And.intro",
"AddTorsor",
"Exists.intro",
"Set.image",
"Module",
"Ring.to... | false |
Set.Icc.convexCombo | Mathlib.Topology.UnitInterval | [
"Real",
"HMul.hMul",
"Real.instSub",
"HSub.hSub",
"Membership.mem",
"Set.Elem",
"Subtype.mk",
"Real.instAdd",
"Real.instOne",
"instHAdd",
"instHSub",
"Set.Icc",
"HAdd.hAdd",
"Real.instMul",
"One.toOfNat1",
"OfNat.ofNat",
"Set.Icc.convexCombo._proof_1",
"Subtype.val",
"Set.instMem... | true |
Digraph.sdiff_adj | Mathlib.Combinatorics.Digraph.Basic | [
"Digraph",
"Digraph.sdiff",
"Iff.rfl",
"SDiff.sdiff",
"And",
"Iff",
"Digraph.Adj",
"Not"
] | true |
smul_add | Mathlib.Algebra.GroupWithZero.Action.Defs | [
"instHSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"DistribSMul.smul_add",
"HAdd.hAdd",
"DistribSMul",
"AddZero.toAdd",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"Eq"
] | true |
HomotopicalAlgebra.LeftHomotopyRel.rightHomotopy._proof_4 | Mathlib.AlgebraicTopology.ModelCategory.Homotopy | [
"CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits",
"HomotopicalAlgebra.PrepathObject.p_snd",
"CategoryTheory.Category.assoc",
"HomotopicalAlgebra.PathObject",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"HomotopicalAlgebra.Cylinder.LeftHomotopy",
"HomotopicalAlgebra.ModelCateg... | false |
Lean.IR.SimpleGroundExpr.recOn | Lean.Compiler.IR.SimpleGroundExpr | [
"Lean.IR.SimpleGroundExpr",
"UInt64",
"Lean.IR.SimpleGroundExpr.ctor",
"String",
"Lean.IR.SimpleGroundExpr.rec",
"Lean.IR.SimpleGroundExpr.reference",
"Lean.IR.SimpleGroundExpr.string",
"Array",
"Lean.IR.SimpleGroundExpr.pap",
"Nat",
"Lean.IR.FunId",
"Lean.Name",
"Lean.IR.SimpleGroundExpr.na... | false |
PNat.caseStrongInductionOn | Mathlib.Data.PNat.Basic | [
"PNat.instOrderBot._proof_1",
"Preorder.toLT",
"instLinearOrderPNat",
"False.elim",
"PartialOrder.toPreorder",
"Subtype.casesOn",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"instOfNatPNatOfNeZeroNat",
"instOfNatNat",
"LE.le",
"Subtype.mk",
"Nat.casesAuxOn... | true |
Std.DTreeMap.Internal.Impl.View.mk._flat_ctor | Std.Data.DTreeMap.Internal.Operations | [
"Std.DTreeMap.Internal.Impl.View",
"Std.DTreeMap.Internal.Impl.View.mk",
"Nat",
"Std.DTreeMap.Internal.Impl.Tree"
] | false |
Function.not_lt_argmin | Mathlib.Order.WellFounded | [
"Function.argmin",
"Set.univ",
"InvImage",
"WellFoundedLT",
"wellFounded_lt",
"LT.lt",
"Set.mem_univ",
"WellFounded.not_lt_min",
"Nonempty",
"InvImage.wf",
"Not",
"LT"
] | true |
Ordinal.le_nfp | Mathlib.SetTheory.Ordinal.FixedPoint | [
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ordinal.iterate_le_nfp",
"instOfNatNat",
"LE.le",
"Ordinal.nfp",
"Nat",
"OfNat.ofNat",
"Ordinal"
] | true |
Finset.product_disjUnion | Mathlib.Data.Finset.Prod | [
"Iff.mpr",
"SProd.sprod",
"Finset.eq_of_veq",
"Finset",
"Disjoint",
"Finset.partialOrder",
"Finset.val",
"Finset.disjUnion",
"Finset.instSProd",
"Finset.disjoint_product",
"Multiset.product_add",
"Or",
"Prod",
"Finset.instOrderBot",
"Eq",
"Or.inr"
] | true |
_private.Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber.0.CircleDeg1Lift.coe_pow.match_1_1 | Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
Bundle.zeroSection_snd | Mathlib.Topology.VectorBundle.Basic | [
"Bundle.zeroSection",
"Bundle.TotalSpace.proj",
"Zero.toOfNat0",
"Bundle.TotalSpace.snd",
"OfNat.ofNat",
"Eq",
"rfl",
"Zero"
