name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Limits.Types.binaryProductCone_pt | Mathlib.CategoryTheory.Limits.Types.Products | [
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.discreteCategory",
"CategoryTheory.Limits.pair",
"CategoryTheory.types",
"Eq.refl",
"Prod",
"Eq",
"CategoryTheory.Limits.Types.binaryProductCone",
"CategoryTheory.Discrete"
] | true |
_private.Mathlib.Util.Delaborators.0.exists_delab.match_5 | Mathlib.Util.Delaborators | [
"of_decide_eq_true",
"Array.getLit",
"Lean.Expr",
"id",
"instOfNatNat",
"dite",
"List.toArray",
"List.cons",
"Array",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.ndrec",
"Eq.refl",
"instDecidableEqNat",
"instLTNat",
"OfNat.ofNat",
"Eq.symm",
"Decidable.decide",
"E... | false |
CategoryTheory.Limits.Pi.map'_comp_π_assoc | Mathlib.CategoryTheory.Limits.Shapes.Products | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasProduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.Pi.map'",
"Eq.mp",
"CategoryTheory.Limits.Pi.π",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Limits.piObj",
"congr",
... | true |
IsUnit.div_self | Mathlib.Algebra.Group.Units.Defs | [
"Eq.mpr",
"MulOne.toOne",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"IsUnit.mul_inv_cancel",
"IsUnit",
"DivisionMonoid",
"id",
"MulOne.toMul",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"div_eq_mul_inv",
"DivisionMonoid.toDivInvMonoid",
"MulOneClas... | true |
MulOpposite.opHomeomorph_symm_apply | Mathlib.Topology.Algebra.Constructions | [
"MulOpposite.opHomeomorph",
"MulOpposite",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Homeomorph.symm",
"MulOpposite.instTopologicalSpaceMulOpposite",
"Homeomorph",
"Eq.refl",
"MulOpposite.unop",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
UniformFun.instMetricSpaceOfBoundedSpace._proof_1 | Mathlib.Topology.MetricSpace.UniformConvergence | [
"instT4SpaceOfT1SpaceOfNormalSpace",
"PseudoMetricSpace.toBornology",
"UniformFun.instPseudoEMetricSpace",
"EMetricSpace.metrizableSpace",
"T3Space.toT0Space",
"PseudoMetricSpace.toUniformSpace",
"UniformFun.instT2Space",
"UniformSpace.completelyNormalSpace_of_isCountablyGenerated_uniformity",
"Unif... | false |
PFunctor.Approx.CofixA.intro | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor",
"PFunctor.A",
"PFunctor.B",
"PFunctor.Approx.CofixA.intro",
"PFunctor.Approx.CofixA",
"Nat",
"Nat.succ"
] | true |
Dyadic.instOrderedRing | Init.Data.Dyadic.Instances | [
"Rat.instOfNat",
"Eq.mpr",
"Rat.instMul",
"Dyadic.toRat_mul",
"HMul.hMul",
"of_decide_eq_true",
"congrArg",
"Dyadic.instLT",
"Dyadic.instLE",
"Rat",
"Dyadic.instDecidableLT",
"Lean.Grind.CommSemiring.toSemiring",
"Lean.Grind.OrderedAdd.mk",
"Rat.mul_lt_mul_of_pos_left",
"Lean.Grind.Semir... | true |
oneLePart_inf_leOnePart_eq_one | Mathlib.Algebra.Order.Group.PosPart | [
"instIsRightCancelMulOfMulRightReflectLE",
"Eq.mpr",
"Lattice",
"MulOne.toOne",
"DivInvMonoid.toInv",
"instHDiv",
"inf_mul",
"InvOneClass.toOne",
"HMul.hMul",
"leOnePart_eq_inv_inf_one",
"DivInvOneMonoid.toInvOneClass",
"instLeOnePart",
"Monoid.toMulOneClass",
"congrArg",
"InvolutiveInv.... | true |
Submodule.Quotient.seminormedAddCommGroup | Mathlib.Analysis.Normed.Group.Quotient | [
"Submodule.Quotient.seminormedAddCommGroup._proof_21",
"Submodule",
"Submodule.Quotient.seminormedAddCommGroup._proof_19",
"SeminormedAddCommGroup",
"Dist.mk",
"Submodule.Quotient.addCommGroup",
"QuotientModule.Quotient.topologicalSpace",
"Submodule.Quotient.seminormedAddCommGroup._proof_5",
"AddCom... | true |
Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence | Mathlib.RingTheory.Polynomial.Chebyshev | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Polynomial.derivative",
"Int.cast",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"Polynomial.eval",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"MulOne.toOne",
"Nat.instMulZeroClass",
"Mat... | true |
