name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
EuclideanDomain.div_dvd_of_dvd | Mathlib.Algebra.EuclideanDomain.Basic | [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"dvd_zero",
"Semigroup.toMul",
"Dvd.dvd",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"MulZeroClass.toMul",
"congrArg",
"CommSemiring.toSemiring",
"semigroupDv... | true |
MagmaCat.inv_hom_apply | Mathlib.Algebra.Category.Semigrp.Basic | [
"MulHom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Iso",
"MagmaCat.instCategory",
"CategoryTheory.Iso.hom_inv_id_apply",
"True",
"eq_self",
"MulHom.funLike",
"MagmaCat.carrier",
"MagmaCat.str",
"MagmaCat.instConcreteCategoryMulHomCarrier",
"of_eq_true",
"congrFun'... | true |
IsPrimitiveRoot.embeddingsEquivPrimitiveRoots.congr_simp | Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots | [
"IsDomain",
"Nat.instMulZeroClass",
"CommRing",
"CommSemiring.toSemiring",
"AlgHom",
"Finset",
"Algebra",
"Polynomial.cyclotomic",
"IsPrimitiveRoot.embeddingsEquivPrimitiveRoots",
"Membership.mem",
"Field.toDivisionRing",
"Eq.rec",
"Irreducible",
"Set.instSingletonSet",
"Equiv",
"Subty... | true |
_private.Init.Grind.Module.Envelope.0.Lean.Grind.IntModule.OfNatModule.exists_true | Init.Grind.Module.Envelope | [
"trivial",
"Exists",
"Lean.Grind.AddCommMonoid.toZero",
"True",
"Exists.intro",
"Lean.Grind.NatModule",
"Zero.toOfNat0",
"OfNat.ofNat",
"Lean.Grind.NatModule.toAddCommMonoid"
] | true |
_private.Mathlib.Algebra.Star.NonUnitalSubalgebra.0.NonUnitalStarSubalgebra.mem_centralizer_iff._simp_1_4 | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"and_congr_right_iff",
"And",
"Iff",
"propext",
"Eq"
] | false |
_private.Lean.Meta.Tactic.Grind.ForallProp.0.Lean.Meta.Grind.propagateForallPropUp.match_1 | Lean.Meta.Tactic.Grind.ForallProp | [
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Expr.forallE",
"Lean.Name",
"_private.Lean.Meta.Tactic.Grind.ForallProp.0.Lean.Meta.Grind.propagateForallPropUp._sparseCasesOn_1",
"Lean.BinderInfo",
"Lean.Expr.ctorIdx"
] | false |
_private.Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions.0.HasMFDerivAt.prodMap._simp_1_2 | Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | [
"mfderiv",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupTangentSpace",
"Set.univ",
"mfderivWithin",
"NormedField.toField",
"instModuleTangentSpace",
"mfderivWithin_univ",
"Field.toSemifield",
"instTopologicalSpaceTangentSpace",
"ContinuousLinearMap",
"TopologicalSpace",
... | false |
min_left_comm | Mathlib.Order.Defs.LinearOrder | [
"Eq.mpr",
"congrArg",
"min_comm",
"LinearOrder",
"id",
"min_assoc",
"Eq.refl",
"LinearOrder.toMin",
"Eq.symm",
"Eq",
"Min.min"
] | true |
ContinuousMap.HomotopyEquiv.trans._proof_2 | Mathlib.Topology.Homotopy.Equiv | [
"ContinuousMap.Homotopic.comp",
"ContinuousMap.HomotopyEquiv.right_inv",
"ContinuousMap.HomotopyEquiv.invFun",
"ContinuousMap.comp",
"TopologicalSpace",
"ContinuousMap.id",
"ContinuousMap.HomotopyEquiv.toFun",
"ContinuousMap.Homotopic.trans",
"ContinuousMap.HomotopyEquiv",
"ContinuousMap.Homotopic... | false |
LinearMap.mul_toMatrix₂_mul | Mathlib.LinearAlgebra.Matrix.SesquilinearForm | [
"Eq.mpr",
"Matrix.toLin",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"HMul.hMul",
"Matrix.module",
"Matrix.transpose_transpose",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Matrix",
"LinearMap.instSMulCommClass",
"Matrix.instHMulOfFintypeOfMulOfAddCommMono... | true |
TestFunction.monoCLM_apply | Mathlib.Analysis.Distribution.TestFunction | [
"ContinuousLinearMap.comp",
"TestFunction.instZero",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"instLinearOrderENat",
"TopologicalSpace.Opens.instPartialOrder",
"TestFunction.toTestF... | true |
Lean.Elab.Level.instMonadRefLevelElabM | Lean.Elab.Level | [
"Pure.pure",
"Lean.Elab.Level.Context.ref",
"Lean.Elab.Level.Context.autoBoundImplicit",
