name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
Set.infs_assoc | Mathlib.Data.Set.Sups | [
"Set.image2_assoc",
"HasInfs.infs",
"SemilatticeInf.toMin",
"SemilatticeInf",
"Set.hasInfs",
"inf_assoc",
"Eq",
"Min.min",
"Set"
] | true |
Filter.cocardinal_aleph0_eq_cofinite | Mathlib.Order.Filter.Cocardinal | [
"Filter.instMembership",
"Eq.mpr",
"Preorder.toLT",
"Cardinal",
"congrArg",
"Compl.compl",
"Iff.rfl",
"PartialOrder.toPreorder",
"setOf",
"Set.Finite",
"Cardinal.mk",
"Membership.mem",
"Filter.ext",
"Set.Elem",
"id",
"Subtype",
"Cardinal.aleph0",
"Set.instCompl",
"funext",
"Car... | true |
Sbtw.left_ne_right | Mathlib.Analysis.Convex.Between | [
"IsOrderedRing",
"AddCommGroup.toAddCommMonoid",
"Wbtw",
"AddCommGroup.toAddGroup",
"PartialOrder",
"AddCommGroup",
"Ne",
"Wbtw.left_ne_right_of_ne_left",
"And",
"And.right",
"And.left",
"Sbtw.wbtw",
"AddTorsor",
"Module",
"Ring.toSemiring",
"Ring",
"Sbtw"
] | true |
_private.Mathlib.RingTheory.Smooth.NoetherianDescent.0.Algebra.Smooth.DescentAux.instFaithfulSMulSubtypeMemSubalgebraSubalgebra._proof_1 | Mathlib.RingTheory.Smooth.NoetherianDescent | [
"Subalgebra.instSetLike",
"Nat.instMulZeroClass",
"CommRing",
"Algebra.Generators.Ring",
"CommSemiring.toSemiring",
"Finset",
"Algebra.Presentation.coeffs",
"_private.Mathlib.RingTheory.Smooth.NoetherianDescent.0.Algebra.Smooth.DescentAux.vars",
"MvPolynomial.coeffs",
"AddMonoidAlgebra.commSemirin... | false |
CategoryTheory.Under.mapCongr._proof_1 | Mathlib.CategoryTheory.Comma.Over.Basic | [
"Eq.mpr",
"CategoryTheory.instCategoryUnder",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"id",
"CategoryTheory.Under",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Under.map",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | false |
PresheafOfModules.instModuleCarrierStalkCommRingCatCarrierAbPresheafOpensCarrier._proof_1 | Mathlib.Algebra.Category.ModuleCat.Stalk | [
"PresheafOfModules.map",
"CategoryTheory.Functor.op",
"instHSMul",
"Opposite",
"CommRingCat.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"ModuleCat",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"CategoryTheory.Concret... | false |
_private.Mathlib.MeasureTheory.Measure.Hausdorff.0.Isometry.hausdorffMeasure_image._simp_1_2 | Mathlib.MeasureTheory.Measure.Hausdorff | [
"MeasureTheory.Measure",
"MeasureTheory.Measure.mkMetric",
"BorelSpace",
"MeasureTheory.OuterMeasure",
"EMetricSpace.toPseudoEMetricSpace",
"EMetricSpace",
"MeasurableSpace",
"PseudoEMetricSpace.toUniformSpace",
"MeasureTheory.OuterMeasure.instFunLikeSetENNReal",
"MeasureTheory.OuterMeasure.mkMetr... | false |
instLawfulMonadTacticM_batteries | Batteries.Lean.LawfulMonad | [
"LawfulMonad",
"Lean.Elab.Tactic.instMonadTacticM",
"_private.Batteries.Lean.LawfulMonad.0.instLawfulMonadTacticM_batteries._proof_1",
"Lean.Elab.Tactic.TacticM"
] | true |
TopologicalSpace.Opens.map_comp_obj' | Mathlib.Topology.Category.TopCat.Opens | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"TopCat.instCategory",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Preorder.smallCategory",
"TopCat.str",
"TopCat.carrier",
"TopologicalSpace.Opens.mk",
"CategoryTheory.CategoryStruct.com... | true |
CategoryTheory.Limits.CatCospanTransformMorphism.whiskerLeft_base | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.whiskerLeft",
"CategoryTheory.Limits.CatCospanTransformMorphism.whiskerLeft",
"CategoryTheory.Limits.CatCospanTransform.comp",
"... | true |
BitVec.extractLsb'_append_eq_of_le | Init.Data.BitVec.Lemmas | [
"BitVec.extractLsb'",
"eq_false",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.extractLsb'_append_eq_of_le._proof_1_1",
"congrArg",
"BitVec.instHAppendHAddNat",
