name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Real.Angle.cos_add_pi_div_two | Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle | [
"Real",
"instHDiv",
"Real.pi",
"Real.Angle",
"Real.Angle.coe",
"AddCommGroup.toAddCommMonoid",
"Real.instDivInvMonoid",
"Nat.instAtLeastTwoHAddOfNat",
"HDiv.hDiv",
"instOfNatNat",
"Real.Angle.induction_on",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"Real.instNeg",
"DivInv... | true |
_private.Mathlib.MeasureTheory.Integral.IntervalIntegral.LebesgueDifferentiationThm.0.IntervalIntegrable.ae_hasDerivAt_integral._proof_1_4 | Mathlib.MeasureTheory.Integral.IntervalIntegral.LebesgueDifferentiationThm | [
"Set.Ioc",
"False",
"Real",
"eq_false",
"Real.instZero",
"AddMonoid.toAddZeroClass",
"Classical.byContradiction",
"Real.decidableLT",
"PseudoMetricSpace.toUniformSpace",
"Set.decidableMemIoc",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.mp",
"id",
"Real.normedAddCommGroup",
"Normed... | false |
Std.Internal.List.maxKey! | Std.Data.Internal.List.Associative | [
"Ord",
"Option.get!",
"List",
"Std.Internal.List.maxKey?",
"Inhabited",
"Sigma"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.get_diff!._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
ContinuousAlternatingMap.coe_restrictScalars | Mathlib.Topology.Algebra.Module.Alternating.Basic | [
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"SMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"ContinuousAlternatingMap.restrictScalars",
"AddCommMonoid",
"TopologicalSpace",
"AddZero.toZero",
"ContinuousAlternatingMap.funLike",
"Semiring.toMon... | true |
Lean.JsonRpc.Notification.mk.sizeOf_spec | Lean.Data.JsonRpc | [
"String",
"Lean.JsonRpc.Notification.mk",
"Lean.JsonRpc.Notification._sizeOf_inst",
"Lean.JsonRpc.Notification",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"String._sizeOf_inst",
"Eq.refl",
"SizeOf",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.LinearAlgebra.LinearPMap.0.LinearPMap.mem_graph_snd_inj'._proof_1_1 | Mathlib.LinearAlgebra.LinearPMap | [
"Submodule",
"False",
"Lean.Grind.nestedProof",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"Classical.byContradiction",
"Subtype.casesOn",
"Membership.mem",
"Exists",
"AddCommGroup",
"Eq.mp",
"id",
"Subtype",
"Prod.mk",
"Prod.fst",
"S... | false |
FinBddDistLat.hom_ext_iff | Mathlib.Order.Category.FinBddDistLat | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"FinBddDistLat.instBoundedOrderCarrier",
"HEq.refl",
"FinBddDistLat.instDistribLatticeCarrier",
"DistribLattice.toLattice",
"Eq.casesOn",
"FinBddDistLat.hom_ext",
"FinBddDistLat",
"Iff",
"BoundedLatticeHom",
"FinBddDistLat.Hom.hom",
"If... | true |
RCLike.continuous_re | Mathlib.Analysis.RCLike.Basic | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"Continuous",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"RCLike.toNormedAlgebra",
"AddMonoid.toAddSemigroup",
"Real.instAddMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"PseudoMetricSp... | true |
MeasureTheory.StronglyMeasurable.add_iff_left | Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic | [
"MeasureTheory.StronglyMeasurable.add_iff_right",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Eq.rec",
"AddZeroClass.toAddZero",
"AddCommGroup",
"add_comm",
"MeasurableSpace",
"TopologicalSpace",
"instHAdd",
"Iff",
"Pi.instAdd",
"AddGroup.toSubNe... | true |
_private.Lean.Elab.Tactic.Grind.Main.0.Lean.Elab.Tactic.elabGrindPattern.elabCnstrs | Lean.Elab.Tactic.Grind.Main | [
"_private.Lean.Elab.Tactic.Grind.Main.0.Lean.Elab.Tactic.elabGrindPattern.elabNotDefEq",
"Pure.pure",
"Lean.Meta.Grind.EMatchTheoremConstraint",
"Lean.TSyntax",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Elab.Term.instMonad... | true |
Lean.Meta.Grind.Arith.Cutsat.ToIntInfo.ofNotLE? | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"Lean.Meta.Grind.Arith.Cutsat.ToIntInfo",