_private.Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality.0.groupCohomology.cocyclesMap_comp._simp_1_1 | Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.HasHomology",
"HomologicalComplex.cyclesMap_comp",
"HomologicalComplex",
"ComplexShape",
"HomologicalComplex.cyclesMap",
"CategoryTheory.Category... | false |
_private.Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence.0.CategoryTheory.Abelian.SpectralObject.coreE₂CohomologicalFin._proof_26 | Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | [
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Int.Linear.norm_le",
"eq_false",
"Int.Linear.Expr.eq_of_norm_eq",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Int.Linear.eq_norm",
"Classical.byContradiction",
"PartialOrde... | false |
CategoryTheory.CanonicallyOverClass.mk | Mathlib.CategoryTheory.Comma.Over.OverClass | [
"CategoryTheory.CanonicallyOverClass.mk",
"semiOutParam",
"CategoryTheory.OverClass",
"CategoryTheory.CanonicallyOverClass",
"CategoryTheory.Category"
] | true |
MeasureTheory.instIsAddRightInvariantHausdorffMeasureOfIsIsometricVAddAddOpposite | Mathlib.MeasureTheory.Measure.Hausdorff | [
"Real",
"IsIsometricVAdd",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"MeasureTheory.Measure.hausdorffMeasure",
"BorelSpace",
"AddZeroClass.toAddZero",
"AddOpposite",
"EMetricSpace.toPseudoEMetricSpace",
"IsometryEquiv.constVAdd",
"IsometryEquiv.map_hausdorffMeasure",
"EMetricSpac... | true |
Lean.Grind.CommRing.Poly.addConst_k_eq_addConst | Init.Grind.Ring.CommSolver | [
"cond",
"Lean.Grind.CommRing.Poly.addConst_k",
"Eq.mpr",
"Lean.Grind.CommRing.Poly.rec",
"Decidable.casesOn",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.add",
"congrArg",
"Decidable",
"Lean.Grind.CommRing.Poly.addConst.go",
"Int.instDecidableEq",
"Eq.mp",
"id",
"instDecidableEqB... | true |
_private.Lean.Meta.Tactic.LibrarySearch.0.Lean.Meta.LibrarySearch.ext | Lean.Meta.Tactic.LibrarySearch | [
"Inhabited.default",
"_private.Lean.Meta.Tactic.LibrarySearch.0.Lean.Meta.LibrarySearch.LibSearchState",
"Lean.instInhabitedEnvExtension",
"Lean.EnvExtension"
] | true |
Fin.map_valEmbedding_univ | Mathlib.Data.Fintype.Fin | [
"Preorder.toLT",
"Finset.univ",
"Iff.of_eq",
"congrArg",
"Function.Surjective.exists",
"Finset",
"Fin.valEmbedding",
"Finset.Iio",
"Finset.ext",
"Nat.instLocallyFiniteOrder",
"Finset.map",
"Membership.mem",
"Exists",
"LocallyFiniteOrder.toLocallyFiniteOrderBot",
"Subtype",
"OrderIso",
... | true |
Std.Tactic.BVDecide.BVExpr.bitblast.goCache_Inv_of_Inv._mutual | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Expr | [
"Std.Tactic.BVDecide.BVExpr.PackedBitVec.bv",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastClz",
"Std.Tactic.BVDecide.BVExpr.bitblast._proof_21",
"Std.Tactic.BVDecide.BVBinOp.eval_or",
"Std.Sat.AIG.RefVec.get",
"Eq.mpr",
"Std.Tactic.BVDecide.BVUnOp.eval_clz",
"PSum.casesOn",
"Std.Sat.AIG.ArbitraryShift... | false |
Nat.ascFactorialBinary._unary | Mathlib.Data.Nat.Factorial.Basic | [
"Nat.ascFactorialBinary.match_1",
"instHDiv",
"HMul.hMul",
"InvImage",
"Nat.ascFactorialBinary._unary._proof_1",
"Nat.ascFactorialBinary._unary._proof_2",
"WellFounded.Nat.fix",
"namedPattern",
"PSigma.casesOn",
"HDiv.hDiv",
"instMulNat",
"instOfNatNat",
"instHAdd",
"Unit",
"HAdd.hAdd",
... | false |
_private.Mathlib.Tactic.CategoryTheory.Coherence.Normalize.0.Mathlib.Tactic.BicategoryLike.evalComp.match_1.splitter | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | [
"Mathlib.Tactic.BicategoryLike.NormalExpr",
"Lean.Expr",
"Mathlib.Tactic.BicategoryLike.Eval.Result",
"_private.Mathlib.Tactic.CategoryTheory.Coherence.Normalize.0.Mathlib.Tactic.BicategoryLike.evalComp.match_1",
"Mathlib.Tactic.BicategoryLike.Eval.Result.mk"
] | true |
_private.Lean.Environment.0.Lean.EnvExtension.ensureExtensionsArraySize.loop | Lean.Environment | [
"Inhabited.default",
"instInhabitedError",
"IO",
"instInhabitedEIO",
"Array",
"Nat",
"Lean.EnvExtensionState",
