name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.CategoryTheory.Monoidal.Free.Coherence.0.CategoryTheory.FreeMonoidalCategory.inclusionObj.match_1.eq_1 | Mathlib.CategoryTheory.Monoidal.Free.Coherence | [
"CategoryTheory.FreeMonoidalCategory.inclusionObj.match_1",
"Unit.unit",
"Unit",
"CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.unit",
"CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject",
"Eq.refl",
"Eq",
"CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.tensor"
] | true |
CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.π_comp_isoHomology_hom | Mathlib.Algebra.Homology.ShortComplex.Abelian | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.opcycles",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasImages.has_image",
"CategoryTheory.ShortComplex.homologyπ",
"CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImage",
"CategoryTheory.Iso.inv_hom_i... | true |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.getD_toArray_ric._simp_1_1 | Init.Data.Range.Polymorphic.NatLemmas | [
"LE.le",
"instLENat",
"Nat.lt_succ_iff",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Nat.succ",
"Eq"
] | false |
Std.DTreeMap.Internal.Impl.Const.maxEntry?.match_1.congr_eq_3 | Std.Data.DTreeMap.Internal.Model | [
"Unit.unit",
"Std.DTreeMap.Internal.Impl.casesOn",
"Std.DTreeMap.Internal.Impl.Const.maxEntry?.match_1",
"Std.DTreeMap.Internal.Impl.inner",
"id",
"heq_of_eq",
"Unit",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | true |
MonoidHom.toFun_eq_coe | Mathlib.Algebra.Group.Hom.Defs | [
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom",
"OneHom.toFun",
"MonoidHom.toOneHom",
"MulOne",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
StarMulEquiv.coe_ofBijective | Mathlib.Algebra.Star.MonoidHom | [
"Monoid",
"StarMulEquiv",
"Monoid.toMulOneClass",
"StarMulEquiv.ofBijective",
"StarMulEquiv.instEquivLike",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Star",
"StarMonoidHom",
"Function.Bijective",
"StarMonoidHom.instFunLike",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.NoInfo | Lean.Elab.DocString.Builtin | [
"_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.NoInfo.mk"
] | true |
Frm.ofHom | Mathlib.Order.Category.Frm | [
"FrameHom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Frm.str",
"Order.Frame.toCompleteLattice",
"CategoryTheory.ConcreteCategory.ofHom",
"Frm.instConcreteCategoryFrameHomCarrier",
"CategoryTheory.Category.toCategoryStruct",
"Frm.carrier",
"FrameHom.instFunLike",
"Frm",
"Order.F... | true |
_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.List.IsZeckendorfRep.sum_fib_lt._simp_1_8 | Mathlib.Data.Nat.Fib.Zeckendorf | [
"List.Pairwise",
"List.IsChain",
"Trans",
"List",
"propext",
"List.isChain_iff_pairwise",
"Eq.symm",
"Eq"
] | false |
Aesop.IndexMatchResult.mk.injEq | Aesop.Index.Basic | [
"Aesop.IndexMatchResult.mk.inj",
"Eq.propIntro",
"Lean.injEq_helper",
"Aesop.IndexMatchResult",
"Aesop.Substitution",
"Aesop.IndexMatchResult.mk",
"Array",
"And",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Aesop.IndexMatchLocation",
"Option"
] | true |
_private.Mathlib.Algebra.Group.Submonoid.Units.0.Subgroup.mem_ofUnits_iff_exists_isUnit.match_1_1 | Mathlib.Algebra.Group.Submonoid.Units | [
"Monoid",
"IsUnit",
"Membership.mem",
"Exists",
"Units",
"Subgroup",
"Units.instGroup",
"Exists.casesOn",
"Exists.intro",
"IsUnit.unit",
"SetLike.instMembership",
"Subgroup.instSetLike"
] | false |
Lean.Doc.DocCommandExpander | Lean.Elab.DocString | [
"Lean.TSyntax",
"Lean.Doc.Block",
"List.cons",
"Array",
"Lean.Doc.DocM",
"Lean.ElabBlock",
"StateT",
"Lean.SyntaxNodeKind",
"Lean.ElabInline",
"Lean.Name.mkStr1",
"List.nil"
] | true |
ContinuousAffineMap.neg_contLinear | Mathlib.Topology.Algebra.ContinuousAffineMap | [
"ContinuousAffineMap.contLinear",
"AddCommGroup.toAddCommMonoid",