"Lean.Expr",
"Option"
] | true |
Nat.exists_eq_pow_of_pow_eq_pow | Mathlib.Data.Nat.Factorization.Basic | [
"Nat.gcd",
"Nat.exists_eq_pow_of_exponent_coprime_of_pow_eq_pow",
"Nat.gcd_dvd_left",
"Eq.mpr",
"Nat.Coprime",
"Nat.div_mul_cancel",
"instHDiv",
"HMul.hMul",
"congrArg",
"Nat.gcd_ne_zero_left",
"Nat.instMonoid",
"Exists",
"Eq.rec",
"Eq.mp",
"id",
"HDiv.hDiv",
"Ne",
"instMulNat",
... | true |
CategoryTheory.Abelian.SpectralObject.δ_δ._auto_1 | Mathlib.Algebra.Homology.SpectralObject.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.GroupTheory.Index.0.Subgroup.index_inf_le._simp_1_1 | Mathlib.GroupTheory.Index | [
"Group",
"Subgroup",
"Subgroup.relIndex",
"Nat",
"Subgroup.index",
"Subgroup.instTop",
"Top.top",
"Eq.symm",
"Eq",
"Subgroup.relIndex_top_right"
] | false |
LLVM.Module.ptr | Lean.Compiler.IR.LLVMBindings | [
"LLVM.Module",
"USize",
"LLVM.Context"
] | true |
SeminormedCommRing.induced._proof_2 | Mathlib.Analysis.Normed.Ring.Basic | [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Real.instLE",
"Semigroup.toMul",
"Real",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Ring.toNonAssocRing",
"NonUnitalSeminormedRing.norm_mul_le",
"SeminormedRing.toRing",
"NonUnitalNonAs... | false |
_private.Mathlib.Analysis.Normed.Unbundled.SmoothingSeminorm.0.μ_limsup_le_one | Mathlib.Analysis.Normed.Unbundled.SmoothingSeminorm | [
"Iff.mpr",
"Real.instIsOrderedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"ConditionallyCompleteLattice.toInfSet",
"mul_nonneg",
"Real.instPow",
"Nat.instLattice",
"Real.partialOrder",
"Real.instLE",
"Real",
"CommRing",
"Preorder.toLT",
"Set.mem_Ioo",
"Lattice.toSemilatticeSup",
... | true |
CategoryTheory.Sieve.generate_mono | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.Presieve",
"PartialOrder.toPreorder",
"Monotone",
"CategoryTheory.Sieve.giGenerate",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Sieve",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"CategoryTheory.instCompleteLatticePresieve",
"CategoryTh... | true |
ConcaveOn.le_map_average | Mathlib.Analysis.Convex.Integral | [
"MeasureTheory.ae",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real.partialOrder",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"CompleteSpace",
"instSMulOfMul",
"NormedSpace",
"Real.instRCLike",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMono... | true |
isMulFreimanIso_empty | Mathlib.Combinatorics.Additive.FreimanHom | [
"MulOne.toOne",
"IsMulFreimanIso",
"Set.bijOn_empty",
"Multiset.map",
"Monoid.toMulOneClass",
"congrArg",
"Multiset.prod",
"Membership.mem",
"Multiset",
"instOfNatNat",
"IsMulFreimanIso.mk",
"iff_self",
"Multiset.instMembership",
"MulOneClass.toMulOne",
"Iff",
"CommMonoid.toMonoid",
... | true |
List.map_coe_finRange_eq_range | Batteries.Data.List.Lemmas | [
"List.ext_getElem",
"congrArg",
"List.map",
"List.length_range",
"Eq.rec",
"Fin.mk",
"List.getElem_range",
"List.range",
"Fin.val",
"GetElem.getElem",
"forall_prop_domain_congr",
"List",
"List.getElem_map",
"Nat",
"congr",
"LT.lt",
"True",
"List.length_finRange",
"eq_self",
"Eq... | true |
_private.Init.Data.String.Decode.0.ByteArray.utf8DecodeChar?.utf8Size_assemble₄ | Init.Data.String.Decode | [
"Iff.mpr",
"Char.utf8Size_eq_four_iff",
"Option.some",
"instOfNatNat",
"ByteArray.utf8DecodeChar?.assemble₄",
"Char.val",
"Nat",
"instLTUInt32",
"LT.lt",
"UInt32",
"Char",
"_private.Init.Data.String.Decode.0.ByteArray.utf8DecodeChar?.le_val_assemble₄",
"OfNat.ofNat",
"UInt8",
"Eq",
"UI... | true |
Std.Net.interfaceAddresses | Std.Net.Addr | [
"Inhabited.default",
"instInhabitedError",
"IO",
"Std.Net.InterfaceAddress",
"instInhabitedEIO",
"Array",
"IO.Error"
] | true |
_private.Mathlib.Geometry.Manifold.Notation.0.Manifold.Elab.totalSpaceMk.match_3 | Mathlib.Geometry.Manifold.Notation | [
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Expr.app",