"HSub.hSub",
"BitVec",
"instSubNat",
"BitVec.extractLsb'_append_eq_ite._proof_2",
"LE.le",
"instLENat",
"dite",
"instHAdd",
"instHS... | true |
CategoryTheory.CostructuredArrow.isSeparating_proj_preimage | Mathlib.CategoryTheory.Generator.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CostructuredArrow.isSeparating_inverseImage_proj",
"CategoryTheory.CostructuredArrow",
"CategoryTheory.instCategoryCostructuredArrow",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty.IsSeparating",
"CategoryTheory.ObjectProperty.invers... | true |
UInt16.toUSize_shiftLeft | Init.Data.UInt.Bitwise | [
"instModUInt16",
"congrArg",
"UInt16.toUSize_mod",
"HShiftLeft.hShiftLeft",
"instShiftLeftUInt16",
"USize.toUInt16",
"instModUSize",
"instHMod",
"instOfNatNat",
"USize.toUInt16_shiftLeft_mod",
"Bool.true",
"UInt16.toUSize",
"HMod.hMod",
"UInt16",
"UInt16.toUSize_ofNat",
"eq_true_of_dec... | true |
_private.Mathlib.MeasureTheory.OuterMeasure.AE.0.MeasureTheory.union_ae_eq_right._simp_1_2 | Mathlib.MeasureTheory.OuterMeasure.AE | [
"MeasureTheory.ae",
"Prop.le",
"instZeroENNReal",
"SDiff.sdiff",
"ENNReal",
"propext",
"Zero.toOfNat0",
"Filter.EventuallyLE",
"MeasureTheory.OuterMeasureClass",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"FunLike",
"MeasureTheory.ae_le_set",
"Set.instSDiff",
"Set"
] | false |
Function.Even | Mathlib.Algebra.Group.EvenFunction | [
"Neg",
"Eq",
"Neg.neg"
] | true |
Mathlib.Meta.NormNum.IsNNRat.to_isRat | Mathlib.Tactic.NormNum.Result | [
"Int.cast",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Int.cast_natCast",
"Mathlib.Meta.NormNum.IsRat.mk",
"HMul.hMul",
"Ring.toNonAssocRing",
"congrArg",
"_private.Mathlib.Tactic.NormNum.Result.0.Mathlib.Meta.NormNum.IsNNRat.to_isRat.match_1_1",
"AddGroupWithOne.toAddMonoidWithOne",
"Invertible.... | true |
Lean.Lsp.VersionedTextDocumentIdentifier.casesOn | Lean.Data.Lsp.Basic | [
"Lean.Lsp.VersionedTextDocumentIdentifier.mk",
"Lean.Lsp.VersionedTextDocumentIdentifier.rec",
"Lean.Lsp.DocumentUri",
"Lean.Lsp.VersionedTextDocumentIdentifier",
"Nat",
"Option"
] | false |
Nat.stirlingSecond._sunfold | Mathlib.Combinatorics.Enumerative.Stirling | [
"HMul.hMul",
"Nat.stirlingFirst.match_1",
"instMulNat",
"instOfNatNat",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.stirlingSecond",
"instHMul"
] | false |
smoothPresheafCommGroup._proof_2 | Mathlib.Geometry.Manifold.Sheaf.Smooth | [
"Opposite",
"NormedSpace",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"instTopENat",
"TopologicalSpace.Opens.instPartialOrder",
"PartialOrder.toPreorder",
"CommGrpCat.instCategory",
"Quiver.Hom.unop",
"TopologicalSpace.Opens",
"CategoryTheory.CategoryStruct.id",
"DivInvMonoid.toMo... | false |
AffineIsometryEquiv.toAffineIsometry | Mathlib.Analysis.Normed.Affine.Isometry | [
"NormedCommRing.toNormedRing",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"NormedSpace",
"AffineIsometryEquiv.toAffineEquiv",
"NormedSpace.toModule",
"AffineIsometryEquiv",
"AffineIsometry.mk",
"NormedField",
"PseudoMetricSpace",
"NormedAddTorsor.toAddTorsor",
"SeminormedAddCommGroup.toAdd... | true |
Lean.Elab.Tactic.withCaseRef | Lean.Elab.Tactic.Basic | [
"Lean.mkNullNode",
"Lean.Syntax",
"List.toArray",
"List.cons",
"Lean.MonadRef",
"Monad",
"Lean.withRef",
"List.nil"
] | true |
CStarMatrix.mapₗ | Mathlib.Analysis.CStarAlgebra.CStarMatrix | [
"CStarMatrix.instModule",
"LinearMap.instFunLike",
"RingHom",
"LinearMap",
"AddCommMonoid",
"CStarMatrix.mapₗ._proof_1",
"CStarMatrix",
"LinearMap.mk",
"Semiring",
"AddCommSemigroup.toAddCommMagma",
"AddHom.mk",
"CStarMatrix.instAddCommMonoid",
"Module",
"AddCommMonoid.toAddCommSemigroup",... | true |
HasLineDerivWithinAt.mono | Mathlib.Analysis.Calculus.LineDeriv.Basic | [