"IO.Error"
] | true |
Real.differentiableAt_mulExpNegMulSq | Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq | [
"NormedCommRing.toNormedRing",
"DifferentiableAt.mul",
"Real",
"Semiring.toModule",
"RCLike.toNormedAlgebra",
"HMul.hMul",
"Real.denselyNormedField",
"Real.instRCLike",
"DifferentiableAt.fun_neg",
"DifferentiableAt",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.to... | true |
Lean.Meta.Simp.ConfigCtx.etaStruct._inherited_default | Init.MetaTypes | [
"id",
"Lean.Meta.EtaStructMode.all",
"Lean.Meta.EtaStructMode"
] | false |
_private.Mathlib.RingTheory.Perfectoid.BDeRham.0.term𝕎_ | Mathlib.RingTheory.Perfectoid.BDeRham | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
CoxeterMatrix.Group | Mathlib.GroupTheory.Coxeter.Basic | [
"PresentedGroup",
"CoxeterMatrix",
"CoxeterMatrix.relationsSet"
] | true |
_private.Mathlib.Topology.MetricSpace.Pseudo.Defs.0.Metric.boundedSpace_iff_edist._simp_1_1 | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"NNDist.nndist",
"PseudoMetricSpace.toBornology",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toNNDist",
"Preorder.toLE",
"Exists",
"NNReal",
"LE.le",
"BoundedSpace",
"NNReal.instPartialOrder",
"PseudoMetricSpace",
"propext",
"Metric.boundedSpace_iff_nndist",
"Eq"
] | false |
FractionalIdeal.coe_inv_of_ne_zero | Mathlib.RingTheory.FractionalIdeal.Inverse | [
"Eq.mpr",
"Submodule",
"IsDomain",
"Subtype.mk.congr_simp",
"CommRing",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"FractionalIdeal.isFractional_div_of_ne_zero",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"IsFractionRing",
... | true |
RootPairing.Equiv.weightEquiv_comp_toLin | Mathlib.LinearAlgebra.RootSystem.Hom | [
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"RootPairing.Equiv.comp",
"RootPairing.Hom.comp",
"LinearEquiv.ext",
"AddCommGroup",
"RootPairing.Equiv.toHom",
"LinearMap",
"RootPairing.Equiv.weightEquiv",
"RootPairing.Hom",
"Comm... | true |
SchwartzMap.convolution._proof_5 | Mathlib.Analysis.Fourier.Convolution | [
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"Field.toSemifield",
"Field.toCommRing",
"smulCommClass_self",
"RCLike.toDenselyNormedField",
"RCLike",
"Semifield.toDivisionSemiring",
"CommMonoid.toMonoid",
"Monoid.toSemigroup",
"DivisionSemiring... | false |
Lean.Grind.IntInterval.nonEmpty_of_mem | Init.Grind.ToInt | [
"Eq.mpr",
"Lean.Grind.IntInterval.instMembershipInt",
"Membership.mem",
"Eq.mp",
"id",
"Int",
"LE.le",
"Lean.Grind.IntInterval.co",
"Lean.Grind.IntInterval.ii",
"Int.instLTInt",
"Lean.Grind.IntInterval.ci",
"Bool.true",
"_private.Init.Grind.ToInt.0.Lean.Grind.IntInterval.nonEmpty_of_mem._pro... | true |
Finset.aestronglyMeasurable_prod | Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable | [
"MeasureTheory.Measure",
"Multiset.map",
"Monoid.toMulOneClass",
"Finset",
"Multiset.mem_map",
"Membership.mem",
"Exists",
"Eq.rec",
"Multiset",
"MulOne.toMul",
"Pi.commMonoid",
"Finset.val",
"Finset.prod",
"MeasurableSpace",
"TopologicalSpace",
"Multiset.instMembership",
"MulOneClas... | true |
TensorAlgebra.ofDirectSum_comp_toDirectSum | Mathlib.LinearAlgebra.TensorAlgebra.ToTensorPower | [
"PiTensorProduct.instModule",
"TensorAlgebra.ofDirectSum_of_tprod",
"AlgHom.toLinearMap",
"NonAssocSemiring.toAddCommMonoidWithOne",
"TensorAlgebra.tprod",
"instAddCommMonoidDirectSum",
"LinearMap.ext",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoid.toAddZeroClas... | true |
Representation.linearizeMap.eq_1 | Mathlib.RepresentationTheory.Action | [
"Monoid",
"Semiring.toModule",
"Finsupp.module",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"Finsupp.lmapDomain",
"Finsupp.instAddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Representation.IntertwiningMa... | true |
CategoryTheory.SmallObject.π'FunctorObj | Mathlib.CategoryTheory.SmallObject.Construction | [
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.SmallObject.FunctorObjIndex",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Discrete.functor",