"Lean.Expr.ctorIdx",
"_private.Mathlib.Geometry.Manifold.Notation.0.Manifold.Elab.findModelFiber?._sparseCasesOn_1"
] | false |
NNRat.smulDivisionSemiring | Mathlib.Algebra.Field.Defs | [
"SMul",
"DivisionSemiring.nnqsmul",
"NNRat",
"SMul.mk",
"DivisionSemiring"
] | true |
Std.TreeSet.Raw.mem_erase | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.WF.out",
"Membership.mem",
"Ordering",
"Ordering.eq",
"Std.TreeSet.Raw.instMembership",
"Ne",
"Std.TransCmp",
"And",
"Std.TreeSet.Raw",
"Unit",
"Iff",
"Std.TreeSet.Raw.erase",
"Std.TreeSet.Raw.inner",
"Std.TreeMap.Raw.mem_erase",
"Std.TreeSet.Raw.WF"
] | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RatAddSound.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.sat_of_confirmRupHint_of_insertRat_fold._simp_1_9 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RatAddSound | [
"List.map",
"Membership.mem",
"Exists",
"List",
"And",
"List.instMembership",
"propext",
"List.mem_map",
"Eq"
] | false |
Std.TreeMap.Raw.mem_map | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.WF.out",
"Membership.mem",
"Ordering",
"Std.TreeMap.Raw.instMembership",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw.map",
"Std.TreeMap.Raw",
"Iff",
"Std.DTreeMap.Raw.mem_map"
] | true |
ONote.opowAux2 | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.instMul",
"ONote.split'",
"HMul.hMul",
"ONote.instAdd",
"ONote.oadd",
"ONote.instZero",
"instOfNatPNatOfNeZeroNat",
"ONote.mulNat",
"instCommMonoidPNat",
"Monoid.toPow",
"ONote.split",
"ONote.instOne",
"instHAdd",
"Unit",
"HPow.hPow",
"HAdd.hAdd",
"CommMonoid.toMonoid",
"ONo... | true |
CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap_comm | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.RightHomologyMapData.φH",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ShortComplex.rightHomology",
"Quiver.Hom",
"CategoryTheory.ShortComplex.RightHomo... | true |
WittVector.ghostComponent_zero_verschiebungFun | Mathlib.RingTheory.WittVector.Verschiebung | [
"Eq.mpr",
"MulOne.toOne",
"wittPolynomial",
"WittVector.ghostComponent_apply",
"aeval_wittPolynomial",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Nat.Prime",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"MvPolynomial.aev... | true |
_private.Mathlib.AlgebraicTopology.SimplexCategory.Basic.0.SimplexCategory.intervalEdge._proof_3 | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"Lean.RArray.leaf",
"False",
"of_decide_eq_true",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",
... | false |
_private.Mathlib.GroupTheory.Coxeter.Length.0.CoxeterSystem.not_isReduced_alternatingWord._proof_1_1 | Mathlib.GroupTheory.Coxeter.Length | [
"Lean.RArray.leaf",
"False",
"Lean.Grind.not_not",
"of_decide_eq_true",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"CoxeterMatrix.M",
"Classical.byContradiction",
"HSub.hSub",
"Nat.ToInt.add_congr",
"Group",
"Lean.Grind.Nat.lt_eq",
"Eq.mp",
"Lean.RArray.branch",
"Nat.ToInt.natCast... | false |
Compactum.instTopologicalSpaceA._proof_1 | Mathlib.Topology.Category.Compactum | [
"Set.univ",
"CategoryTheory.ofTypeMonad",
"Membership.mem",
"Filter.sets",
"CategoryTheory.Monad.Algebra.A",
"Ultrafilter.monad",
"Compactum.str",
"CategoryTheory.types",
"Ultrafilter.lawfulMonad",
"Compactum",
"Ultrafilter",
"Set.instMembership",
"Ultrafilter.toFilter",
"Filter.univ_sets"... | false |
AddMonoidAlgebra.le_inf_support_pow | Mathlib.Algebra.MonoidAlgebra.Degree | [
"Iff.mpr",
"OrderDual.ofDual_le_ofDual",
"OrderDual.instLE",
"AddMonoidAlgebra.semiring",
"OrderDual.addRightMono",
"instHSMul",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"Multiset.map",
"OrderDual.ofDual",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddMonoid.toNSMul",
... | true |
Std.Do.SPred.not_cons | Std.Do.SPred.SPred | [
"ULift",
"List.cons",
"List",
"Std.Do.SPred",
"Std.Do.SPred.not",
"Std.Do.SVal",
"Eq",
"rfl"