"instMonadReaderOfReaderTOfMonad",
"EStateM.instMonad",
"MonadReader.read",
"Lean.Syntax",
"ReaderT.instMonad",
"Lean.Elab.Level.Context.options",
"instMonadWithReaderOfMonadWithReaderOf",
"Lean.Elab.Level.C... | true |
DivisibleHull.instLinearOrder._proof_7 | Mathlib.GroupTheory.DivisibleHull | [
"PNat.val",
"LocalizedModule.liftOn₂",
"instHSMul",
"Submonoid.mul",
"instLinearOrderPNat",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"LinearOrder",
"DecidableRel",
"PartialOrder.toPreorder",
"AddMonoid.toNSMul",
"Preorder.toLE",
"DivisibleHull",
"Membership.mem",
"nonZeroDiviso... | false |
Subring.closure_union | Mathlib.Algebra.Ring.Subring.Basic | [
"Lattice.toSemilatticeSup",
"Subring.instSetLike",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Set.instUnion",
"SemilatticeSup.toMax",
"NonAssocRing",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"SetLike.coe",
"Subring",
"Max.max",
"Subri... | true |
LinearEquiv.funCongrLeft._proof_3 | Mathlib.Algebra.Module.Equiv.Basic | [
"LinearMap.id",
"Pi.Function.module",
"Pi.addCommMonoid",
"Equiv.instEquivLike",
"LinearMap.ext",
"LinearMap.instFunLike",
"RingHomInvPair.triples₂",
"Equiv",
"LinearEquiv.automorphismGroup._proof_7",
"LinearMap",
"AddCommMonoid",
"funext",
"LinearMap.comp",
"LinearMap.funLeft",
"RingHom... | false |
Quiver.FreeGroupoid.lift_spec | Mathlib.CategoryTheory.Groupoid.FreeGroupoid | [
"Eq.mpr",
"CategoryTheory.Functor",
"Quiver.Symmetrify.lift",
"Quiver.Symmetrify.lift_spec",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Quotient",
"congrArg",
"CategoryTheory.Quotient.category",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"Quiver.symmetrifyQuiver... | true |
Int.one_bmod | Init.Data.Int.DivMod.Lemmas | [
"Eq.mpr",
"Int.instDiv",
"instHDiv",
"congrArg",
"Int.bmod_eq_emod_of_lt",
"Int.instDecidableEq",
"_private.Init.Data.Int.DivMod.Lemmas.0.Int.one_bmod._proof_1_2",
"id",
"HDiv.hDiv",
"instHMod",
"instOfNatNat",
"Int",
"LE.le",
"instLENat",
"Nat.cast",
"Int.instLTInt",
"instHAdd",
"... | true |
Std.Sat.AIG.RefVec.get_push_ref_eq' | Std.Sat.AIG.RefVec | [
"Std.Sat.AIG.RefVec.get",
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.Fanin.gate",
"Std.Sat.AIG.Ref.mk",
"Vector.push",
"Vector",
"Std.Sat.AIG.RefVec.push",
"congrArg",
"Vector.instGetElemNatLt",
"Std.Sat.AIG.Fanin.mk",
"GetElem.getElem.congr_simp",
"Std.Sat.AIG.Fanin.invert",
"id",
"Vector.getElem_p... | true |
Finset.prod_finset_product_right' | Mathlib.Algebra.BigOperators.Group.Finset.Sigma | [
"Finset",
"Membership.mem",
"Prod.fst",
"Finset.prod",
"Finset.prod_finset_product_right",
"And",
"Iff",
"Finset.instSetLike",
"Prod",
"Eq",
"CommMonoid",
"Prod.snd",
"SetLike.instMembership"
] | true |
_private.Mathlib.Order.WithBot.0.WithBot.forall_coe_le_iff_le._simp_1_1 | Mathlib.Order.WithBot | [
"WithBot.instPreorder",
"WithBot.some",
"WithBot",
"Preorder.toLE",
"WithBot.eq_bot_iff_forall_le",
"Bot.bot",
"LE.le",
"NoBotOrder",
"propext",
"Eq",
"WithBot.bot",
"Preorder"
] | false |
CategoryTheory.Bimon.ofMonComonObj_comon_counit_hom | Mathlib.CategoryTheory.Monoidal.Bimon_ | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bimon.ofMonComonObjX",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.ComonObj.counit",
"CategoryTheory.Mon.monMonoidal",
"CategoryTheory.BraidedCategory",
"CategoryTheory.Comon.instCategory",
... | true |
Aesop.Goal.traceTreeCore | Aesop.Tree.Tracing | [
"Inhabited.default",
"Aesop.Goal",
"Lean.Meta.MetaM",
"Aesop.TraceOption",
"Unit",
"Lean.Meta.instInhabitedMetaM"
] | true |
CategoryTheory.Functor.ShiftSequence.shiftIso_zero | Mathlib.CategoryTheory.Shift.ShiftSequence | [
"CategoryTheory.Functor",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Functor.ShiftSequence",
"CategoryTheory.Functor.id",
"CategoryTheory.shiftFunctorZero",
"AddZeroClass.toAddZero",
"CategoryTheory.I... | true |