"CategoryTheory.SmallObject.functorObjLeft._proof_1",
"CategoryTh... | true |
CategoryTheory.NatIso.prod_hom | Mathlib.CategoryTheory.Products.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.NatTrans.prod",
"CategoryTheory.Functor.category",
"CategoryTheory.Iso",
"CategoryTheory.Functor.prod",
"CategoryTheory.NatIso.prod",
"CategoryTheory.prod'",
"Eq.refl",
"CategoryTheory.Category.toCa... | true |
WeierstrassCurve.Jacobian.Nonsingular | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Basic | [
"Finsupp.instAddZeroClass",
"Nat.instMulZeroClass",
"CommRing",
"WeierstrassCurve.Jacobian.polynomialX",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"RingHom",
"Ne",
"instOfNatNat",
"WeierstrassCurve.Jacobian.Equation",
"WeierstrassCurve.Jacobian",
"MvPolynomi... | true |
CategoryTheory.Triangulated.SpectralObject.mk.inj | Mathlib.CategoryTheory.Triangulated.SpectralObject | [
"CategoryTheory.Functor",
"CategoryTheory.Triangulated.SpectralObject",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Triangulated.SpectralObject.mk.noConfusion",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheor... | true |
Lean.Doc.Parser.instReprUnorderedListType | Lean.DocString.Parser | [
"Lean.Doc.Parser.instReprUnorderedListType.repr",
"Repr.mk",
"Lean.Doc.Parser.UnorderedListType",
"Repr"
] | true |
OrderIso.coe_toEquiv | Mathlib.Order.Hom.Basic | [
"Equiv.instEquivLike",
"Equiv",
"OrderIso",
"LE.le",
"LE",
"instFunLikeOrderIso",
"RelIso.toEquiv",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
Composition.toCompositionAsSet_blocks | Mathlib.Combinatorics.Enumerative.Composition | [
"Composition.orderEmbOfFin_boundaries",
"Iff.mpr",
"CompositionAsSet.card_boundaries_eq_succ_length",
"CompositionAsSet.boundary.eq_1",
"Eq.mpr",
"Composition.toCompositionAsSet",
"Nat.instMulZeroClass",
"Finset.orderEmbOfFin",
"Composition.length",
"congrArg",
"List.eq_of_sum_take_eq",
"Compo... | true |
List.map_prod_left_eq_zip | Init.Data.List.Zip | [
"Eq.mpr",
"congrArg",
"List.map",
"Eq.rec",
"id",
"Prod.mk",
"List.zip",
"List.zip_map'",
"List.map_id_fun'",
"List",
"congrFun",
"True",
"eq_self",
"of_eq_true",
"Eq.refl",
"congrFun'",
"Prod",
"Eq.symm",
"Eq",
"Eq.trans"
] | true |
_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Impl.updateCell._proof_7 | Std.Data.DTreeMap.Internal.Model | [
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.Balanced.leaf._simp_1",
"Std.DTreeMap.Internal.Impl.leaf",
"of_eq_true"
] | false |
Filter.Tendsto.squeeze | Mathlib.Topology.Order.Basic | [
"tendsto_of_tendsto_of_tendsto_of_le_of_le",
"OrderTopology",
"Preorder.toLE",
"nhds",
"LE.le",
"Pi.hasLe",
"TopologicalSpace",
"Filter.Tendsto",
"Filter",
"Preorder"
] | true |
PrimeSpectrum.localization_comap_isEmbedding | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"PrimeSpectrum.localization_comap_isInducing",
"IsLocalization",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"PrimeSpectrum.localization_comap_injective",
"PrimeSpectrum",
"Topology.IsEmbedding",
... | true |
CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.op | Mathlib.CategoryTheory.Localization.Opposite | [
"CategoryTheory.Functor.op",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.op._proof_2",
"CategoryTheory.Functor.comp",
"CategoryTheory.MorphismProperty.IsInvertedBy.rightOp",
"CategoryTheory.MorphismProperty.op... | true |
_private.Init.Data.Array.Basic.0.Array.isPrefixOfAux._proof_1 | Init.Data.Array.Basic | [
"LE.le",
"instLENat",
"Array",
"Nat",
"LT.lt",
"instLTNat",
"Nat.lt_of_lt_of_le",
"Array.size"
] | false |
WithBot.instBoundedOrder.eq_1 | Mathlib.Order.WithBot | [
"WithBot.instBoundedOrder",
"WithBot",
"WithBot.instOrderBot",
"WithBot.instOrderTop",
"OrderTop",
"LE",
"Eq.refl",
"BoundedOrder.mk",
"BoundedOrder",
"Eq",
"WithBot.instLE"
] | true |
Ideal.span_singleton_mem_isPrincipalSubmonoid | Mathlib.RingTheory.Ideal.IsPrincipal | [