] | true |
mersenne_le_mersenne._simp_1 | Mathlib.NumberTheory.LucasLehmer | [
"mersenne_le_mersenne",
"LE.le",
"instLENat",
"mersenne",
"Nat",
"propext",
"Eq"
] | false |
MeasureTheory.exists_mem_forall_mem_nhdsWithin_pos_measure | Mathlib.MeasureTheory.OuterMeasure.Basic | [
"ENNReal.instCanonicallyOrderedAdd",
"Mathlib.Tactic.Push.not_forall_eq",
"Filter.instMembership",
"Mathlib.Tactic.Push.not_exists._simp_1",
"Eq.mpr",
"Mathlib.Tactic.Push.not_and_eq",
"Mathlib.Tactic.Contrapose.contrapose₂",
"Preorder.toLT",
"congrArg",
"instIsBotZeroClass",
"SecondCountableTop... | true |
NumberField.Units.dirichletUnitTheorem.logSpace.congr_simp | Mathlib.NumberTheory.NumberField.Units.Regulator | [
"Eq.refl",
"NumberField.Units.dirichletUnitTheorem.logSpace",
"Eq",
"Field",
"NumberField"
] | true |
CategoryTheory.LocalizerMorphism.homMap.eq_1 | Mathlib.CategoryTheory.Localization.HomEquiv | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.LocalizerMorphism.catCommSq",
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.LocalizerMorphism.homMap",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"Ca... | true |
FirstOrder.Language.BoundedFormula.IsQF.toPrenexImpRight | Mathlib.ModelTheory.Complexity | [
"FirstOrder.Language.BoundedFormula.imp",
"FirstOrder.Language.Relations.boundedFormula",
"FirstOrder.Language.BoundedFormula.toPrenexImpRight",
"FirstOrder.Language.Term.bdEqual",
"FirstOrder.Language.Term",
"Sum",
"_private.Mathlib.ModelTheory.Complexity.0.FirstOrder.Language.BoundedFormula.IsQF.toPre... | true |
padicNorm.sum_lt | Mathlib.NumberTheory.Padics.PadicNorm | [
"Rat.addCommMonoid",
"Iff.mpr",
"lt_of_le_of_lt",
"Nat.Prime",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"padicNorm.nonarchimedean",
"Finset",
"Rat",
"PartialOrder.toPreorder",
"Rat.linearOrder",
"Membership.mem",
"Finset.sup'_lt_iff",
"SemilatticeInf.toPartialOrder",
"Fact",
"Distr... | true |
CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transformObjPrecomposeObjSquare_iso_inv_app_snd_app | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.snd",
"CategoryTheory.Functor",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheor... | true |
Matroid.closure_loops_union_eq | Mathlib.Combinatorics.Matroid.Loop | [
"congrArg",
"Set.instUnion",
"Set.union_comm",
"Matroid.closure_union_loops_eq",
"True",
"eq_self",
"Matroid.closure",
"of_eq_true",
"congrFun'",
"Union.union",
"Eq",
"Matroid",
"Eq.trans",
"Matroid.loops",
"Set"
] | true |
CategoryTheory.PreZeroHypercover.inv_hom_h₀ | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.Hom.h₀",
"CategoryTheory.PreZeroHypercover.inv_hom_s₀_apply",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.eqToHom_naturality._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"Exists",
"CategoryTheory.Cat... | true |
AddCommGrpCat.imageIsoRange._proof_1 | Mathlib.Algebra.Category.Grp.Images | [
"CategoryTheory.Limits.HasImages.has_image",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"AddCommGrpCat",
"CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.hasImages_of_hasStrongEpiM... | false |
Lean.Meta.GeneralizeTelescope.generalizeTelescopeAux | Lean.Meta.GeneralizeTelescope | [
"Inhabited.default",
"Lean.Meta.GeneralizeTelescope.Entry",
"Lean.Expr",
"Lean.Meta.MetaM",
"Array",
"Lean.Meta.instInhabitedMetaM",
"Nat"
] | true |
Array.Matcher.Iterator.recOn | Batteries.Data.Array.Match | [
"Array.Matcher.table",
"Array.Matcher.Iterator.rec",
"instOfNatNat",
"Std.Iterator",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Array.Matcher",
"instAddNat",
"Array.Matcher.Iterator",
"Std.IterM",
"Array.PrefixTable.size",
"OfNat.ofNat",
"Fin",
"BEq",
"Array.Matcher.Iterator.mk"
] | false |
EReal.tendsto_toReal | Mathlib.Topology.Instances.EReal.Lemmas | [
"Eq.mpr",
"Real",
"EReal.nhds_coe",
"congrArg",
"Filter.tendsto_id",
"Filter.map",
"EReal.instTopologicalSpace",