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedSpace",
"HasLineDerivWithinAt",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"AddZer... | true |
_private.Lean.Server.ProtocolOverview.0.Lean.Server.Overview.NotificationOverview.mk.sizeOf_spec | Lean.Server.ProtocolOverview | [
"_private.Lean.Server.ProtocolOverview.0.Lean.Server.Overview.ProtocolExtensionKind._sizeOf_inst",
"_private.Lean.Server.ProtocolOverview.0.Lean.Server.Overview.ProtocolExtensionKind",
"String",
"instSizeOfDefault",
"Lean.JsonRpc.MessageDirection._sizeOf_inst",
"_private.Lean.Server.ProtocolOverview.0.Lea... | true |
LinearMap.equivOfDetNeZero._proof_3 | Mathlib.LinearAlgebra.Determinant | [
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"Field.toSemifield",
"smulCommClass_self",
"Semifield.toDivisionSemiring",
"CommMonoid.toMonoid",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"DivisionSemiring.toSemiring",
"Module.toDistribMulAction",
"Semigroup... | false |
Lean.Meta.Simp.Arith.Nat.ToLinear.State.mk.injEq | Lean.Meta.Tactic.Simp.Arith.Nat.Basic | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Expr",
"Array",
"Lean.Meta.Simp.Arith.Nat.ToLinear.State.mk.inj",
"And",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Lean.Meta.Simp.Arith.Nat.ToLinear.State.mk",
"Lean.Meta.Simp.Arith.Nat.ToLinear.State",
"Lean.Meta.KExprMap"
] | true |
Equiv.subtypeSubtypeEquivSubtype_apply_coe | Mathlib.Logic.Equiv.Basic | [
"Equiv.instEquivLike",
"Equiv",
"Subtype",
"Equiv.subtypeSubtypeEquivSubtype",
"Eq.refl",
"Subtype.val",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Subtype.val_prop | Mathlib.Data.Subtype | [
"Membership.mem",
"Subtype",
"Subtype.prop",
"Subtype.val",
"Set.instMembership",
"Set"
] | true |
CategoryTheory.ObjectProperty.productToFamily | Mathlib.CategoryTheory.Generator.Basic | [
"CategoryTheory.Comma.right",
"CategoryTheory.ObjectProperty.ι",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.discreteCategory",
"PUnit",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.fromPUnit",
"CategoryTheory.ObjectProperty.FullSubcategory",
"Category... | true |
SubMulAction.ofStabilizer.conjMap | Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer | [
"SubMulAction.instSetLike",
"MulAction.stabilizerEquivStabilizer",
"instHSMul",
"MulEquiv.instEquivLike",
"SubMulAction.ofStabilizer.conjMap._proof_1",
"Subgroup.mul",
"Group",
"Membership.mem",
"Subgroup.instMulAction",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"MulActionHom.mk",
"S... | true |
_private.Mathlib.RingTheory.Ideal.Lattice.0.Ideal.eq_top_of_isUnit_mem.match_1_1 | Mathlib.RingTheory.Ideal.Lattice | [
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"Exists",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Exists.casesOn",
"Exists.intro",
"Semiring",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"MonoidWithZero.toMonoid",
"Semiring.toMonoidWithZero",
"instHMul"
] | false |
CategoryTheory.Bicategory.rightAdjointSquareConjugate.vcomp | Mathlib.CategoryTheory.Bicategory.Adjunction.Mate | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Bicategory.whiskerLeft",
"CategoryTheory.Bicategory.homCategory"
] | true |
_private.Mathlib.Data.Set.Subsingleton.0.Set.nontrivial_coe_sort._simp_1_1 | Mathlib.Data.Set.Subsingleton | [
"Nontrivial",
"Set.univ",
"propext",
"Set.Nontrivial",
"Eq.symm",
"Eq",
"Set.nontrivial_univ_iff"
] | false |
Filter.filter_eq_iff | Mathlib.Order.Filter.Basic | [
"Filter.sets",
"congr_arg",
"Iff",
"Iff.intro",
"Filter.filter_eq",
"Eq",
"Filter",
"Set"
] | true |
Hyperreal.archimedeanClassMk_nonneg_of_tendsto | Mathlib.Analysis.Real.Hyperreal | [
"Hyperreal.instField",