] | true |
Std.ExtDTreeMap.Const.getKey!_insertManyIfNewUnit_list_of_mem | Std.Data.ExtDTreeMap.Lemmas | [
"Eq.mpr",
"Std.ExtDTreeMap.mk",
"Std.DTreeMap",
"congrArg",
"Std.ExtDTreeMap.getKey!.congr_simp",
"instForInOfForIn'",
"Membership.mem",
"Ordering",
"inferInstance",
"id",
"Std.TransCmp",
"Id",
"Std.ExtDTreeMap.getKey!",
"Membership",
"Std.DTreeMap.Const.insertManyIfNewUnit",
"List",
... | true |
MeasureTheory.measurePreserving_prod_div_swap | Mathlib.MeasureTheory.Group.Prod | [
"MeasureTheory.MeasurePreserving",
"MeasureTheory.Measure",
"instHDiv",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"Prod.mk",
"MeasureTheory.Measure.IsMu... | true |
Lean.RBNode.WellFormed.recOn | Lean.Data.RBMap | [
"Lean.RBNode",
"Ordering",
"Lean.RBNode.WellFormed.insertWff",
"Lean.RBNode.WellFormed.eraseWff",
"Lean.RBNode.WellFormed.rec",
"Lean.RBNode.WellFormed.leafWff",
"Lean.RBNode.WellFormed",
"Lean.RBNode.leaf",
"Lean.RBNode.insert",
"Lean.RBNode.erase",
"Eq"
] | false |
Nat.Subtype.orderIsoOfNat | Mathlib.Order.OrderIsoNat | [
"Preorder.toLT",
"RelEmbedding.natLT",
"PartialOrder.toPreorder",
"Classical.propDecidable",
"Membership.mem",
"Set.Elem",
"OrderIso",
"LE.le",
"Nat.Subtype.ofNat",
"instLENat",
"Nat.Subtype.orderIsoOfNat._proof_2",
"Nat",
"LT.lt",
"RelEmbedding.orderEmbeddingOfLTEmbedding",
"Nat.instPar... | true |
_private.Mathlib.Algebra.MvPolynomial.Rename.0.MvPolynomial.killCompl_map._simp_1_1 | Mathlib.Algebra.MvPolynomial.Rename | [
"AlgHom.coe_toRingHom",
"AlgHom.algHomClass",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"RingHom",
"CommSemiring",
"RingHom.instFunLike",
"RingHomClass.toRingHom",
"Semiring",
"AlgHomClass.toRingHomClass",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe"
] | false |
CompleteSublattice.mem_sSup | Mathlib.Order.CompleteLattice.SetLike | [
"Iff.mpr",
"Sublattice",
"CompleteSublattice.instSupSet",
"SetLike.mem_mk_set._simp_1",
"sSupHomClass.map_sSup",
"Iff.of_eq",
"congrArg",
"CompleteSublattice.toSublattice",
"Set.mem_iUnion._simp_1",
"CompleteSublattice.subtype",
"Membership.mem",
"Exists",
"CompleteLattice.toConditionallyCom... | true |
Multiset.coe_attach | Mathlib.Data.Multiset.Defs | [
"Membership.mem",
"Multiset",
"Subtype",
"List",
"Multiset.ofList",
"List.instMembership",
"Eq",
"List.attach",
"Multiset.attach",
"rfl"
] | true |
_private.Mathlib.Tactic.HigherOrder.0.Tactic.mkHigherOrderType._sparseCasesOn_1 | Mathlib.Tactic.HigherOrder | [
"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 |
SemilinearIsometryEquivClass.mk | Mathlib.Analysis.Normed.Operator.LinearIsometry | [
"Norm.norm",
"Real",
"SeminormedAddCommGroup",
"outParam",
"AddCommGroup.toAddCommMonoid",
"SemilinearIsometryEquivClass",
"RingHom",
"SemilinearIsometryEquivClass.mk",
"RingHomInvPair",
"SeminormedAddCommGroup.toNorm",
"EquivLike",
"SeminormedAddCommGroup.toAddCommGroup",
"Semiring",
"Mod... | true |
StieltjesFunction.measure_univ | Mathlib.MeasureTheory.Measure.Stieltjes | [
"Eq.mpr",
"OrderTopology",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"ENNReal.ofReal",
"congrArg",
"Real.instSub",
"SecondCountableTopology",
"LinearOrder",
"Set.univ",
"PartialOrder.toPreorder",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"Filt... | true |
Lean.ParseImports.keyword | Lean.Elab.ParseImportsFast | [
"String",