"EReal.canLift",
"PseudoMetricSpace.toUniformSpace",
"EReal",
"Filter.tendsto_map'_iff",
"Function.comp",
"Exists",
"nhds",
"instTopEReal",
"id",
"Ne",
"Bot.bot",
"And... | true |
UniformContinuous.prodMk_right | Mathlib.Topology.UniformSpace.Basic | [
"UniformContinuous",
"UniformSpace",
"instUniformSpaceProd",
"UniformContinuous.prodMk",
"Prod.mk",
"uniformContinuous_id",
"uniformContinuous_const",
"UniformContinuous.comp",
"Prod"
] | true |
FinEnum.pempty._proof_1 | Mathlib.Data.FinEnum | [
"Membership.mem",
"PEmpty",
"PEmpty.elim",
"List",
"List.instMembership",
"List.nil"
] | false |
CategoryTheory.SplitEpi.ext_iff | Mathlib.CategoryTheory.EpiMono | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.SplitEpi.section_",
"Eq.casesOn",
"Iff",
"CategoryTheory.SplitEpi.ext",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.SplitEpi",
"Eq.symm",
"Eq",
... | true |
Pi.mulSingle_inv | Mathlib.Algebra.Group.Pi.Lemmas | [
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"Pi.instInv",
"MonoidHom.mulSingle",
"DivisionMonoid.toDivInvOneMonoid",
"DivInvMonoid.toMonoid",
"Pi.divisionMonoid",
"Group.toDivInvMonoid",
"Inv.inv",
"MonoidHom.map_inv",
"I... | true |
_private.Init.Data.List.Lemmas.0.List.singleton_eq_append_iff._simp_1_1 | Init.Data.List.Lemmas | [
"eq_comm",
"propext",
"Eq"
] | false |
Set.mulAction._proof_2 | Mathlib.Algebra.Group.Action.Pointwise.Set.Basic | [
"Monoid",
"Semigroup.toMul",
"instHSMul",
"HMul.hMul",
"Set.image2_assoc",
"Set.image2",
"MulAction",
"Monoid.toSemigroup",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Eq",
"SemigroupAction.mul_smul",
"instHMul",
"Set"
] | false |
_private.Mathlib.Order.Interval.Set.WithBotTop.0.WithTop.preimage_coe_Ico._simp_1_1 | Mathlib.Order.Interval.Set.WithBotTop | [
"Set.Ici",
"Set.Ici_inter_Iio",
"Set.instInter",
"Set.Ico",
"Inter.inter",
"Eq.symm",
"Set.Iio",
"Eq",
"Preorder",
"Set"
] | false |
String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher.mk.noConfusion | Init.Data.String.Pattern.Basic | [
"HEq.refl",
"String.Slice",
"id",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher.mk",
"heq_of_eq",
"Eq.refl",
"HEq",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher.noConfusion",
"String.Slice.Pos",
"... | false |
Real.isFiniteMeasure_restrict_Ioc | Mathlib.MeasureTheory.Measure.Lebesgue.Basic | [
"Set.Ioc",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"MeasurableSet",
"ENNReal.ofReal",
"congrArg",
"Real.instSub",
"Set.univ",
"MeasureTheory.MeasureSpace.toMeasurableSpace",
"PartialOrder.toPreorder",
"MeasureTheory.Measure.restrict_apply",
"HSub.hSub",
"Real.measureSpace",
"Me... | true |
NatPow.noConfusionType | Init.Prelude | [
"NatPow",
"Nat",
"HEq",
"NatPow.casesOn"
] | false |
NonUnitalSubsemiring.mem_inf | Mathlib.RingTheory.NonUnitalSubsemiring.Defs | [
"NonUnitalSubsemiring.instMin",
"Iff.rfl",
"Membership.mem",
"And",
"Iff",
"NonUnitalSubsemiring.instSetLike",
"NonUnitalSubsemiring",
"NonUnitalNonAssocSemiring",
"SetLike.instMembership",
"Min.min"
] | true |
HasSubset.mk._flat_ctor | Init.Core | [
"HasSubset.mk",
"HasSubset"
] | false |
AddEquiv.withZeroCongr_symm | Mathlib.Algebra.Group.WithOne.Basic | [
"WithZero.instAdd",
"WithZero",
"AddEquiv",
"Eq",
"AddEquiv.withZeroCongr",
"Add",
"rfl",
"AddEquiv.symm"
] | true |
Submonoid.map_inl | Mathlib.Algebra.Group.Submonoid.Operations | [
"Set.mem_singleton",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"MonoidHom.instFunLike",
"Set.eq_of_mem_singleton",
"MonoidHom",
"MonoidHom.inl",
"Prod.instMulOneClass",
"Membership.mem",
"Eq.rec",
"Bot.bot",
"Submonoid.ext",
"Prod.fst",
"Submonoid.map",
"MulOneClass.toMulOne",
"A... | true |
_private.Lean.Compiler.IR.ToIR.0.Lean.IR.ToIR.lowerAlt.match_1 | Lean.Compiler.IR.ToIR | [
"False",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Array.casesOn",