"IsTopologicalAddTorsor",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"ContinuousAffineMap",
"addGroupIsAddTorsor",
"ContinuousAffineMap.instNeg",
"ContinuousLinearMap",
"TopologicalSpace",
"ContinuousLinearMap.neg",
"AddTorsor",... | true |
_private.Mathlib.Analysis.Complex.HasPrimitives.0.Complex.mem_ball_of_map_im_aux₁ | Mathlib.Analysis.Complex.HasPrimitives | [
"instInnerProductSpaceRealComplex",
"Complex.verticalSegment_eq",
"Complex.mul_im",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Set.Icc_self",
"Real.partialOrder",
"Real",
"Complex.mul_re",
"HMul.hMul",
"Real.lattice",
"sub_self",
"Real.instZero",
... | true |
Summable.le_tsum | Mathlib.Topology.Algebra.InfiniteSum.Order | [
"AddMonoid.toAddZeroClass",
"SummationFilter",
"Preorder.toLE",
"le_hasSum",
"AddZeroClass.toAddZero",
"Ne",
"LE.le",
"AddCommMonoid",
"TopologicalSpace",
"AddZero.toZero",
"Summable.hasSum",
"tsum",
"SummationFilter.LeAtTop",
"SummationFilter.NeBot",
"Zero.toOfNat0",
"OrderClosedTopol... | true |
Subfield.card_bot | Mathlib.FieldTheory.Finite.Basic | [
"Eq.mpr",
"Subfield.toDivisionRing",
"Nat.Prime",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"Nat.instMonoid",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Preorder.toLE",
"RingHom",
"Membership.mem",
"Field.toDivisionRing",
... | true |
_private.Std.Time.Format.Basic.0.Std.Time.GenericFormat.parseBuilder!.match_1 | Std.Time.Format.Basic | [
"Except.ok",
"String",
"Except.error",
"Except.casesOn",
"Except"
] | false |
Subarray.mergeSort._unsafe_rec | Init.Data.Array.Sort.Basic | [
"Std.Rci.mk",
"Subarray",
"instHDiv",
"Subarray.mergeSort._auto_1",
"Std.Slice.toArray",
"Std.Rio.mk",
"instSliceableSubarrayNat_2",
"HDiv.hDiv",
"instOfNatNat",
"SubarrayIterator",
"instSliceableSubarrayNat_7",
"autoParam",
"dite",
"Array",
"instHAdd",
"_private.Init.Data.Array.Sort.B... | false |
ExtremallyDisconnected.disjoint_closure_of_disjoint_isOpen | Mathlib.Topology.ExtremallyDisconnected | [
"ExtremallyDisconnected.open_closure",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Disjoint",
"CompleteLattice.toConditionallyCompleteLattice",
"Disjoint.closure_right",
"TopologicalSpace",
"closure",
"CompleteDistribLattice.toFrame",
"CompleteBooleanAlgebra.toCompleteLattice",
"Conditiona... | true |
Std.TreeSet.Raw.contains_ofList | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.contains",
"Std.TreeSet.Raw.ofList",
"List.contains",
"Ordering",
"Std.TransCmp",
"List",
"Std.LawfulBEqCmp",
"Std.TreeMap.Raw.contains_unitOfList",
"Bool",
"BEq",
"Eq"
] | true |
instDeterministicStochMkWideSubcategorySFinKerStochHomMkOfIsDeterministicCarrierObj | Mathlib.Probability.Kernel.Category.Stoch | [
"CategoryTheory.ComonObj.comul",
"instIsStableUnderComonoidSFinKerStochHom",
"SFinKer.instMonoidalCategory",
"SFinKer.deterministic_deterministic",
"ProbabilityTheory.IsZeroOrMarkovKernel.isFiniteKernel",
"CategoryTheory.WideSubcategory.obj",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"... | true |
HomologicalComplex.biprod_lift_fst_f_assoc | Mathlib.Algebra.Homology.HomologicalComplexBiprod | [
"CategoryTheory.Category.assoc",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.biprod_lift_fst_f",
"congrArg",
"HomologicalComplex",
"Eq.mp",
"CategoryTheory.Limits.HasBinaryBiproduct",
"id",
"Mathlib.... | true |
Std.Sat.CNF.numLiterals_pos | Std.Sat.CNF.RelabelFin | [
"Nat.zero_le",
"Std.Sat.CNF",
"Nat.lt_of_le_of_lt",
"instOfNatNat",
"Std.Sat.CNF.VarMem",
"Std.Sat.CNF.lt_numLiterals",
"Nat",
"LT.lt",
"instLTNat",
"OfNat.ofNat",
"Std.Sat.CNF.numLiterals"
] | true |
_private.Mathlib.Util.Export.0.Lean.Export.MethodsRefPointed | Mathlib.Util.Export | [
"Inhabited.default",
"NonemptyType",
"instInhabitedNonemptyType"
] | true |
Array.size | Init.Prelude | [
"Array.toList",
"Array",
"Nat",
"List.length"