"ToString.toString",
"instAppendString",
"instHAppendOfAppend",
"Lean.ParseImports.skip",
"Lean.ParseImports.State.mkError",
"Lean.ParseImports.Parser",
"Lean.ParseImports.keywordCore",
"Lean.ParseImports.State",
"HAppend.hAppend",
"instToStringString"
] | true |
CategoryTheory.Pretriangulated.TriangleOpEquivalence.counitIso_inv_app_hom₁ | Mathlib.CategoryTheory.Triangulated.Opposite.Triangle | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",... | true |
Preorder.frestrictLe₂.congr_simp | Mathlib.Probability.Kernel.IonescuTulcea.Maps | [
"Finset",
"Preorder.toLE",
"Membership.mem",
"LocallyFiniteOrderBot",
"Eq.rec",
"Subtype",
"LE.le",
"Finset.instSetLike",
"Preorder.frestrictLe₂",
"Finset.Iic",
"Eq.refl",
"Subtype.val",
"Eq",
"SetLike.instMembership",
"Preorder"
] | true |
_private.Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory.0.CategoryTheory.Functor.cartesianMonoidalCategory._simp_5 | Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso",
"CategoryTheory.Iso.cancel_iso_hom_right",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Iso.hom",
"Eq",
"CategoryTheory.Category"
] | false |
Matroid.uniqueBaseOn_restrict | Mathlib.Combinatorics.Matroid.Constructions | [
"Eq.mpr",
"congrArg",
"Matroid.uniqueBaseOn_restrict'",
"id",
"HasSubset.Subset",
"Set.instInter",
"Matroid.uniqueBaseOn",
"Inter.inter",
"Set.inter_right_comm",
"Eq.refl",
"Matroid.restrict",
"Eq",
"Matroid",
"Set.inter_eq_self_of_subset_left",
"Set.instHasSubset",
"Set"
] | true |
FirstOrder.Language.Term.realize_var | Mathlib.ModelTheory.Semantics | [
"FirstOrder.Language.Structure",
"FirstOrder.Language.Term.var",
"FirstOrder.Language.Term.realize",
"FirstOrder.Language",
"Eq",
"rfl"
] | true |
GromovHausdorff.instInhabitedGHSpace._proof_2 | Mathlib.Topology.MetricSpace.GromovHausdorff | [
"Set.singleton_nonempty",
"Real",
"instAddCommGroupPreLp",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Set.instSingletonSet",
"Subtype",
"Real.normedAddCommGroup",
"AddSubgroup",
"Set.Nonempty",
"lp",
"AddSubgroup.instSetLike",
"Nat",
"AddSubgroup.zero",
"ENNReal",
"PreLp",
"Zero.t... | false |
Substring.Raw.ValidFor.dropWhile | Batteries.Data.String.Lemmas | [
"String.toList_ofList",
"Eq.mpr",
"Substring.Raw.str",
"List.append_assoc",
"List.takeWhile_append_dropWhile",
"_private.Batteries.Data.String.Lemmas.0.Substring.Raw.ValidFor.dropWhile.match_1_1",
"congrArg",
"Substring.Raw.mk",
"String",
"String.utf8Len",
"Substring.Raw.ValidFor.of_eq",
"Subs... | true |
CategoryTheory.GrothendieckTopology.plusMap_toPlus | Mathlib.CategoryTheory.Sites.Plus | [
"CategoryTheory.GrothendieckTopology.diagramPullback._proof_3",
"CategoryTheory.GrothendieckTopology.Cover.toMultiequalizer",
"CategoryTheory.Limits.multiequalizer",
"CategoryTheory.Functor.op",
"CategoryTheory.Limits.MulticospanShape.snd",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Li... | true |
ZMod.eq_one_or_isUnit_sub_one | Mathlib.FieldTheory.Finite.Basic | [
"ZMod.isUnit_iff_coprime",
"Eq.mpr",
"Nat.Coprime",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Mathlib.Tactic.Contrapose.contrapose₂",
"Nat.instMulZeroClass",
"Nat.instOrderedSub",
"NeZero.mk",
"Nat.coprime_zero_right",
"Nat.Prime",
"Preorder... | true |
Lean.Compiler.LCNF.SpecEntry.alreadySpecialized | Lean.Compiler.LCNF.SpecInfo | [
"Bool",