"Eq.casesOn",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Purity.pure",
"Array",
"Lean.Compiler.LCNF.Code",
"List",
"Lean.Compiler.LCNF.Alt.casesOn",
"Lean.Compiler.LCNF.Alt.alt",
"Lean.Compiler.LCNF.Purity.impu... | false |
CategoryTheory.ShortComplex.LeftHomologyMapData.ofZeros._proof_2 | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.ShortComplex.LeftHomologyData.ofZeros",
"CategoryTheory.Category.... | false |
List.rec | Init.Prelude | [
"List.cons",
"List",
"List.nil"
] | false |
AddEquiv.withBotCongr_toAddHom | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"WithBot",
"AddHom",
"AddHom.withBotMap",
"AddHomClass.toAddHom",
"AddEquiv.withBotCongr",
"AddEquivClass.instAddHomClass",
"AddEquiv.instAddEquivClass",
"AddEquiv",
"WithBot.add",
"AddEquiv.instEquivLike",
"Eq",
"Add",
"rfl",
"EquivLike.toFunLike"
] | true |
Algebra.PreSubmersivePresentation.ofAlgEquiv_toPresentation | Mathlib.RingTheory.Extension.Presentation.Submersive | [
"CommRing",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.PreSubmersivePresentation.toPresentation",
"Algebra.PreSubmersivePresentation.ofAlgEquiv",
"CommRing.toCommSemiring",
"AlgEquiv",
"Algebra.PreSubmersivePresentation",
"Eq.refl",
"Algebra.Presentation.ofAlgEquiv",
"Algebra.Presentation",
... | true |
Array.toListRev_iterM | Std.Data.Iterators.Lemmas.Producers.Monadic.Array | [
"Pure.pure",
"Array.toListRev_eq",
"Std.Iterators.Types.ArrayIterator",
"congrArg",
"Monad.toApplicative",
"Array.iterM",
"Std.IterM.toListRev",
"LawfulMonad",
"instOfNatNat",
"Applicative.toPure",
"Array.toList",
"Array",
"Array.toListRev_iterFromIdxM",
"List",
"Nat",
"congr",
"True... | true |
Choose.choose_modEq_prod_range_choose_nat | Mathlib.Data.Nat.Choose.Lucas | [
"Int.instCommMonoid",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.Prime",
"Nat.choose",
"instHDiv",
"congrArg",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"Choose.choose_modEq_prod_range_choose",
"Int.natCast_modEq_iff",
"cast",
"Fact",
"Int.natCast_modEq_iff._simp_1",
"i... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.insertUnitInvariant_insertRupUnits._simp_1_2 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult | [
"Exists",
"exists_and_right",
"And",
"propext",
"Eq"
] | false |
Metric.cthickening_eq_iInter_cthickening' | Mathlib.Topology.MetricSpace.Thickening | [
"Set.Subset.antisymm",
"Iff.mpr",
"Eq.mpr",
"Set.Ioc",
"Metric.cthickening_mono",
"ENNReal.instAdd",
"lt_add_of_pos_right",
"Real.partialOrder",
"Real",
"ENNReal.ofNNReal",
"Set.Ioi",
"Preorder.toLT",
"Real.instZero",
"ENNReal.ofReal",
"Real.instAddMonoid",
"congrArg",
"instIsLeftCan... | true |
_private.Init.Grind.Ordered.Linarith.0.Lean.Grind.Linarith.le_norm._simp_1_2 | Init.Grind.Ordered.Linarith | [
"HSub.hSub",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Lean.Grind.AddCommMonoid.toAdd",
"Lean.Grind.AddCommGroup.toSub",
"Lean.Grind.AddCommGroup",
"Lean.Grind.AddCommGroup.toAddCommMonoid",
"Lean.Grind.AddCommGroup.toNeg",
"Eq.symm",
"Eq",
"Neg.neg",
"Lean.Grind.AddCommGroup.sub_eq_add_neg"
] | false |
FractionalIdeal.coeIdeal_ne_one | Mathlib.RingTheory.FractionalIdeal.Operations | [
"not_iff_not",
"Iff.mpr",
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"IsFractionRing",
"Algebra",
"nonZeroDivisors",
"Ne",
"Ideal",
"Field.toSemifield",
"Field.toCommRing",
"Submodule.one",
"FractionalIdeal.coeIdeal_eq_one",
"FractionalIdeal",
"CommRing.toCommSemiring"... | true |
mul_inv_le_iff₀' | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"CommMonoidWithZero.toCommMonoid",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Preorder.toLT",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"CommMonoid.toCommSemigroup",
"DivInvOneMonoid.toInvOneClass",
"MulZeroClass.toMul",
"congrArg",
"Iff.rfl",
"P... | true |
SheafOfModules.IsQuasicoherent.nonempty_quasicoherentData._autoParam | Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Module.Baer.instSemilatticeInfExtensionOf | Mathlib.Algebra.Module.Injective | [