] | true |
_private.Mathlib.RingTheory.Smooth.IntegralClosure.0.TensorProduct.toIntegralClosure_bijective_of_isStandardEtale._simp_1_5 | Mathlib.RingTheory.Smooth.IntegralClosure | [
"Subalgebra.instSetLike",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"Membership.mem",
"Exists",
"AlgHom.mem_range",
"CommSemiring",
"propext",
"Semiring",
"Subalgebra",
"Eq.symm",
"Eq",
"DFunLike.coe",
"SetLike.instMembership",
"AlgHom.range"
] | false |
ComputeAsymptotics.MultiseriesExpansion.Multiseries.tail | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | [
"ComputeAsymptotics.Basis",
"Real",
"Stream'.Seq.tail",
"Prod",
"ComputeAsymptotics.MultiseriesExpansion",
"ComputeAsymptotics.MultiseriesExpansion.Multiseries"
] | true |
_private.Mathlib.Topology.Order.DenselyOrdered.0.closure_Ioo._simp_1_1 | Mathlib.Topology.Order.DenselyOrdered | [
"Membership.mem",
"Insert.insert",
"HasSubset.Subset",
"Set.insert_subset_iff",
"And",
"Set.instInsert",
"propext",
"Eq",
"Set.instMembership",
"Set.instHasSubset",
"Set"
] | false |
cond_false | Init.SimpLemmas | [
"cond",
"Bool.false",
"Eq",
"rfl"
] | true |
IsRelUpperSet.prop_of_mem | Mathlib.Order.UpperLower.Relative | [
"Membership.mem",
"LE.le",
"IsRelUpperSet",
"LE",
"And.left",
"Set.instMembership",
"Set"
] | true |
Lean.Lsp.instBEqDiagnosticWith | Lean.Data.Lsp.Diagnostics | [
"Lean.Lsp.DiagnosticWith",
"BEq.mk",
"Lean.Lsp.instBEqDiagnosticWith.beq",
"BEq"
] | true |
LinearEquiv.ofIsUnitDet._proof_6 | Mathlib.LinearAlgebra.Determinant | [
"LinearMap.map_add",
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"AddCommGroup",
"LinearMap",
"instHAdd",
"CommRing.toCommSemiring",
"HAdd.hAdd",
"AddCommSemigroup.toAddCommMagma",
"Module",
"AddCommMonoid.toAddCommSemigroup",
"RingHom.id... | false |
LipschitzWith.prod_snd | Mathlib.Topology.EMetricSpace.Lipschitz | [
"le_max_right",
"Prod.pseudoEMetricSpaceMax",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"LipschitzWith",
"LipschitzWith.of_edist_le",
"NNReal",
"PseudoEMetricSpace",
"Prod.fst",
"PseudoEMetricSpace.toEDist",
"WeakPseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniformSpace",
"ENNReal.i... | true |
Ordnode.brecOn.eq | Mathlib.Data.Ordmap.Ordnode | [
"Ordnode.below",
"Ordnode",
"Ordnode.brecOn.go",
"Ordnode.node",
"Ordnode.casesOn",
"Nat",
"Ordnode.brecOn",
"Ordnode.nil",
"Eq.refl",
"Eq"
] | true |
Nat.abs_sub_ceil_le | Mathlib.Algebra.Order.Floor.Semiring | [
"Iff.mpr",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"abs",
"abs_le",
"LinearOrder",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoi... | true |
Seminorm.comp_smul_apply | Mathlib.Analysis.Seminorm | [
"Seminorm.instSeminormClass",
"Norm.norm",
"SeminormedRing.toNorm",
"Real",
"instHSMul",
"HMul.hMul",
"SeminormedCommRing",
"CommSemiring.toSemiring",
"SeminormedCommRing.toCommRing",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.ins... | true |
Batteries.RBNode.forIn.visit._sunfold | Batteries.Data.RBMap.Basic | [
"Pure.pure",
"Batteries.RBNode",
"Monad.toApplicative",
"ForInStep.bindM",
"Batteries.RBNode.forIn.visit.match_1",
"Applicative.toPure",
"ForInStep",
"Batteries.RBColor",
"Batteries.RBNode.forIn.visit",
"Monad",
"ForInStep.yield"
] | false |
Matrix.cons_val_succ | Mathlib.Data.Fin.VecNotation | [
"Fin.cons_succ",
"Fin.succ",
"congrArg",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"of_eq_true",
"instAddNat",
"congrFun'",
"OfNat.ofNat",
"Fin",
"Eq",
"Matrix.vecCons",
"Eq.trans"
] | true |
UniformOnFun.congrRight._proof_2 | Mathlib.Topology.UniformSpace.UniformConvergenceTopology | [
"UniformContinuous",
"UniformSpace",
"Equiv.instEquivLike",
"UniformOnFun.postcomp_uniformContinuous",
"UniformOnFun.uniformSpace",
"Function.comp",
"Equiv",
"UniformOnFun.toFun",
"UniformEquiv.symm",
"UniformEquiv.uniformContinuous",
"UniformOnFun.ofFun",
"UniformOnFun",