"Lean.Compiler.LCNF.SpecEntry"
] | true |
NumberField.IsCMField.starRing._proof_2 | Mathlib.NumberTheory.NumberField.CMField | [
"Eq.mpr",
"AlgEquiv.instEquivLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Subfield.toAlgebra",
"CommRing.toNonUnitalCommRing",
"NumberField.maximalRealSubfield",
"congrArg",
"NNRat.instSemifield",
"DivisionSemiring.toNNRatAlgebra",
"Subfield.instSubfieldClass",
"Rat",
"AddGroupWith... | false |
_private.Mathlib.Analysis.Calculus.BumpFunction.SmoothApprox.0.ContinuousMap.dense_setOf_contDiff._simp_1_2 | Mathlib.Analysis.Calculus.BumpFunction.SmoothApprox | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
MeasurableSpace.DynkinSystem.ext | Mathlib.MeasureTheory.PiSystem | [
"Function.onFun",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"MeasurableSpace.DynkinSystem.mk",
"Compl.compl",
"Disjoint",
"_private.Mathlib.MeasureTheory.PiSystem.0.MeasurableSpace.DynkinSystem.ext.match_1_1",
"CompleteLattice.toConditionallyCompleteLattice",
"Set.instCompl",
"MeasurableSpa... | true |
CategoryTheory.Abelian.PreservesCoimageImageComparison.iso_inv_left | Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.Abelian.image",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Comma.left",
"CategoryTheory.Limits.cokerne... | true |
CategoryTheory.Idempotents.Karoubi.decompId_i_f | Mathlib.CategoryTheory.Idempotents.Karoubi | [
"CategoryTheory.Idempotents.Karoubi.Hom.f",
"CategoryTheory.Idempotents.Karoubi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Idempotents.Karoubi.p",
"CategoryTheory.Idempotents.Karoubi.X",
"CategoryTheory.Idempotents.Karoubi.mk",
"Cate... | true |
_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.isVertexCover_empty._simp_1_2 | Mathlib.Combinatorics.SimpleGraph.VertexCover | [
"SimpleGraph.Adj",
"Bot.bot",
"SimpleGraph",
"SimpleGraph.eq_bot_iff_forall_not_adj",
"propext",
"SimpleGraph.completeAtomicBooleanAlgebra",
"CompleteBooleanAlgebra.toBooleanAlgebra",
"Eq",
"Not",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
"BooleanAlgebra.toBot"
] | false |
CategoryTheory.Limits.yonedaCompLimIsoCocones_inv_app | Mathlib.CategoryTheory.Limits.Types.Yoneda | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Opposite.small",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.limitCompYonedaIsoCocone._proof_1",
"CategoryTheory.Functor.comp",
"Catego... | true |
CategoryTheory.ShortComplex.opcyclesMap'_neg | Mathlib.Algebra.Homology.ShortComplex.Preadditive | [
"NegZeroClass.toNeg",
"Inhabited.default",
"CategoryTheory.ShortComplex.instNegHom",
"CategoryTheory.ShortComplex.RightHomologyMapData.opcyclesMap'_eq",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.RightHomologyData",
"congrArg",
"CategoryTheory.ShortComplex",... | true |
toModuleCatFromModuleCatLinearEquiv._proof_3 | Mathlib.RingTheory.Morita.Matrix | [
"Submodule",
"Matrix.scalar",
"instHSMul",
"Pi.addCommMonoid",
"Ring.toNonAssocRing",
"ModuleCat",
"ZeroHom.toFun",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Matrix",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"MatrixModCat.toModuleCatObj._p... | false |
Mathlib.Tactic.Monoidal.Context | Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes | [
"Mathlib.Tactic.Monoidal.Context.mk"
] | true |
ContinuousLinearMap.isometry_iff_adjoint_comp_self | Mathlib.Analysis.InnerProductSpace.Adjoint | [