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"Real.instArchimedean",
"instNoMaxOrderOfNontrivial",
"congrArg",
"ArchimedeanClass.instLinearOrder",
"Filter.Germ.Tendsto",
"Hyperreal.tendsto_iff_forall",
"PartialOrder.toPreorder",
"PseudoMetric... | true |
_private.Mathlib.Topology.Compactification.OnePoint.Basic.0.OnePoint.isOpen_iff_of_mem._simp_1_1 | Mathlib.Topology.Compactification.OnePoint.Basic | [
"Compl.compl",
"Set.instCompl",
"IsClosed",
"TopologicalSpace",
"propext",
"IsOpen",
"Eq",
"isClosed_compl_iff",
"Set"
] | false |
ProbabilityTheory.Kernel.eq_rnDeriv_measure | Mathlib.Probability.Kernel.RadonNikodym | [
"MeasureTheory.ae",
"Eq.mpr",
"MeasureTheory.Measure.withDensity",
"ProbabilityTheory.IsFiniteKernel",
"ProbabilityTheory.Kernel.coe_add",
"MeasureTheory.Measure",
"Measurable.aemeasurable",
"Measurable.comp",
"congrArg",
"MeasureTheory.IsFiniteMeasure.toSigmaFinite",
"Measurable",
"MeasureThe... | true |
Multiset.cons_lt_cons_iff._simp_1 | Mathlib.Data.Multiset.ZeroCons | [
"Preorder.toLT",
"PartialOrder.toPreorder",
"Multiset",
"Multiset.cons",
"LT.lt",
"Multiset.cons_lt_cons_iff",
"propext",
"Eq",
"Multiset.instPartialOrder"
] | false |
SemilatInfCat.hasForgetToPartOrd._proof_2 | Mathlib.Order.Category.Semilat | [
"SemilatInfCat.isOrderTop",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartOrd.instCategory",
"InfHomClass.toOrderHomClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatInfCat.isSemilatticeInf",
"InfHom.instInfHomClass",
"SemilatticeInf.toPartialOrder",
"id",
"InfHom",
... | false |
CommMonCat.coyonedaType._proof_4 | Mathlib.Algebra.Category.MonCat.Yoneda | [
"Pi.monoidHom",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.category",
"Quiver.Hom.unop",
"CategoryTheory.CategoryStruct.id",
"id",
"CommMonCat.str",
"MonoidHom.comp... | false |
Subgroup._sizeOf_inst | Mathlib.Algebra.Group.Subgroup.Defs | [
"Group",
"Subgroup",
"Subgroup._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
_private.Mathlib.Analysis.Calculus.FDeriv.Measurable.0.FDerivMeasurableAux.isOpen_A_with_param._simp_1_3 | Mathlib.Analysis.Calculus.FDeriv.Measurable | [
"Real",
"Real.instLT",
"Membership.mem",
"Metric.ball",
"Metric.mem_ball",
"PseudoMetricSpace",
"LT.lt",
"propext",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.Algebra.Polynomial.RuleOfSigns.0.Polynomial.succ_signVariations_le_X_sub_C_mul._proof_1_8 | Mathlib.Algebra.Polynomial.RuleOfSigns | [
"Polynomial.C",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"of_decide_eq_true",
"eq_false",
"Lean.Grind.CommRing.Expr.var",
"Polynomial.signVariations_le_eraseLead_succ",
"Polynomial.signVariations",
"Lean.Grind.Order.le_of_eq... | false |
Ordinal.cof_le_card | Mathlib.SetTheory.Cardinal.Cofinality | [
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Cardinal.mk",
"SemilatticeInf.toPartialOrder",
"Eq.mp",
"DistribLattice.toLattice",
"linearOrder_toType",
"LE.le",
"Cardinal.instLE",
"Ordinal.card",
"Ordinal.cof_toType",
"congr",
"Cardinal.mk_toType",
"Ordinal.cof",
"Order.cof",
"... | true |
BitVec.clzAuxRec_eq_clzAuxRec_of_le | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"False",
"Nat.recAux",
"congrArg",
"BitVec.getLsbD_of_ge",
"HSub.hSub",
"Bool.false_eq_true",
"BitVec",
"BitVec.getLsbD",
"id",
"instDecidableEqBool",
"instSubNat",
"instOfNatNat",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.clzAuxRec_eq_clzAuxRec_of_le._proof_1_2",
"LE.le",
"... | true |
ModuleCat.rec | Mathlib.Algebra.Category.ModuleCat.Basic | [
"_private.Mathlib.Algebra.Category.ModuleCat.Basic.0.ModuleCat.mk",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"Module",
"Ring.toSemiring",
"Ring"
] | false |