"DFunLike.coe",
"... | false |
_private.Mathlib.Topology.Connected.Basic.0.IsConnected.iUnion_of_chain._proof_1_1 | Mathlib.Topology.Connected.Basic | [
"Set.inter_isAssoc",
"Lean.RArray.leaf",
"False",
"Lean.Grind.AC.Expr.op",
"Order.succ",
"eq_false",
"Set.inter_isComm",
"congrArg",
"LinearOrder",
"Lean.Grind.AC.Expr",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Lean.Grind.AC.Context",
"Lean.Grind.AC.imp_eq",
"Membership.m... | false |
Lean.Lsp.CompletionOptions.mk.noConfusion | Lean.Data.Lsp.LanguageFeatures | [
"String",
"id",
"Array",
"Lean.Lsp.CompletionOptions",
"Lean.Lsp.CompletionOptions.noConfusion",
"Lean.Lsp.CompletionOptions.mk",
"Bool",
"Eq",
"Option"
] | false |
_private.Lean.Expr.0.Lean.Expr.getNumHeadLambdas._sparseCasesOn_1 | Lean.Expr | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero._simp_1_3 | Mathlib.Data.Matrix.Mul | [
"funext_iff",
"propext",
"Eq"
] | false |
PMF.mem_support_uniformOfFinset_iff | Mathlib.Probability.Distributions.Uniform | [
"SetLike.mem_coe._simp_1",
"congrArg",
"Finset",
"Membership.mem",
"PMF.support",
"iff_self",
"PMF.support_uniformOfFinset",
"Iff",
"SetLike.coe",
"Finset.instSetLike",
"True",
"Finset.Nonempty",
"of_eq_true",
"congrFun'",
"PMF.uniformOfFinset",
"Set.instMembership",
"SetLike.instMem... | true |
CategoryTheory.Abelian.AbelianStruct.imageι_π | Mathlib.CategoryTheory.Abelian.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryTheory.Abelian.AbelianStruct.imageι",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTheory.Preadditive",
"CategoryTheory.Abeli... | true |
_private.Mathlib.Data.Prod.Lex.0.Prod.Lex.toLex_covBy_toLex_iff._simp_1_5 | Mathlib.Data.Prod.Lex | [
"Preorder.toLT",
"Preorder.toLE",
"LT.lt",
"isMin_iff_forall_not_lt",
"propext",
"Eq",
"Not",
"IsMin",
"Preorder"
] | false |
CategoryTheory.FreeBicategory.normalize._proof_9 | Mathlib.CategoryTheory.Bicategory.Coherence | [
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Path.nil",
"CategoryTheory.eqToHom",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"CategoryTheory.eqToIso",
"CategoryTheory.Bicategory.w... | false |
LinearOrder.max_def._autoParam | Mathlib.Order.Defs.LinearOrder | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Nat.count_add' | Mathlib.Data.Nat.Count | [
"Eq.mpr",
"congrArg",
"id",
"add_comm",
"Nat.count_add",
"funext",
"instHAdd",
"HAdd.hAdd",
"DecidablePred",
"Nat",
"True",
"Nat.count",
"eq_self",
"of_eq_true",
"Nat.count.congr_simp",
"instAddNat",
"Eq.refl",
"congrFun'",
"AddCommSemigroup.toAddCommMagma",
"Eq",
"Nat.instAd... | true |
Std.DHashMap.Raw.Const.forMUncurried_eq_forM_toList | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.Const.toList",
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.Const.forMUncurried",
"Std.DHashMap.Internal.Raw₀.Const.forM_eq_forM_toList",
"Std.DHashMap.Raw",
"Prod.mk",
"LawfulMonad",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"Subtype.mk",
"PUnit",
"Nat",
"Std.DHa... | true |
_private.Init.Data.Vector.InsertIdx.0.Vector.insertIdx_eraseIdx_of_ge._proof_1 | Init.Data.Vector.InsertIdx | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.... | false |
denomsClearable_C_mul_X_pow | Mathlib.Algebra.Polynomial.DenomsClearable | [
"Eq.mpr",
"Polynomial.C",
"Polynomial.eval",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"MulOne.toOne",
"Nat.instOrderedSub",
"Semigroup.toMul",
"Nat.instIsOrderedAddMonoid",
"Semiring.toModule",
"HMul.hMul",
"AddLeftCancelSemigrou... | true |
Submodule.Quotient.seminormedAddCommGroup._proof_5 | Mathlib.Analysis.Normed.Group.Quotient | [
"Submodule",
"Real",
"SeminormedAddCommGroup",
"QuotientAddGroup.instSeminormedAddCommGroup._proof_2",
"Real.instZero",
"Dist.mk",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.seminormedAddCommGroup._aux_3",
"Submodule.hasQuotient",