"ContinuousLinearMap.comp",
"LinearIsometryEquiv.instEquivLike",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"NormedSpace.toIsBoundedSMul",
... | true |
_private.Lean.Compiler.IR.EmitUtil.0.Lean.IR.CollectUsedDecls.collectFnBody._sparseCasesOn_4 | Lean.Compiler.IR.EmitUtil | [
"Lean.IR.FnBody.case",
"Lean.IR.FnBody.jdecl",
"Lean.IR.Expr",
"Nat.ne_of_beq_eq_false",
"Lean.IR.FnBody.uset",
"Lean.IR.FnBody.ret",
"Lean.IR.FnBody.inc",
"Lean.IR.Arg",
"Lean.IR.Param",
"Lean.IR.CtorInfo",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.IR.FnBody.rec",
"Lean.I... | false |
Nat.EqResult.false.injEq | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat | [
"Nat.EqResult.false.inj",
"Eq.propIntro",
"Lean.Expr",
"Nat.EqResult.false",
"Nat.EqResult",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
OrderDual.instIsLeftCancelAdd | Mathlib.Algebra.Order.Group.Synonym | [
"IsLeftCancelAdd",
"OrderDual",
"OrderDual.instAdd",
"Add"
] | true |
Int.add | Init.Data.Int.Basic | [
"Int.add.match_1",
"Int.ofNat",
"Int",
"instHAdd",
"HAdd.hAdd",
"Int.subNatNat",
"Nat",
"instAddNat",
"Int.negSucc",
"Nat.succ"
] | true |
CategoryTheory.GrothendieckTopology.Cover.instInhabited | Mathlib.CategoryTheory.Sites.Grothendieck | [
"Preorder.toLE",
"CategoryTheory.GrothendieckTopology.instPreorderCover",
"OrderTop.toTop",
"CategoryTheory.GrothendieckTopology.Cover",
"CategoryTheory.GrothendieckTopology",
"Inhabited",
"Top.top",
"CategoryTheory.GrothendieckTopology.Cover.instOrderTop",
"CategoryTheory.Category",
"Inhabited.mk... | true |
Std.Do.SPred.entails_3._simp_1 | Std.Do.SPred.DerivedLaws | [
"Std.Do.SPred.entails",
"List.cons",
"propext",
"Std.Do.SPred",
"Std.Do.SPred.entails_3",
"Eq",
"ULift.down",
"List.nil"
] | false |
List.forall₂_reverse_iff | Mathlib.Data.List.Forall2 | [
"Eq.mpr",
"congrArg",
"id",
"List.rel_reverse",
"List",
"Iff",
"List.reverse_reverse",
"Iff.intro",
"List.reverse",
"List.Forall₂",
"Eq.symm",
"Eq"
] | true |
Lean.Elab.Tactic.TacticParsedSnapshot.below | Lean.Elab.Term.TermElabM | [
"Task",
"Lean.Elab.Tactic.TacticParsedSnapshot.rec",
"Lean.Syntax",
"Lean.Elab.Tactic.TacticFinishedSnapshot",
"Lean.Elab.Tactic.TacticParsedSnapshot",
"Lean.Language.SnapshotTask",
"Array",
"List",
"PProd",
"PUnit",
"Lean.Language.SnapshotTask.ReportingRange",
"Lean.Language.Snapshot",
"IO.... | false |
ENat.iSup_add_iSup_of_monotone | Mathlib.Data.ENat.Lattice | [
"instCompleteLinearOrderENat",
"CommSemiring.toSemiring",
"iSup",
"covariant_swap_add_of_covariant_add",
"add_le_add",
"Monotone",
"Preorder.toLE",
"instAddENat",
"instPreorderENat",
"Exists.imp",
"_private.Mathlib.Data.ENat.Lattice.0.ENat.iSup_add_iSup_of_monotone.match_1_1",
"LE.le",
"Cond... | true |
Aesop.Frontend.Parser.«feature(_)» | Aesop.Frontend.RuleExpr | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | true |
_private.Mathlib.Analysis.Complex.Conformal.0.isConformalMap_complex_linear._simp_1_4 | Mathlib.Analysis.Complex.Conformal | [
"False",
"eq_false",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"three_ne_zero",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
Std.ExtTreeSet.get!_min! | Std.Data.ExtTreeSet.Lemmas | [
"_private.Std.Data.ExtTreeSet.Lemmas.0.Std.ExtTreeSet.ext",
"Ordering",
"Std.ExtTreeSet.inner",
"mt",
"Ne",
"Std.TransCmp",