Filter.tendsto_atTop_pure | Mathlib.Order.Filter.AtTopBot.Tendsto | [
"Pure.pure",
"PartialOrder.toPreorder",
"Filter.tendsto_pure_pure",
"Preorder.toLE",
"Eq.rec",
"PartialOrder",
"Filter.OrderTop.atTop_eq",
"OrderTop",
"Filter.atTop",
"Filter.instPure",
"OrderTop.toTop",
"Filter.Tendsto",
"Top.top",
"Eq.symm",
"Eq",
"Filter"
] | true |
Lean.Meta.Match.Example.var | Lean.Meta.Match.Basic | [
"Lean.Meta.Match.Example",
"Lean.FVarId",
"Lean.Meta.Match.Example.var"
] | true |
GradedTensorProduct.lift._proof_3 | Mathlib.LinearAlgebra.TensorProduct.Graded.Internal | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"Algebra.to_smulCommClass",
"instDistribSMul",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddZero.toZero",
"CommRing.toCommS... | false |
_private.Std.Time.Zoned.Offset.0.Std.Time.TimeZone.instDecidableEqOffset.decEq._proof_2 | Std.Time.Zoned.Offset | [
"False",
"Std.Time.TimeZone.Offset",
"Std.Time.Second.Offset",
"Std.Time.TimeZone.Offset.ofSeconds",
"Eq",
"Not",
"Std.Time.TimeZone.Offset.ofSeconds.noConfusion"
] | false |
Lean.Meta.DSimp.Config.decide | Init.MetaTypes | [
"Lean.Meta.DSimp.Config",
"Bool"
] | true |
hasProd_unique._simp_2 | Mathlib.Topology.Algebra.InfiniteSum.Basic | [
"Inhabited.default",
"Unique",
"SummationFilter",
"HasProd",
"TopologicalSpace",
"True",
"eq_true",
"SummationFilter.LeAtTop",
"Unique.instInhabited",
"optParam",
"hasProd_unique",
"Eq",
"CommMonoid",
"SummationFilter.unconditional"
] | false |
Bundle.Trivialization.prod.eq_1 | Mathlib.Topology.VectorBundle.Constructions | [
"Set.instSProd",
"Bundle.Trivialization.prod._proof_6",
"Bundle.Trivialization.Prod.continuous_inv_fun",
"SProd.sprod",
"Set.univ",
"instTopologicalSpaceProd",
"Bundle.Trivialization.prod._proof_5",
"OpenPartialHomeomorph.mk",
"Set.instInter",
"Inter.inter",
"TopologicalSpace",
"Bundle.TotalSp... | true |
CategoryTheory.Comma.mapLeftComp_hom_app_right | Mathlib.CategoryTheory.Comma.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Comma",
"CategoryTheory.Comma.mapLeftComp",
"CategoryTheory.commaCat... | true |
HNNExtension.NormalWord.instMulAction | Mathlib.GroupTheory.HNNExtension | [
"HNNExtension.NormalWord",
"HNNExtension.NormalWord.instMulAction._proof_4",
"HMul.hMul",
"HNNExtension.NormalWord.ReducedWord.toList",
"Monoid.toMulOneClass",
"HNNExtension.NormalWord.mk",
"HNNExtension.NormalWord.instMulAction._proof_3",
"Group",
"HNNExtension.NormalWord.mem_set",
"MulOne.toMul"... | true |
CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair_hom_app | Mathlib.CategoryTheory.Limits.Shapes.Reflexive | [
"CategoryTheory.Limits.WalkingReflexivePair.Hom.reflexion",
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingReflexivePair.zero",
"CategoryTheory.Limits.reflexivePair.diagramIsoReflexivePair",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTh... | true |
Topology.IsEmbedding.prodMap | Mathlib.Topology.Constructions.SumProd | [
"Function.Injective.prodMap",
"instTopologicalSpaceProd",
"Prod.map",
"Topology.IsInducing",
"Topology.IsEmbedding.isInducing",
"TopologicalSpace",
"Topology.IsInducing.prodMap",
"Topology.IsEmbedding.injective",
"Topology.IsEmbedding",
"Prod",
"Topology.IsEmbedding.mk"
] | true |
Std.DTreeMap.Internal.Impl.maxEntry?.match_1 | Std.Data.DTreeMap.Internal.Queries | [
"Unit.unit",
"Std.DTreeMap.Internal.Impl.casesOn",
"namedPattern",
"Std.DTreeMap.Internal.Impl.inner",
"Unit",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | false |
HasFDerivWithinAt.const_sub | Mathlib.Analysis.Calculus.FDeriv.Add | [
"Pure.pure",
"NormedCommRing.toNormedRing",
"NormedRing.toRing",
"HasFDerivAtFilter.const_sub",
"NormedSpace",
"SProd.sprod",
"nhdsWithin",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"HasFDerivWithinAt",