"HasQuotient.Quotient",
"SeminormedAddCommGroup.toAddCom... | false |
CochainComplex.homologyδOfTriangle_homologyMap | Mathlib.Algebra.Homology.DerivedCategory.HomologySequence | [
"HomologicalComplex.homologyFunctor",
"CochainComplex.homologyδOfTriangle",
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"instCategoryDerivedCategory",
"CategoryTheory.Functor",
"DerivedCategory.instHasZeroObject",
"HomologicalComplex.instCategory",
"DerivedCa... | true |
ModularForm.is_invariant_const | Mathlib.NumberTheory.ModularForms.SlashActions | [
"Int.instAddCommGroup",
"UpperHalfPlane.glAction",
"Real.instIsOrderedRing",
"Units.val",
"NormedCommRing.toSeminormedCommRing",
"Matrix.SpecialLinearGroup.coeToGL_det",
"MulOne.toOne",
"Real.partialOrder",
"Real",
"instHSMul",
"Matrix.SpecialLinearGroup",
"MonoidHom.instFunLike",
"InvOneCla... | true |
zmultiplesHom | Mathlib.Data.Int.Cast.Lemmas | [
"instHSMul",
"AddMonoid.toAddZeroClass",
"zmultiplesHom._proof_5",
"add_zsmul",
"AddZeroClass.toAddZero",
"Equiv.mk",
"AddMonoidHom.mk",
"Equiv",
"Int",
"Int.instAddMonoid",
"ZeroHom.mk",
"AddZero.toZero",
"AddGroup",
"AddGroup.toSubNegMonoid",
"instOfNat",
"zmultiplesHom._proof_2",
... | true |
Aesop.Script.UScript.render | Aesop.Script.UScript | [
"Pure.pure",
"Array.mkEmpty",
"Aesop.Script.Step.render",
"instForInOfForIn'",
"Monad.toApplicative",
"Array.instMembership",
"MProd.snd",
"inferInstance",
"MProd.mk",
"MProd.fst",
"ForIn.forIn",
"Applicative.toPure",
"Membership",
"ForInStep",
"_private.Aesop.Script.UScript.0.Aesop.Scri... | true |
CompactlySupportedContinuousMap.pullback_addMonoidHom._proof_3 | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"instSeparatelyContinuousAddOfContinuousAdd",
"CompactlySupportedContinuousMap.hasCompactSupport",
"AddMonoid.toAddSemigroup",
"instVAddOfAdd",
"R1Space",
"congrArg",
"CompactlySupportedContinuo... | false |
Real.rpow_div_two_eq_sqrt | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.div_congr",
"Real.instPow",
"Real.instLE",
"Real",
"instHDiv",
"Mathlib.Meta.NormNum.IsNat.to_isNNRat",
"GroupWithZero.toDivisionMonoid",
"Mathlib.Tactic.Ring.Common.mul_con... | true |
Algebra.FormallySmooth.of_restrictScalars | Mathlib.RingTheory.Smooth.Basic | [
"Ideal.Quotient.isScalarTower",
"Iff.mpr",
"Eq.mpr",
"MulOne.toOne",
"CommRing",
"Semiring.toModule",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom.comp_assoc",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"IsScalarTower.toAlgHom",
"Algebra",
"RingHom",
"Algebr... | true |
RestrictedProduct.evalMonoidHom._proof_1 | Mathlib.Topology.Algebra.RestrictedProduct.Basic | [
"SetLike",
"Monoid",
"MulOne.toOne",
"Monoid.toMulOneClass",
"RestrictedProduct.instDFunLike",
"RestrictedProduct",
"MulOneClass.toMulOne",
"SetLike.coe",
"One.toOfNat1",
"RestrictedProduct.instMonoidCoeOfSubmonoidClass",
"SubmonoidClass",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"Filter",
... | false |
Std.Sat.AIG.RefVec.map.go._unary | Std.Sat.AIG.RefVecOperator.Map | [
"Std.Sat.AIG.RefVec.get",
"Std.Sat.AIG.Entrypoint.aig",
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.RefVec.map._proof_2",
"Std.Sat.AIG.RefVec.push",
"InvImage",
"HSub.hSub",
"WellFounded.Nat.fix",
"Eq.rec",
"PSigma.casesOn",
"Std.Sat.AIG.Entrypoint",
"instSubNat",
"instOfNatNat",
"Std.Sat.AIG.Entrypo... | false |
padicNorm.padicNorm_p | Mathlib.NumberTheory.Padics.PadicNorm | [
"Rat.instOfNat",
"False",
"Nat.instMulZeroClass",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"eq_false",
"congrArg",
"AddMonoid.toAddZeroClass",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"DivInvMonoid.toZPow",
... | true |
_private.Mathlib.Topology.Semicontinuity.Hemicontinuity.0.upperHemicontinuous_iff_isClosed_compl_preimage_Iic_compl._simp_1_1 | Mathlib.Topology.Semicontinuity.Hemicontinuity | [
"Compl.compl",
"Set.instCompl",