"Std.ExtTreeMap.getKey!_minKey!",
"Std.ExtTreeSet.get!",
"Unit",
"Std.ExtTreeMap",
"Std.ExtTreeSet.min!",
"Std.ExtTreeSet",
"Inhabited",
"Std.ExtTreeSet.instEmptyColl... | true |
Subgroup.subgroupOf_inj._simp_2 | Mathlib.Algebra.Group.Subgroup.Map | [
"Subgroup.subgroupOf_inj",
"Subgroup.subgroupOf",
"Group",
"Membership.mem",
"Subtype",
"Subgroup",
"Subgroup.instMin",
"propext",
"Subgroup.toGroup",
"Eq",
"SetLike.instMembership",
"Min.min",
"Subgroup.instSetLike"
] | false |
LinearIsometry.coe_toSpanSingleton | Mathlib.Analysis.Normed.Operator.Basic | [
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"SeminormedAddCommGroup",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"Field.toSemifield",
"LinearMap",
"Real.instOne",
"SeminormedAddCommGroup.toNorm",
"Semifield.toDivisionSemiring... | true |
HasDerivWithinAt.mono | Mathlib.Analysis.Calculus.Deriv.Basic | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUnif... | true |
_private.Mathlib.Order.Interval.Set.Basic.0.Set.instNoMinOrderElemIoc.match_1 | Mathlib.Order.Interval.Set.Basic | [
"Set.Ioc",
"Subtype.casesOn",
"Membership.mem",
"Set.Elem",
"Subtype.mk",
"Set.instMembership",
"Preorder",
"Set"
] | false |
List.Perm.pairwise_iff | Init.Data.List.Perm | [
"List.Perm.nil_eq",
"Iff.mpr",
"Eq.mpr",
"List.Pairwise",
"congrArg",
"Membership.mem",
"Exists",
"id",
"List.Perm",
"List.Perm.subset",
"List.Perm.trans",
"List.cons",
"List.pairwise_cons",
"instHAppendOfAppend",
"List",
"List.Pairwise.nil",
"And",
"Iff",
"Exists.casesOn",
"Li... | true |
Set.Ioo.pos | Mathlib.Algebra.Order.Interval.Set.Instances | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"PartialOrder.toPreorder",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"PartialOrder",
"Set.Elem",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"And.left",
"NonAssocSemiring.toNonUnitalNonAssocS... | true |
IsFractionRing.algHom_commutes | Mathlib.RingTheory.Localization.FractionRing | [
"Eq.mpr",
"RingHom.instRingHomClass",
"CommRing",
"instHDiv",
"AlgHom.algHomClass",
"GroupWithZero.toDivInvMonoid",
"congrArg",
"CommSemiring.toSemiring",
"IsFractionRing",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"Algebra",
"DivisionSemiring.toGroupWithZero",
"RingHom",
"Algebra.t... | true |
_private.Lean.Meta.Tactic.FunInd.0.Lean.Tactic.FunInd.M2.branch | Lean.Meta.Tactic.FunInd | [
"controlAt",
"instMonadControlTOfPure",
"Lean.MVarId",
"Lean.Expr",
"Lean.Meta.MetaM",
"StateT.monadControl",
"Applicative.toPure",
"StateT.instAlternative",
"Array",
"_private.Lean.Meta.Tactic.FunInd.0.Lean.Tactic.FunInd.M2",
"Lean.Meta.instMonadMetaM",
"Alternative.toApplicative",
"Monad.t... | true |
OrderIso.smulRight_symm_apply | Mathlib.Algebra.Order.Module.Defs | [
"GroupWithZero.toMonoidWithZero",
"instHSMul",
"Preorder.toLT",
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"GroupWithZero",
"Preorder.toLE",
"DivisionMonoid.toDivInvOneMonoid",
"RelIso.symm",
"PosSMulMono",
"LE.le",
"RelIso",
"Inv.inv",
"MonoidWithZero.toMulZeroOneC... | true |
_private.Mathlib.RingTheory.Ideal.GoingUp.0.Ideal.isMaximal_of_isIntegral_of_isMaximal_comap.match_1_1 | Mathlib.RingTheory.Ideal.GoingUp | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Submodule.instPartialOrder",
"LE.le",
"Ideal",
"And.casesOn",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"And",