"NormedField.toField",
"NormedAddGroup.toAddGroup",
"Fie... | true |
Std.DHashMap.Raw.Equiv.size_eq | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"LawfulHashable",
"Std.DHashMap.Raw.Equiv",
"Subtype.mk",
"EquivBEq",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Std.DHashMap.Internal.AssocList",
"Hashable",
"Std.DHashMap.Raw.size",
"in... | true |
CoxeterSystem.mk.noConfusion | Mathlib.GroupTheory.Coxeter.Basic | [
"Monoid.toMulOneClass",
"HEq.refl",
"CoxeterSystem.mk",
"Group",
"CoxeterMatrix.Group",
"id",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"CoxeterMatrix",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"heq_of_eq",
"CoxeterSystem.noConfusion",
"CoxeterMatrix.instGroupGroup",
"MulEquiv",
... | false |
CategoryTheory.Classifier.mono_truth._autoParam | Mathlib.CategoryTheory.Topos.Classifier | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Submonoid.isScalarTower | Mathlib.Algebra.Group.Submonoid.MulAction | [
"IsScalarTower",
"SMul",
"Membership.mem",
"inferInstance",
"Subtype",
"Submonoid.smul",
"Submonoid.instIsScalarTowerSubtypeMem",
"Submonoid.instSetLike",
"MulOneClass",
"SetLike.instMembership",
"Submonoid"
] | true |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec.0.BitVec.instDecidableEqLiteral.decEq._proof_3 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec | [
"False",
"BitVec.Literal.mk.noConfusion",
"BitVec",
"BitVec.Literal.mk",
"Nat",
"HEq",
"Eq",
"Not",
"BitVec.Literal"
] | false |
Lean.Lsp.DeleteFile.Options.ignoreIfNotExists | Lean.Data.Lsp.Basic | [
"Lean.Lsp.DeleteFile.Options",
"Bool"
] | true |
LieAlgebra.IsEngelian._proof_2 | Mathlib.Algebra.Lie.Engel | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"AddCommGroup",
"IsScalarTower.left",
"CommRing.toCommSemiring",
"Monoid.toSemigroup",
"Monoid.toMulAction",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMonoid.toAddMonoid",
"Module",
... | false |
Rat.mk'_pow._proof_2 | Mathlib.Data.Rat.Defs | [
"instPowNat",
"False",
"eq_false",
"congrArg",
"false_and",
"Ne",
"instOfNatNat",
"instNatPowNat",
"And",
"HPow.hPow",
"Nat",
"True",
"of_eq_true",
"congrFun'",
"instHPow",
"OfNat.ofNat",
"not_false_eq_true",
"Eq",
"Not",
"Eq.trans",
"Nat.pow_eq_zero._simp_1"
] | false |
_private.Mathlib.Algebra.Lie.OfAssociative.0.termφ | Mathlib.Algebra.Lie.OfAssociative | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
Mathlib.Tactic.Conv.Path.rec | Mathlib.Tactic.Widget.Conv | [
"Mathlib.Tactic.Conv.Path.type",
"Mathlib.Tactic.Conv.Path.arg",
"Nat",
"Mathlib.Tactic.Conv.Path.fun",
"Mathlib.Tactic.Conv.Path.body",
"Bool",
"Lean.Name",
"Mathlib.Tactic.Conv.Path"
] | false |
List.pmap.eq_1 | Init.Data.List.Attach | [
"Membership.mem",
"List.pmap",
"List",
"List.instMembership",
"Eq.refl",
"Eq",
"List.nil"
] | true |
Int64.instLawfulOrderOrd | Init.Data.Ord.SInt | [
"Std.le_total",
"Std.LawfulOrderOrd",
"isLE_compareOfLessAndEq",
"Std.LawfulOrderOrd.mk",
"instLTInt64",
"Int64.decLt",
"Int64.instOrd",
"Int64",
"isGE_compareOfLessAndEq",
"Std.IsLinearOrder.toIsPartialOrder",
"instLawfulOrderLTInt64",
"Int64.decLe",
"Std.not_le",
"Std.instAntisymmLeOfIsP... | true |
EuclideanGeometry.Sphere.orthRadius_eq_orthRadius_iff._simp_1 | Mathlib.Geometry.Euclidean.Sphere.OrthRadius | [
"InnerProductSpace.toNormedSpace",
"Real",
"Real.instRCLike",
"NormedSpace.toModule",
"EuclideanGeometry.Sphere",
"EuclideanGeometry.Sphere.orthRadius_eq_orthRadius_iff",
"Real.instRing",
"NormedAddTorsor.toAddTorsor",
"MetricSpace",
"propext",
"EuclideanGeometry.Sphere.orthRadius",
"NormedAdd... | false |
Lean.Meta.SizeOfSpecNested.Context.recOn | Lean.Meta.SizeOf | [
"Lean.Meta.SizeOfSpecNested.Context.mk",