"Module.Baer.instPartialOrderExtensionOf",
"Preorder.toLT",
"AddCommGroup.toAddCommMonoid",
"Module.Baer.instSemilatticeInfExtensionOf._proof_3",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup",
"Module.Baer.instSemilatticeInfExtensionOf._proof_2",
"LinearMap",
"Module.Baer.instMinExten... | true |
Prod.instMeasurableSingletonClass | Mathlib.MeasureTheory.MeasurableSpace.Constructions | [
"Set.instSProd",
"MeasurableSet.singleton",
"MeasurableSet",
"SProd.sprod",
"MeasurableSingletonClass",
"Eq.rec",
"Set.instSingletonSet",
"MeasurableSet.prod",
"Prod.mk",
"Set.singleton_prod_singleton",
"MeasurableSpace",
"MeasurableSingletonClass.mk",
"_private.Mathlib.MeasureTheory.Measura... | true |
Quaternion.imI_smul | Mathlib.Algebra.Quaternion | [
"NegZeroClass.toNeg",
"CommRing",
"instHSMul",
"QuaternionAlgebra.imI",
"CommSemiring.toSemiring",
"SMul",
"AddGroupWithOne.toAddMonoidWithOne",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"AddMonoidWithOne.toOne",
"Co... | true |
Function.nontrivial | Mathlib.Logic.Nontrivial.Basic | [
"Nontrivial",
"Nonempty.elim",
"Pi.nontrivial_at",
"Nontrivial.to_nonempty",
"Nonempty"
] | true |
_private.Init.Data.List.Lex.0.List.lex_trans.match_1_3 | Init.Data.List.Lex | [
"List.Lex.casesOn",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"List.Lex.nil",
"List.Lex.rel",
"List.cons",
"List",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"List.ctorIdx",
"List.cons.noConfusion",
"List.Lex",
"List.Lex.cons",
"List.nil"
] | false |
FirstOrder.Field.FieldAxiom | Mathlib.ModelTheory.Algebra.Field.Basic | [
"FirstOrder.Field.FieldAxiom.leftDistrib",
"FirstOrder.Field.FieldAxiom.existsPairNE",
"FirstOrder.Field.FieldAxiom.oneMul",
"FirstOrder.Field.FieldAxiom.mulAssoc",
"FirstOrder.Field.FieldAxiom.zeroAdd",
"FirstOrder.Field.FieldAxiom.mulComm",
"FirstOrder.Field.FieldAxiom.addAssoc",
"FirstOrder.Field.F... | true |
_private.Mathlib.Data.Finset.SDiff.0.Finset.instGeneralizedBooleanAlgebra._proof_6 | Mathlib.Data.Finset.SDiff | [
"Finset.bot_eq_empty",
"Lean.Grind.eq_false_of_not_eq_true",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Lattice.toSemilatticeSup",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Finset",
"OrderBot.toBot",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Lean.Grind.and_eq_of_eq_tr... | false |
IsFreeGroup.Generators | Mathlib.GroupTheory.FreeGroup.IsFreeGroup | [
"Group",
"IsFreeGroup.nonempty_basis",
"FreeGroupBasis",
"Nonempty",
"Exists.choose",
"IsFreeGroup"
] | true |
Lean.Grind.CommRing.Stepwise.inv | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommSemiring.toSemiring",
"Lean.Grind.AddCommMonoid.toZero",
"Int.instNegInt",
"Int",
"Lean.Grind.CommRing.Stepwise.mul_cert",
"Bool.true",
"Lean.Grind.CommRing.toCommSemiring",
"instOfNat",
"Lean.Grind.CommRing.Poly.denote",
"Lean.Grind.CommRing.toRing",
... | true |
_private.Mathlib.LinearAlgebra.Span.Basic.0.Submodule.prod_sup_prod._simp_1_3 | Mathlib.LinearAlgebra.Span.Basic | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
Stream'.Seq.notMem_nil._simp_1 | Mathlib.Data.Seq.Defs | [
"Stream'.Seq",
"False",
"eq_false",
"Membership.mem",
"Stream'.Seq.nil",
"Stream'.Seq.notMem_nil",
"Stream'.Seq.instMembership",
"Eq"
] | false |
IsDiscreteValuationRing.quotient.eq_1 | Mathlib.RingTheory.DiscreteValuationRing.Basic | [
"Semigroup.toMul",
"CommRing",
"Dvd.dvd",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"semigroupDvd",
"Classical.propDecidable",
"SemigroupWithZero.toSemigroup",
"IsDiscreteValuationRing.quotient",
"NonUnitalSemiring.toSemigroupWithZero",
"dite",
"NonUnitalCommSem... | true |
HahnModule.instZero._aux_1 | Mathlib.RingTheory.HahnSeries.Multiplication | [
"SMul",
"HahnModule",
"PartialOrder",
"Pi.instZero",
"HahnSeries.mk",