"CommRing.toCommSemiring",
"Exists.casesO... | false |
MultilinearMap.freeFinsuppEquiv._proof_7 | Mathlib.LinearAlgebra.Multilinear.Finsupp | [
"Finsupp.smulZeroClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"Finsupp.module",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"instDistribSMul",
"AddMonoid.toAddZeroClass",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"Algebra.id"... | false |
Lean.Elab.Term.mkNoImplicitLambdaAnnotation | Lean.Elab.Term.TermElabM | [
"Lean.Elab.Term.hasNoImplicitLambdaAnnotation",
"Lean.Expr",
"instDecidableEqBool",
"Lean.mkAnnotation",
"Bool.true",
"Bool",
"Lean.Name.mkStr1",
"Eq",
"ite"
] | true |
MeasureTheory.piContent_eq_measure_pi | Mathlib.Probability.ProductMeasure | [
"MeasurableSet.preimage",
"Finset.mem_univ",
"MeasurableEquiv.instEquivLike",
"Eq.mpr",
"MeasureTheory.Measure",
"Equiv.instEquivLike",
"MeasureTheory.Measure.pi_map_piCongrLeft",
"MeasurableSet",
"Finset.univ",
"ENNReal.instAddCommMonoid",
"congrArg",
"MeasureTheory.piContent_cylinder",
"Me... | true |
Matrix.transpose_eq_natCast | Mathlib.Data.Matrix.Diagonal | [
"Matrix",
"AddMonoid.toAddZeroClass",
"Matrix.transpose_eq_diagonal",
"AddZeroClass.toAddZero",
"Matrix.instNatCastOfZero",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"AddZero.toZero",
"Iff",
"Matrix.transpose",
"Nat",
"AddMonoidWithOne.toAddMonoid",
"Eq",
"AddMonoidWithOne",
"DecidableEq... | true |
Lean.Elab.Do.ContInfo.toContInfoRef | Lean.Elab.Do.Basic | [
"Classical.ofNonempty",
"Lean.Elab.Do.ContInfoRef",
"Lean.Elab.Do.instNonemptyContInfoRef",
"Lean.Elab.Do.ContInfo"
] | true |
Batteries.UnionFind.recOn | Batteries.Data.UnionFind.Basic | [
"Batteries.UnionFind.rankD",
"Batteries.UFNode",
"Batteries.UnionFind.mk",
"Batteries.UnionFind.parentD",
"Ne",
"Array",
"Batteries.UnionFind.rec",
"Nat",
"LT.lt",
"Batteries.UnionFind",
"instLTNat",
"Array.size"
] | false |
derivationOfSectionOfKerSqZero_apply_coe | Mathlib.RingTheory.Smooth.Kaehler | [
"Derivation",
"derivationOfSectionOfKerSqZero",
"CommRing",
"Semiring.toModule",
"AlgHom.algHomClass",
"IsScalarTower.right",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"AlgHom",
"Submodule.addCommMonoid",
"AlgHom.funLike",
"AlgHom.id",
"HSub.hSub",
"Algebra",
"Algebra.toSM... | true |
Finset.coe_zero | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Finset.coe_singleton",
"Finset",
"Set.zero",
"SetLike.coe",
"Finset.instSetLike",
"Zero.toOfNat0",
"Finset.zero",
"OfNat.ofNat",
"Eq",
"Zero",
"Set"
] | true |
«term_≃⋆+*_» | Mathlib.Algebra.Star.StarRingHom | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
_private.Mathlib.RingTheory.Smooth.IntegralClosure.0.exists_derivative_mul_eq_and_isIntegral_coeff._simp_1_8 | Mathlib.RingTheory.Smooth.IntegralClosure | [
"propext",
"Eq",
"forall_apply_eq_imp_iff₂"
] | false |
CategoryTheory.CosimplicialObject.augmentOfIsInitial_right | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"CategoryTheory.Comma.right",
"CategoryTheory.CosimplicialObject",
"CategoryTheory.Functor.id",
"CategoryTheory.Limits.IsInitial",
"CategoryTheory.CosimplicialObject.const",
"CategoryTheory.CosimplicialObject.instCategory",
"Eq.refl",
"CategoryTheory.CosimplicialObject.augmentOfIsInitial",
"Eq",
"... | true |
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