"IsClosed",
"TopologicalSpace",
"propext",
"IsOpen",
"Eq.symm",
"Eq",
"isOpen_compl_iff",
"Set"
] | false |
_private.Mathlib.Geometry.Manifold.Immersion.0.Manifold.isLocalSourceTargetProperty_immersionAtProp._proof_1_4 | Mathlib.Geometry.Manifold.Immersion | [
"False",
"NormedSpace",
"eq_false",
"congrArg",
"HEq.refl",
"Classical.byContradiction",
"Function.comp",
"Membership.mem",
"PartialEquiv.symm",
"Set.EqOn.eq_of_mem",
"Eq.mp",
"id",
"Set.EqOn",
"TopologicalSpace",
"ModelWithCorners",
"congr",
"True",
"eq_true",
"of_eq_true",
"e... | false |
_private.Lean.Elab.DeclModifiers.0.Lean.Elab.expandDeclId.match_1 | Lean.Elab.DeclModifiers | [
"Prod.mk",
"Lean.Name",
"Prod",
"Prod.casesOn"
] | false |
iteratedDeriv_fun_id | Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | [
"NormedCommRing.toNormedRing",
"NormedRing.toRing",
"AddGroupWithOne.toAddMonoidWithOne",
"NormedField.toField",
"id",
"instOfNatNat",
"NormedCommRing.toNonUnitalNormedCommRing",
"Field.toSemifield",
"NonUnitalNormedRing.toNormedAddCommGroup",
"AddMonoidWithOne.toOne",
"Semifield.toDivisionSemir... | true |
Nat.lt_mul_of_div_lt | Init.Data.Nat.Lemmas | [
"Iff.mpr",
"False",
"instHDiv",
"HMul.hMul",
"Function.comp",
"GE.ge",
"HDiv.hDiv",
"instMulNat",
"instOfNatNat",
"Nat.lt_of_not_ge",
"LE.le",
"instLENat",
"Nat",
"LT.lt",
"Nat.not_le_of_gt",
"Nat.instDiv",
"Nat.le_div_iff_mul_le",
"instLTNat",
"OfNat.ofNat",
"instHMul"
] | true |
Aesop.RuleTacDescr.forwardMatches.noConfusion | Aesop.RuleTac.Descr | [
"Aesop.ForwardRuleMatch",
"Aesop.RuleTacDescr",
"id",
"Array",
"Aesop.RuleTacDescr.forwardMatches",
"Aesop.RuleTacDescr.noConfusion",
"Eq"
] | false |
HNNExtension.NormalWord.group_smul_toList | Mathlib.GroupTheory.HNNExtension | [
"HNNExtension.NormalWord",
"instHSMul",
"HNNExtension.NormalWord.ReducedWord.toList",
"Group",
"Units",
"DivInvMonoid.toMonoid",
"Subgroup",
"HNNExtension.NormalWord.instMulAction",
"Int",
"Int.instMonoid",
"Group.toDivInvMonoid",
"List",
"HNNExtension.NormalWord.toReducedWord",
"Monoid.to... | true |
Real.sin_add_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Real",
"Real.pi",
"Real.sin_antiperiodic",
"Real.instAdd",
"instHAdd",
"HAdd.hAdd",
"Real.instNeg",
"Eq",
"Real.sin",
"Neg.neg"
] | true |
Lean.Elab.Tactic.evalSleep._regBuiltin.Lean.Elab.Tactic.evalSleep_1 | Lean.Elab.Tactic.BuiltinTactic | [
"Lean.Elab.Tactic.tacticElabAttribute",
"IO",
"Lean.Elab.Tactic.evalSleep",
"Unit",
"Lean.Elab.Tactic.Tactic",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
CStarMatrix.ofMatrixStarAlgEquiv | Mathlib.Analysis.CStarAlgebra.CStarMatrix | [
"Matrix.instStar",
"Matrix.smul",
"Matrix.add",
"Matrix.instMulOfFintypeOfAddCommMonoid",
"Matrix",
"CStarMatrix.ofMatrixStarAlgEquiv._proof_1",
"SMul",
"StarRingEquiv.mk",
"StarAlgEquiv",
"Distrib.toAdd",
"CStarMatrix.instStar",
"StarAddMonoid.toInvolutiveStar",
"instDistribOfSemiring",
"... | true |
HomologicalComplex.instHasMapProdObjGradedObjectFunctorMapBifunctorXπ | Mathlib.Algebra.Homology.BifunctorAssociator | [
"_private.Mathlib.Algebra.Homology.BifunctorAssociator.0.HomologicalComplex.instHasMapProdObjGradedObjectFunctorMapBifunctorXπ._proof_1",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.GradedObject.HasMap",
"CategoryTheory.Functor.category",
"HomologicalComplex",
"Co... | true |
GroupExtension.Equiv.mk.injEq | Mathlib.GroupTheory.GroupExtension.Defs | [
"MulEquiv.instEquivLike",
"MonoidHom.instFunLike",
"MonoidHom",
"Eq.propIntro",
"Monoid.toMulOneClass",
"Group",
"Function.comp",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"GroupExtension.rightHom",
"GroupExtension.inl",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"GroupExtension.Equiv"... | true |
CategoryTheory.Mon.mkIso.eq_1 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Mon.mkIso'",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon.mkIso",