"Iff.mpr",
"Submodule",
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Membership.mem",
"Algebra.id",
"Set.instSingletonSet",
"Ideal",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"Ideal.isPrincipalSubmonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
... | true |
CategoryTheory.sum.inlCompInverseAssociator_inv_app_down_down | Mathlib.CategoryTheory.Sums.Associator | [
"CategoryTheory.Functor",
"CategoryTheory.sum",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.sum.inlCompInverseAssociator",
"Sum",
"CategoryTheory.Sum.inr_",
"Category... | true |
OrderIso.pnatIsoNat_apply | Mathlib.Data.PNat.Basic | [
"instLinearOrderPNat",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"instLENat",
"RelIso",
"RelIso.instFunLike",
"Nat",
"PNat.natPred",
"Eq.refl",
"OrderIso.pnatIsoNat",
"Eq",
"DFunLike.coe",
"instDistribLatticeOfLine... | true |
Simps.copyFirst | Mathlib.Tactic.Simps.NotationClass | [
"Pure.pure",
"Inhabited.default",
"Array.push",
"Lean.Meta.State",
"Option.getD",
"Option.some",
"Array.map",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instOfNatNat",
"Applicative.toPure",
"Simps.findArgType",
"Array",
"Lean.instInhabitedExpr",
"Lean.Core.CoreM",
"StateRefT'",... | true |
CategoryTheory.Limits.CatCospanTransformMorphism.ctorIdx | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | [
"CategoryTheory.Functor",
"Nat",
"CategoryTheory.Limits.CatCospanTransformMorphism",
"CategoryTheory.Limits.CatCospanTransform",
"CategoryTheory.Category"
] | false |
CategoryTheory.Limits.preservesFiniteBiproductsOfPreservesBiproducts | Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"Finite",
"CategoryTheory.Limits.PreservesFiniteBiproducts",
"inferInstance",
"CategoryTheory.Limits.PreservesBiproducts.preserves",
"CategoryTheory.Limits.preservesBiproducts_shrink",
"CategoryTheory.Limits.PreservesBiproductsOfShape... | true |
LinearIndependent.map' | Mathlib.LinearAlgebra.LinearIndependent.Basic | [
"Eq.mpr",
"Submodule",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"LinearMap.ker",
"LinearMap.instFunLike",
"Preorder.toLE",
"Disjoint",
"Function.comp",
"AddCommGroup",
"id",
"Submodule.instPartialOrder",
"Bot.bot",
"LinearMap",
"Submodu... | true |
Lean.Meta.Grind.getFnRoots | Lean.Meta.Tactic.Grind.Beta | [
"Pure.pure",
"Option.isNone",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.ENode.self",
"Lean.Meta.Grind.Goal",
"StateRefT'.instAlternativeOfMonad",
"Array.push",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Sym.isSameExpr",
"Lean.Meta.Sym.Context",
"Option.getD",
"ReaderT.instMonad",
"Lea... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RatAddResult.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.clear_insertRat._proof_1_5 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RatAddResult | [
"Std.Tactic.BVDecide.LRAT.Internal.Assignment.hasAssignment",
"Lean.Omega.LinearCombo.coordinate_eval_6",
"False",
"Exists.choose_spec",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Std.Tactic.BVDecide.LRAT.Internal.Assignment.addAssignment",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.... | false |
ContRepresentation.restrict | Mathlib.RepresentationTheory.Continuous.Basic | [
"Monoid",
"ContinuousLinearMap.semiring",
"MonoidHom",
"Monoid.toMulOneClass",
"AddCommGroup.toAddCommMonoid",
"ContRepresentation",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"MonoidHom.comp",
"ContRepresentation._proof_1",
"MulZeroOneClass.toMulOneClass",
"ContinuousLinearMap",
"instMulZer... | true |
even_abs | Mathlib.Algebra.Order.Group.Unbundled.Abs | [
"AddGroup.toSubtractionMonoid",
"abs",
"LinearOrder",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribLattice.toLattice",
"abs_by_cases",
"AddGroup",
"Iff",
"AddGroup.toSubNegMonoid",
"Even",
"AddZero.toAdd",
"SubNegMonoid.toAddMonoid",
"instDistribLatticeOfLinea... | true |