"Lean.NameMap",
"Lean.Expr",
"Lean.Meta.SizeOfSpecNested.Context",
"Array",
"Lean.Meta.SizeOfSpecNested.Context.rec",
"Lean.Name",
"Lean.InductiveVal"
] | false |
Pi.algebraMap._proof_2 | Mathlib.Algebra.Algebra.Pi | [
"Pi.Function.module",
"RingHom.instRingHomClass",
"instHSMul",
"Semiring.toModule",
"Pi.addCommMonoid",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Algebra",
"RingHom",
"Function.comp",
"algebraMap",
"AddZeroClass.toA... | false |
Lean.Grind.CommRing.Poly.denote_insert | Init.Grind.Ring.CommSolver | [
"cond",
"Ordering.gt",
"Lean.Grind.AddCommMonoid.add_left_comm",
"Int.cast",
"Eq.mpr",
"Lean.Grind.Ring.intCast_zero",
"Decidable.casesOn",
"instHSMul",
"Lean.Grind.Ring.zsmul_eq_intCast_mul",
"Lean.Grind.CommRing.Poly",
"HMul.hMul",
"Lean.Grind.CommRing.Poly.add",
"congrArg",
"Lean.Grind.... | true |
DyckStep.D | Mathlib.Combinatorics.Enumerative.DyckWord | [
"DyckStep.D",
"DyckStep"
] | true |
ProbabilityTheory.gaussianPDF_def | Mathlib.Probability.Distributions.Gaussian.Real | [
"Real",
"ENNReal.ofReal",
"NNReal",
"ENNReal",
"ProbabilityTheory.gaussianPDFReal",
"Eq",
"ProbabilityTheory.gaussianPDF",
"rfl"
] | true |
ContinuousOn.strictAntiOn_of_injOn_Icc | Mathlib.Topology.Order.IntermediateValue | [
"OrderTopology",
"Preorder.toLT",
"LinearOrder",
"StrictAntiOn",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"ContinuousOn.strictMonoOn_of_injOn_Icc",
"Topol... | true |
Ideal.idealProdEquiv.match_1 | Mathlib.RingTheory.Ideal.Prod | [
"Prod.mk",
"Ideal",
"Semiring",
"Prod",
"Prod.casesOn"
] | false |
Mathlib.Tactic.Abel.abelNFConv | Mathlib.Tactic.Abel | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.Parser.Tactic.optConfig",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | true |
CategoryTheory.CatCenter.smul_iso_hom_eq | Mathlib.CategoryTheory.Center.Basic | [
"Units.val",
"CategoryTheory.Functor",
"CategoryTheory.CatCenter",
"instHSMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"Units",
"CategoryTheory.Iso",
"CategoryTheory.End.monoid",
"CategoryTheory.CatCenter.instSMul... | true |
_private.Lean.CoreM.0.Lean.Core.wrapAsync.match_3 | Lean.CoreM | [
"Prod.mk",
"Prod",
"Prod.casesOn",
"Lean.NameGenerator"
] | false |
_private.Init.Data.BitVec.Lemmas.0.BitVec.twoPow_le_toInt_sub_toInt_iff._proof_1_6 | Init.Data.BitVec.Lemmas | [
"Lean.Omega.Decidable.and_or_not_and_not_of_iff",
"instPowNat",
"instDecidableNot",
"Int.instDiv",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Lean.Omega.Int.le_of_not_lt",
"instHDiv",
"HMul.hMul",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega... | false |
Int.Linear.Expr.var.injEq | Init.Data.Int.Linear | [
"Eq.propIntro",
"Int.Linear.Var",
"Int.Linear.Expr.var.inj",
"Int.Linear.Expr",
"Eq.ndrec",
"Int.Linear.Expr.var",
"Eq.refl",
"Eq"
] | true |
CategoryTheory.Abelian.comp_epiDesc | Mathlib.CategoryTheory.Abelian.Basic | [
"CategoryTheory.Limits.IsColimit.fac",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Abelian.epiDesc",
"CategoryTheory.Limits.WalkingParallelPair.one",
"CategoryTheory.NonPreadditiveAbelian.has_kernels",
"Ca... | true |
Algebra.intTraceAux | Mathlib.RingTheory.IntegralClosure.IntegralRestrict | [
"Subalgebra.instSetLike",
"AlgHom.toLinearMap",
"Submodule",
"IsIntegralClosure",
"CommRing",
"LinearMap.restrictScalars",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"galRestrict'._proof_2",
"CommRing.toNonUnitalCommRing",
"IsIntegralClosure.equiv",
"CommSemiring.toS... | true |
LinearEquiv.isUnit_det' | Mathlib.LinearAlgebra.Determinant | [
"LinearEquiv.symm",
"CommRing",
"MonoidHom.instFunLike",
"MonoidHom",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"IsUnit.of_mul_eq_one",