"CategoryTheory.Iso",
"CategoryTheory.Mon.mkIso._proof_1",
"CategoryTheory.MonObj.one",
"CategoryTheory.Mon",
"CategoryTheory.Mon.X",
"CategoryTheor... | true |
_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.CtorHeaderResult.levels | Lean.Elab.StructInst | [
"Lean.Level",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.CtorHeaderResult",
"List"
] | true |
AddChar.toAddMonoidHom_apply | Mathlib.Algebra.Group.AddChar | [
"Monoid",
"Equiv.instEquivLike",
"AddChar.toAddMonoidHom",
"Monoid.toMulOneClass",
"Additive",
"AddMonoid.toAddZeroClass",
"AddChar",
"AddZeroClass.toAddZero",
"Equiv",
"Additive.addZeroClass",
"Additive.ofMul",
"AddMonoid",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"Eq",
"DFunLike.c... | true |
DistribMulActionHom.toAddActionHom_injective | Mathlib.GroupTheory.GroupAction.Hom | [
"Monoid",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"DistribMulActionHom",
"DistribMulActionHom.ext",
"MulActionHom.congr_fun",
"DistribMulActionHom.instFunLike",
"MulOneClass.toMulOne",
"MulActionSemiHomClass.toMulActionHom",
"AddMonoid",
"DistribMulActionHom.instAddDistri... | true |
Std.Internal.List.eraseKey_cons | Std.Data.Internal.List.Associative | [
"cond",
"Std.Internal.List.eraseKey",
"List.cons",
"List",
"BEq.beq",
"Sigma.mk",
"BEq",
"Eq",
"Sigma",
"rfl"
] | true |
Nat.Linear.PolyCnstr.ctorIdx | Init.Data.Nat.Linear | [
"Nat",
"Nat.Linear.PolyCnstr"
] | false |
Localization.localRingEquiv._proof_5 | Mathlib.RingTheory.Localization.AtPrime.Basic | [
"CommSemiring.toSemiring",
"RingEquiv.instEquivLike",
"RingEquiv.instRingEquivClass",
"Distrib.toAdd",
"instDistribOfSemiring",
"CommSemiring",
"Distrib.toMul",
"RingEquiv",
"RingEquivClass.toRingHomClass",
"Semiring.toNonAssocSemiring",
"EquivLike.toFunLike",
"RingHomClass"
] | false |
PiTensorProduct.dualDistribInvOfBasis._proof_5 | Mathlib.LinearAlgebra.PiTensorProduct.Dual | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"smulCommClass_self",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.toCommSemiring",
"CommMonoid.toMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"Module.toDistribMul... | false |
_private.Lean.Compiler.LCNF.ReduceArity.0.Lean.Compiler.LCNF.FindUsed.visit.match_1 | Lean.Compiler.LCNF.ReduceArity | [
"Lean.Compiler.LCNF.Arg.casesOn",
"False",
"Lean.FVarId.casesOn",
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.Code.setTag",
"Lean.Compiler.LCNF.Code.unreach",
"HEq.refl",
"Lean.Compiler.LCNF.Code.fun",
"False.elim",
"Lean.Compiler.LCNF.Code.cases",
"Lean.Compiler.LCNF.Code.casesOn",
"Lean.Co... | false |
Std.TreeMap.minKeyD_alter_eq_self | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.alter",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Std.TreeMap.isEmpty",
"Bool.true",
"And",
"Iff",
"Std.TreeMap.instMembership",
"Std.DTreeMap.Const.minKeyD_alter_eq_self",
"Std.TreeMap.instGetElem?Mem",
"Std.TreeMap.minKeyD",
"Bool",
"GetElem?.getE... | true |
Std.HashSet.get_inter | Std.Data.HashSet.Lemmas | [
"Std.HashSet.instMembership",
"Std.HashSet",
"Membership.mem",
"Std.HashSet.get",
"LawfulHashable",
"Inter.inter",
"Bool.true",
"And",
"Unit",
"Std.HashSet.instInter",
"EquivBEq",
"Std.HashSet.inner",
"Std.HashSet.contains",
"And.left",
"Iff.mp",
"Bool",
"Hashable",
"Std.HashMap.ge... | true |
_private.Mathlib.Data.Set.Prod.0.Set.Disjoint.set_prod_right.match_1_3 | Mathlib.Data.Set.Prod | [
"Set.instSProd",
"SProd.sprod",
"Membership.mem",
"Prod.mk",
"Prod",
"Prod.casesOn",
"Set.instMembership",
"Set"
] | false |
MeasureTheory.OuterMeasure.instDistribMulAction._proof_1 | Mathlib.MeasureTheory.OuterMeasure.Operations | [
"Monoid",
"instHSMul",
"instSMulOfMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"MeasureTheory.OuterMeasure.instSMul",
"AddZeroClass.toAddZero",
"MeasureTheory.OuterMeasure",