Mathlib.Tactic.LibraryRewrite.getImportRewrites | Mathlib.Tactic.Widget.LibraryRewrite | [
"Mathlib.Tactic.LibraryRewrite.RewriteLemma",
"Lean.Expr",
"Lean.Meta.MetaM",
"Mathlib.Tactic.LibraryRewrite.checkAndSortRewriteLemmas",
"Mathlib.Tactic.LibraryRewrite.Rewrite",
"Array",
"Lean.Meta.instMonadMetaM",
"Mathlib.Tactic.LibraryRewrite.getImportCandidates",
"Lean.Name",
"Monad.toBind",
... | true |
Lean.Meta.Grind.Arith.Linear.NatStruct.addRightCancelInst? | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"Lean.Expr",
"Lean.Meta.Grind.Arith.Linear.NatStruct",
"Option"
] | true |
CategoryTheory.Sieve.functorPushforward_extend_eq | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"congrArg",
"Exists",
"CategoryTheory.Sieve.le_generate",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Functor.map",
"And.casesOn",
"funext",
"And",... | true |
Cardinal.toNat_injOn | Mathlib.SetTheory.Cardinal.ToNat | [
"StrictMonoOn.injOn",
"Nat.instMulZeroOneClass",
"Cardinal",
"CommSemiring.toSemiring",
"Cardinal.commSemiring",
"PartialOrder.toPreorder",
"Cardinal.toNat",
"MonoidWithZeroHom.funLike",
"Cardinal.toNat_strictMonoOn",
"Cardinal.aleph0",
"instMulZeroOneClassOfSemiring",
"Cardinal.partialOrder",... | true |
Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndHyp.noConfusionType | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndFlatten | [
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndHyp",
"Lean.FVarId",
"Lean.Meta.Hypothesis",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndHyp.casesOn",
"Eq"
] | false |
Matroid.comapOn_rankFinite | Mathlib.Combinatorics.Matroid.Map | [
"Eq.mpr",
"Matroid.comapOn.eq_1",
"Matroid.comapOn",
"congrArg",
"Matroid.restrict_rankFinite",
"inferInstance",
"id",
"Matroid.comap_rankFinite",
"Matroid.comap",
"Matroid.restrict",
"Matroid.RankFinite",
"Eq",
"Matroid",
"Set"
] | true |
Std.TreeMap.Raw.minEntryD | Std.Data.TreeMap.Raw.Basic | [
"Std.DTreeMap.Raw.Const.minEntryD",
"Ordering",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Prod"
] | true |
CategoryTheory.Limits.hasFiniteWidePullbacks_opposite_iff | Mathlib.CategoryTheory.Limits.Opposites | [
"Eq.mpr",
"Opposite",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.Limits.HasFiniteWidePullbacks",
"congrArg",
"CategoryTheory.Limits.HasLimitsOfShape",
"Finite",
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.Ha... | true |
Lean.Elab.Command.Structure.StructFieldViewDefault.optParam.elim | Lean.Elab.Structure | [
"PULift.up",
"Lean.Elab.Command.Structure.StructFieldViewDefault",
"Lean.Syntax",
"Lean.Elab.Command.Structure.StructFieldViewDefault.ctorElim",
"Nat",
"Lean.Elab.Command.Structure.StructFieldViewDefault.optParam",
"Eq.symm",
"Eq",
"Lean.Elab.Command.Structure.StructFieldViewDefault.ctorIdx"
] | false |
Nontrivial.to_nonempty | Mathlib.Logic.Nontrivial.Defs | [
"Nontrivial",
"Exists",
"Ne",
"Nonempty.intro",
"_private.Mathlib.Logic.Nontrivial.Defs.0.Nontrivial.to_nonempty.match_1",
"Nonempty",
"exists_pair_ne"
] | true |
Complex.cos_eq_zero_iff | Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Complex.exp_eq_exp_iff_exists_int",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOn... | true |
BddDistLat.dual._proof_2 | Mathlib.Order.Category.BddDistLat | [
"BoundedLatticeHom.dual",
"Equiv.instEquivLike",
"BddDistLat.isBoundedOrder",
"BddDistLat.instDistribLatticeCarrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"BddDistLat.of",
"Preorder.toLE",
"BddDistLat",
"OrderDual.instDistribLattice",
"SemilatticeI... | false |
CategoryTheory.StructuredArrow.ofCommaSndEquivalence._proof_2 | Mathlib.CategoryTheory.Comma.Over.Basic | [
"Eq.mpr",
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Comma.fst",
"CategoryTheory.StructuredArrow.ofCommaSndEquivalenceInverse",
"CategoryTheory.Comma.left",
"Categ... | false |
_private.Mathlib.NumberTheory.PellMatiyasevic.0.Pell.isPell_iff_mem_unitary.match_1_1 | Mathlib.NumberTheory.PellMatiyasevic | [
"Zsqrtd.casesOn",