"HahnSeries.instZero._proof_1",
"Zero.toOfNat0",
"OfNat.ofNat",
"Zero"
] | false |
RingCat.ringObj._aux_13 | Mathlib.Algebra.Category.Ring.Limits | [
"CategoryTheory.Functor",
"Semigroup.toMul",
"RingCat.ring",
"CategoryTheory.Functor.comp",
"Mul",
"RingHom",
"RingCat.instConcreteCategoryRingHomCarrier",
"RingCat",
"RingHom.instFunLike",
"RingCat.instCategory",
"Semiring.toMonoid",
"CategoryTheory.types",
"CategoryTheory.forget",
"Monoi... | false |
HomogeneousLocalization.awayMap | Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization | [
"HomogeneousLocalization.hasPow._proof_2",
"SetLike",
"Function.LeftInverse",
"CommRing",
"HMul.hMul",
"Subring.inclusion",
"Subring.instSetLike",
"HomogeneousLocalization.range_awayMapAux_subset",
"Algebra.algebraMap",
"AddGroupWithOne.toAddGroup",
"HomogeneousLocalization",
"CommSemiring.toS... | true |
Function.Injective.distribSMul | Mathlib.Algebra.GroupWithZero.Action.Defs | [
"instHSMul",
"SMulZeroClass",
"SMul",
"AddMonoidHom.toZeroHom",
"AddZeroClass.toAddZero",
"DistribSMul.mk",
"DistribSMul.toSMulZeroClass",
"Function.Injective.smulZeroClass",
"AddZero.toZero",
"AddZeroClass",
"DistribSMul",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"Function.Injective",
"Fu... | true |
CommRingCat.pushoutCoconeIsColimit._proof_5 | Mathlib.Algebra.Category.Ring.Constructions | [
"Eq.mpr",
"MulOne.toOne",
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingSpan",
"CommRing",
"Algebra.to_smulCommClass",
"DFunLike.congr_fun",
"CommRingCat.hom_ext",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRingCat.Hom.hom",
"AlgHom.algHomClass",
"HMul.hMul",
"CommRingCa... | false |
PiTensorProduct.isEmptyEquiv._proof_5 | Mathlib.LinearAlgebra.PiTensorProduct | [
"PiTensorProduct.instModule",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Semiring.toModule",
"SemilinearMapClass.toMulActionSemiHomClass",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"MultilinearMap.addCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",... | false |
ContinuousMap.instMetrizableSpace | Mathlib.Topology.Metrizable.ContinuousMap | [
"TopologicalSpace.MetrizableSpace.toPseudoMetrizableSpace",
"TopologicalSpace.MetrizableSpace",
"ContinuousMap",
"ContinuousMap.instPseudoMetrizableSpace",
"TopologicalSpace",
"TopologicalSpace.MetrizableSpace.toT0Space",
"TopologicalSpace.MetrizableSpace.mk",
"WeaklyLocallyCompactSpace",
"Continuou... | true |
AlgebraicGeometry.instLocallyQuasiFiniteMorphismRestrict | Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite | [
"CommRing",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"AlgebraicGeometry.IsZariskiLocalAtTarget.restrict",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"CommRingCat",
"PartialOrder.toPreorder",
"TopologicalSpace.O... | true |
CategoryTheory.Functor.lanCompIsoOfPreserves | Mathlib.CategoryTheory.Functor.KanExtension.Preserves | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.HasLeftKanExtension",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.PreservesLeftKanExtensions",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.lan",
"CategoryTheory.Functor... | true |
_private.Mathlib.Topology.Category.Profinite.Nobeling.Successor.0.Profinite.NobelingProof.C0_projOrd._simp_1_2 | Mathlib.Topology.Category.Profinite.Nobeling.Successor | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"not_lt",
"LT.lt",
"propext",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
ProbabilityTheory.Kernel.zero_prod | Mathlib.Probability.Kernel.Composition.Prod | [
"congrArg",
"ProbabilityTheory.Kernel.comp",
"ProbabilityTheory.Kernel.zero_comp",
"MeasurableSpace",
"ProbabilityTheory.Kernel.parallelComp",
"True",
"eq_self",
"of_eq_true",
"Zero.toOfNat0",
"congrFun'",
"Prod",
"OfNat.ofNat",
"Eq",
"ProbabilityTheory.Kernel",
"ProbabilityTheory.Kernel... | true |
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