"Function.hasSMul",
"DistribSMul.toSMulZeroClass",
... | false |
CategoryTheory.StructuredArrow.isEquivalence_pre | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.comp",
"CategoryTheory.discreteCategory",
"PUnit",
"CategoryTheory.Comma.isEquivalence_preRight",
"CategoryTheory.StructuredArrow.pre",
"CategoryTheory.instCategoryStructuredArrow",
"CategoryTheory.Functor.fromPUnit",
"CategoryTheory.Functor.IsEquiva... | true |
QuadraticMap.Isometry.fst_comp_inr | Mathlib.LinearAlgebra.QuadraticForm.Prod | [
"QuadraticMap.Isometry.comp",
"QuadraticMap.instZero",
"CommSemiring.toSemiring",
"QuadraticMap.Isometry.inr",
"QuadraticMap.Isometry.ext",
"AddCommMonoid",
"CommSemiring",
"QuadraticMap.prod",
"Zero.toOfNat0",
"QuadraticMap.Isometry.instZeroOfNat",
"Module",
"Prod",
"Prod.instModule",
"Of... | true |
HomologicalComplex.homotopyCofiber.d.eq_1 | Mathlib.Algebra.Homology.HomotopyCofiber | [
"NegZeroClass.toNeg",
"HomologicalComplex.instCategory",
"HomologicalComplex.homotopyCofiber.X",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"DecidableRel",
"HomologicalComplex",
"SubtractionMonoid.toSubNegZeroMonoid",
"Comp... | true |
lowerSemiContinuous_neg_iff._simp_1 | Mathlib.Topology.Semicontinuity.Basic | [
"NegZeroClass.toNeg",
"Pi.instNeg",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"PartialOrder",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"UpperSemicontinuous",
"LowerSemicontinuous",
"... | false |
NumberField.IsCMField.unitsMulComplexConjInv._proof_1 | Mathlib.NumberTheory.NumberField.CMField | [
"Rat.nontrivial",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Field.toDivisionRing",
"Algebra.IsIntegral",
"DivisionRing.toRing",
"NumberField.to_finiteDimensional",
"Algebra.IsIntegral.of_finite",
"Field.toSemifield",
"Field.toCommRing",
"instIsDomain",
"DivisionRing.toRatAlgebra",
"CharZ... | false |
Int.ModEq.prod | Mathlib.Algebra.BigOperators.ModEq | [
"Int.instCommMonoid",
"Finset",
"Membership.mem",
"Int",
"Finset.val",
"Finset.prod",
"Finset.instSetLike",
"Int.ModEq",
"Int.ModEq.multisetProd_map",
"SetLike.instMembership"
] | true |
Prod.divisibleBy._proof_1 | Mathlib.GroupTheory.Divisible | [
"DivisibleBy.div_zero",
"SMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Prod.mk",
"DivisibleBy.div",
"Prod.fst",
"AddZero.toZero",
"Prod.ext",
"AddMonoid",
"Zero.toOfNat0",
"Prod.instAddMonoid",
"Prod",
"OfNat.ofNat",
"Eq",
"Prod.snd",
"DivisibleBy",
"Zero"
] | false |
groupHomology.mapShortComplexH2_τ₂ | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"Rep.V",
"CommRing",
"Finsupp.module",
"groupHomology.mapShortComplexH2",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Group",
"Rep.instCategory",
"Rep.hV1"... | true |
CategoryTheory.leftDual_rightDual | Mathlib.CategoryTheory.Monoidal.Rigid.Basic | [
"CategoryTheory.HasRightDual.rightDual",
"CategoryTheory.HasRightDual",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.hasLeftDualRightDual",
"CategoryTheory.HasLeftDual.leftDual",
"Eq",
"rfl",
"CategoryTheory.Category"
] | true |
Simps.projectionsInfo | Mathlib.Tactic.Simps.Basic | [
"Lean.MessageData",
"Std.instToFormatString",
"String.join",
"Lean.MessageData.joinSep",
"Simps.ProjectionData.isDefault",
"String",
"List.map",
"Lean.MessageData.instAppend",
"Simps.ProjectionData",
"Function.comp",
"Lean.instToMessageDataExpr",
"Lean.Expr",
"instDecidableEqBool",
"Simps.... | true |
Lean.Lsp.DependencyBuildMode.ctorElimType | Lean.Data.Lsp.Extra | [
"cond",
"Nat.ble",
"Lean.Lsp.DependencyBuildMode.once",
"PULift",
"Lean.Lsp.DependencyBuildMode.always",
"Nat",
"Lean.Lsp.DependencyBuildMode.never",
"Lean.Lsp.DependencyBuildMode"
] | false |
Aesop.EqualUpToIdsM.State.ctorIdx | Aesop.Util.EqualUpToIds | [
"Aesop.EqualUpToIdsM.State",
"Nat"
] | false |
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