"Int",
"Zsqrtd.mk",
"Zsqrtd"
] | false |
supClosed_range | Mathlib.Order.SupClosed | [
"Set.image_univ",
"SupClosed.image",
"congrArg",
"Set.univ",
"SemilatticeSup.toMax",
"Eq.mp",
"SupHomClass",
"SupClosed",
"Set.image",
"Set.range",
"SemilatticeSup",
"DFunLike.coe",
"FunLike",
"supClosed_univ",
"Set"
] | true |
CategoryTheory.Limits.Wedge.condition_assoc | Mathlib.CategoryTheory.Limits.Shapes.End | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingMulticospan.instSmallCategory",
"Eq.mp",
"id",
"CategoryTheory.Limits.mul... | true |
UInt64.neg_mul | Init.Data.UInt.Lemmas | [
"instMulUInt64",
"HMul.hMul",
"UInt64",
"BitVec.neg_mul",
"UInt64.toBitVec_inj",
"BitVec",
"instOfNatNat",
"Nat",
"Iff.mp",
"OfNat.ofNat",
"Eq",
"Neg.neg",
"instNegUInt64",
"UInt64.toBitVec",
"instHMul"
] | true |
EsakiaHom.id | Mathlib.Topology.Order.Hom.Esakia | [
"EsakiaHom.id._proof_1",
"EsakiaHom.mk",
"ContinuousOrderHom.id",
"TopologicalSpace",
"EsakiaHom",
"Preorder"
] | true |
Plausible.ArbitraryFueled.ctorIdx | Plausible.ArbitraryFueled | [
"Plausible.ArbitraryFueled",
"Nat"
] | false |
_private.Mathlib.Topology.NhdsWithin.0.mem_nhdsWithin_iff_eventuallyEq._simp_1_1 | Mathlib.Topology.NhdsWithin | [
"Filter.instMembership",
"nhdsWithin",
"Filter.Eventually",
"Membership.mem",
"nhds",
"mem_nhdsWithin_iff_eventually",
"TopologicalSpace",
"propext",
"Eq",
"Set.instMembership",
"Filter",
"Set"
] | false |
TwoP.swapEquiv_inverse_obj_X | Mathlib.CategoryTheory.Category.TwoP | [
"TwoP",
"TwoP.X",
"TwoP.largeCategory",
"TwoP.swapEquiv",
"Eq.refl",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Equivalence.inverse"
] | true |
Set.Accumulate | Mathlib.Data.Set.Accumulate | [
"LE",
"Set.accumulate",
"Set"
] | true |
Multiplicative.mem_toSubgroup | Mathlib.Algebra.Group.Subgroup.Lattice | [
"Multiplicative.group",
"Equiv.instEquivLike",
"Iff.rfl",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"Membership.mem",
"Equiv",
"OrderIso",
"Subgroup",
"AddSubgroup",
"Multiplicative",
"AddGroup",
"Iff",
"AddSubgroup.toSubgroup",
"instFunLikeOrderIso",
... | true |
limsup_add_le._auto_3 | Mathlib.Topology.Algebra.Order.LiminfLimsup | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.Elab.Tactic.forEachVar | Lean.Elab.Tactic.BuiltinTactic | [
"Pure.pure",
"Unit.unit",
"Lean.Elab.Tactic.getFVarId",
"instForInOfForIn'",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"Lean.Elab.Tactic.getMainGoal",
"Lean.Meta.State",
"instMonadLiftT",
"Array.instMembership",
"Lean.Elab.Tactic.Context",
"Lean.Syntax",
"Lean.MVarId",
"inferInstance... | true |
IsometryEquiv.subRight_toEquiv | Mathlib.Topology.MetricSpace.IsometricSMul | [
"IsIsometricVAdd",
"AddMonoid.toAddSemigroup",
"Equiv.subRight",
"IsometryEquiv.toEquiv",
"AddOpposite",
"Equiv",
"PseudoEMetricSpace",
"AddAction.toAddSemigroupAction",
"AddGroup",
"AddSemigroupAction.toVAdd",
"IsometryEquiv.subRight",
"AddGroup.toSubNegMonoid",
"AddOpposite.instAddMonoid",... | true |
Std.Internal.Parsec.String.digit | Std.Internal.Parsec.String | [
"Pure.pure",
"Std.Internal.Parsec.attempt",
"String",
"Std.Internal.Parsec",
"LE.le",
"Std.Internal.Parsec.any",
"Applicative.toPure",
"ToString.toString",
"String.Pos.Raw",
"And",
"instDecidableEqRaw",
"Char.instLE",
"Std.Internal.Parsec.instAlternative",
"String.Pos",
"Alternative.toAp... | true |
Bornology.IsVonNBounded.eq_1 | Mathlib.Analysis.LocallyConvex.Bounded | [
"Filter.instMembership",
"PseudoMetricSpace.toBornology",
"Bornology.IsVonNBounded",
"SMul",
"Membership.mem",
"nhds",
"TopologicalSpace",
"Absorbs",
"Zero.toOfNat0",
"Eq.refl",
"SeminormedRing.toPseudoMetricSpace",
"OfNat.ofNat",
"Eq",
"SeminormedRing",
"Filter",
"Zero",
"Set"
] | true |
PresheafOfModules.instModuleCarrierStalkCommRingCatCarrierAbPresheafOpensCarrier._proof_2 | Mathlib.Algebra.Category.ModuleCat.Stalk | [
"CategoryTheory.Functor.op",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"Opposite",