"Module.End.instSemiring",
"IsUnit",
"AddCommGroup",
"NonAssocSemiring.toMulZeroOneClass",
"LinearMap.det",
"LinearMap",
"MulZeroOneClass... | true |
BoxIntegral.Prepartition.filter | Mathlib.Analysis.BoxIntegral.Partition.Basic | [
"BoxIntegral.Prepartition",
"Classical.propDecidable",
"BoxIntegral.Prepartition.boxes",
"BoxIntegral.Prepartition.mk",
"Finset.filter",
"BoxIntegral.Box",
"BoxIntegral.Prepartition.filter._proof_1",
"BoxIntegral.Prepartition.filter._proof_2"
] | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.twoPow_le_toInt_sub_toInt_iff._proof_1_3 | Init.Data.BitVec.Lemmas | [
"instPowNat",
"instDecidableNot",
"Int.instDiv",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"instHDiv",
"HMul.hMul",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int... | false |
bddAbove_iff_exists_ge | Mathlib.Order.Bounds.Basic | [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"id",
"LE.le",
"BddAbove",
"And",
"Iff",
"Monotone.ball",
"monotone_le",
"propext",
"SemilatticeSup.toPartialOrder",
"exists_ge_and_iff_exists",
"bddAbove_def",
"Eq",
"Semil... | true |
PowerSeries.derivativeFun | Mathlib.RingTheory.PowerSeries.Derivative | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"Distrib.toAdd",
"AddMonoidWithOne.toNatCast",
"PowerSeries.coeff",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"MvPowerSeries.instModule",
"Nat.cast"... | true |
Std.LinearOrderPackage.ctorIdx | Init.Data.Order.PackageFactories | [
"Std.LinearOrderPackage",
"Nat"
] | false |
CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom_assoc | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"Opposite",
"CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Limits.pullback.snd",
"Quiver.Hom.unop",
"Eq.mp",
"id",
... | true |
EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius | Mathlib.Geometry.Euclidean.Angle.Sphere | [
"EuclideanGeometry.oangle",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"InnerProductSpace.toNormedSpace",
"Real.partialOrder",
"Real",
"instHDiv",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"CharZero.NeZero.two",
"Module.Oriented",
"MulZeroClass.toMul",
"Real.instZero",
"Real.instRCLike... | true |
CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverse._proof_2 | Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory | [
"CategoryTheory.Functor",
"CategoryTheory.Mon.instIsMonHomHom",
"CategoryTheory.Mon.Hom",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.Functor.category",
"Categ... | false |
FreeAddMagma | Mathlib.Algebra.Free | [
"FreeAddMagma.of",
"FreeAddMagma.add"
] | true |
CategoryTheory.PreOneHypercover.sieve₁_inter | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"CategoryTheory.Presieve.instHasPullbacksOfArrowsOfHasPullback",
"CategoryTheory.PreZeroHypercover.bind",
"CategoryTheory.Limits.hasPullbackVertPaste",
"CategoryTheory.PreOneHypercover.inter._proof_3",
"CategoryTheory.Limits.limit.π",
"CategoryTheory.PreOneHypercover.inter._proof_7",
"Eq.mpr",
"Catego... | true |
Module.Basis.mk._proof_1 | Mathlib.LinearAlgebra.Basis.Basic | [
"RingHomCompTriple",
"Semiring",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
_private.Lean.Meta.Tactic.Grind.Ctor.0.Lean.Meta.Grind.propagateCtorHetero._sparseCasesOn_3 | Lean.Meta.Tactic.Grind.Ctor | [
"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 |
iInf_ite | Mathlib.Order.CompleteLattice.Basic | [
"iInf",
"CompleteLattice.toLattice",
"SemilatticeInf.toMin",
"CompleteLattice.toCompleteSemilatticeInf",
"iInf_dite",
"DecidablePred",
"CompleteSemilatticeInf.toInfSet",
"CompleteLattice",
"Eq",
"Not",
"Min.min",
"Lattice.toSemilatticeInf",
"ite"
] | true |
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