"CategoryTheory.isCofiltered_of_directed_ge_nonempty",
"TopologicalSpace.Opens.instPartialOrder",
"CommRingCat",
"SemilatticeInf.instIsCodirectedOrder",
"PartialOrder.toPreorder",
"CategoryTheory.Functor... | false |
_private.Batteries.Data.Stream.0.Std.Stream.drop.match_1.eq_1 | Batteries.Data.Stream | [
"Unit.unit",
"Option.some",
"Prod.mk",
"Option.none",
"Unit",
"Eq.refl",
"Prod",
"Std.Stream.drop.match_1",
"Eq",
"Option"
] | true |
MeasureTheory.NullMeasurableSet.preimage | Mathlib.MeasureTheory.Measure.QuasiMeasurePreserving | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"MeasurableSet",
"MeasureTheory.NullMeasurableSet",
"inferInstance",
"Filter.EventuallyEq",
"MeasureTheory.Measure.QuasiMeasurePreserving",
"_private.Mathlib.MeasureTheory.Measure.QuasiMeasurePreserving.0.MeasureTheory.NullMeasurableSet.preimage.match_1_1",... | true |
CategoryTheory.instBicategoryMonoidalSingleObj._proof_12 | Mathlib.CategoryTheory.Bicategory.SingleObj | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalSingleObj",
"inferInstance",
"CategoryTheory.MonoidalCategory.comp_whiskerRight",
"CategoryTheory.MonoidalCategoryStruct.whiskerRight",
"CategoryTheory.MonoidalCategoryStruc... | false |
TensorProduct.lift.equiv._proof_1 | Mathlib.LinearAlgebra.TensorProduct.Basic | [
"Function.LeftInverse",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LinearMap.instSMulCommClass",
"TensorProduct.addCommMonoid",
"RingHom",
"LinearMap.toAddHom",
"LinearMap.module",
"TensorProduct.uncurry",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",... | false |
_private.Mathlib.GroupTheory.HNNExtension.0.HNNExtension.ReducedWord.map_fst_eq_and_of_prod_eq._simp_1_1 | Mathlib.GroupTheory.HNNExtension | [
"instHSMul",
"instSMulOfMul",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"leftCoset_eq_iff",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"M... | false |
_private.Mathlib.Data.Matrix.Reflection.0.Matrix.transposeᵣ.match_1.eq_1 | Mathlib.Data.Matrix.Reflection | [
"Matrix",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"Matrix.transposeᵣ.match_1",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"Eq"
] | true |
CategoryTheory.Grp.mkIso | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Grp.mkIso._auto_1",
"CategoryTheory.Grp.instCategory",
"CategoryTheory.GrpObj.toMonObj",
"CategoryTheory.Grp.grp",
"CategoryTheory.IsMonHom",
"CategoryTheory.Iso",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory... | true |
Std.Internal.List.getValue?._sunfold | Std.Data.Internal.List.Associative | [
"cond",
"Option.some",
"Option.none",
"List",
"BEq.beq",
"Unit",
"Std.Internal.List.getValue?",
"Std.Internal.List.getValue?.match_1",
"BEq",
"Sigma",
"Option"
] | false |
CategoryTheory.BraidedCategory.braiding_tensor_right_hom_assoc | Mathlib.CategoryTheory.Monoidal.Braided.Basic | [
"CategoryTheory.BraidedCategory.braiding_tensor_right_hom",
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker... | true |
_private.Mathlib.NumberTheory.NumberField.Discriminant.Different.0.NumberField.absNorm_differentIdeal._simp_1_1 | Mathlib.NumberTheory.NumberField.Discriminant.Different | [
"IsDomain",
"FractionRing.field",
"IsDedekindDomain.toIsDomain",
"False",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"differentIdeal_ne_bot",
"CommRing.toNonUnitalCommRing",
"eq_false",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"Module.I... | false |
WithTop.top_sub_coe | Mathlib.Algebra.Order.Sub.WithTop | [
"HSub.hSub",
"Bot",
"WithTop.some",
"instHSub",
"WithTop.top",
"WithTop.instSub",
"Top.top",
"Eq",
"rfl",
"Sub",
"WithTop"
] | true |
Lean.Lsp.ShowDocumentClientCapabilities.mk.injEq | Lean.Data.Lsp.Capabilities | [
"Eq.propIntro",
"Lean.Lsp.ShowDocumentClientCapabilities",
"Bool",
"Eq.ndrec",
"Lean.Lsp.ShowDocumentClientCapabilities.mk.inj",
"Eq.refl",
"Lean.Lsp.ShowDocumentClientCapabilities.mk",
"Eq"
] | true |
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