AddMonoidHom.restrictHom._proof_2 | Mathlib.Algebra.Group.Submonoid.Operations | [
"SetLike",
"AddMonoidHom.restrict",
"AddSubmonoidClass.toAddZeroClass",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddSubmonoidClass",
"AddZeroClass.toAddZero",
"Subtype",
"AddMonoidHom.instAddCommMonoid",
"AddMonoidHom.ext",
"AddCommMonoid",
"instHAdd",
"AddZeroClass",
"HAdd.hAdd",
... | false |
Mathlib.Tactic.Monoidal.instMonadMor₂MonoidalM.match_3 | Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Mathlib.Tactic.Monoidal.instMonadMor₁MonoidalM._sparseCasesOn_1",
"Mathlib.Tactic.BicategoryLike.IsoLift",
"Option"
] | false |
Option.get_bind | Init.Data.Option.Lemmas | [
"False.elim",
"Option.casesOn",
"noConfusion_of_Nat",
"Option.some",
"Option.bind",
"Bool.ctorIdx",
"Bool.true",
"Option.none",
"Option.get",
"Option.isSome_of_isSome_bind",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Option.isSome",
"Eq.symm",
"Eq",
"Option.isSome_apply_of_isSome_bind",
"Opti... | true |
Lean.Server.Reference.mk.noConfusion | Lean.Server.References | [
"Lean.Syntax",
"Lean.Server.Reference",
"id",
"Lean.Server.Reference.noConfusion",
"Lean.Elab.ContextInfo",
"Array",
"Bool",
"Lean.Lsp.Range",
"Lean.Elab.Info",
"Eq",
"Lean.Lsp.RefIdent",
"Lean.Server.Reference.mk"
] | false |
Algebra.cardinalMk_adjoin_le | Mathlib.Algebra.FreeAlgebra.Cardinality | [
"Subalgebra.instSetLike",
"Algebra.lift_cardinalMk_adjoin_le",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Cardinal.lift",
"Algebra",
"Preorder.toLE",
"Algebra.adjoin",
"Cardinal.mk",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Semila... | true |
CategoryTheory.Sum.associativityFunctorEquivNaturalityFunctorIso_hom_app_snd_snd | Mathlib.CategoryTheory.Sums.Products | [
"CategoryTheory.Functor",
"CategoryTheory.sum",
"CategoryTheory.sum.associativity",
"CategoryTheory.Equivalence.prod",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Equivalence.congrLeft",
"CategoryTheory.Equivalence.refl",
"CategoryTheory.sum.inrCompInrCompInverseAssociato... | true |
_private.Mathlib.Topology.Instances.ENNReal.Lemmas.0.ENNReal.continuous_pow._simp_1_5 | Mathlib.Topology.Instances.ENNReal.Lemmas | [
"CommSemiring.toSemiring",
"Ne",
"instOfNatNat",
"ENNReal.instCommSemiring",
"Monoid.toPow",
"And",
"HPow.hPow",
"Nat",
"ENNReal",
"Semiring.toMonoid",
"propext",
"ENNReal.instTop",
"instHPow",
"Top.top",
"OfNat.ofNat",
"Eq",
"ENNReal.pow_eq_top_iff"
] | false |
OrderDual.instRightCancelSemigroup._proof_1 | Mathlib.Algebra.Order.Group.Synonym | [
"Semigroup.toMul",
"OrderDual.instIsRightCancelMul",
"RightCancelSemigroup.toSemigroup",
"OrderDual.instMul",
"OrderDual",
"RightCancelSemigroup",
"RightCancelSemigroup.toIsRightCancelMul",
"IsRightCancelMul"
] | false |
AlgebraicGeometry.Scheme.Cover.RelativeGluingData | Mathlib.AlgebraicGeometry.RelativeGluing | [
"AlgebraicGeometry.Scheme.Cover.RelativeGluingData.mk",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.Scheme.OpenCover",
"CategoryTheory.PreZeroHypercover.I₀",
"AlgebraicGeometry.IsOpenImmersion",
"AlgebraicGeometry.Scheme.instCategory",
"AlgebraicGeometry.Scheme.precoverage",
"CategoryTheory.Precove... | true |
_private.Mathlib.Topology.Algebra.ProperAction.Basic.0.properSMul_iff_continuousSMul_ultrafilter_tendsto.match_1_1 | Mathlib.Topology.Algebra.ProperAction.Basic | [
"instHSMul",
"ContinuousSMul",
"instTopologicalSpaceProd",
"Group",
"Exists",
"nhds",
"DivInvMonoid.toMonoid",
"Prod.mk",
"Prod.fst",
"And.casesOn",
"Group.toDivInvMonoid",
"TopologicalSpace",
"And",
"Filter.Tendsto",
"MulAction",
"And.intro",
"Monoid.toSemigroup",
"HSMul.hSMul",
... | false |
Module.AEval.instAddCommGroup._proof_3 | Mathlib.Algebra.Polynomial.Module.AEval | [
"AddMonoid.toAddSemigroup",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Module.AEval",
"Algebra",
"AddCommGroup.toAddGroup",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul... | false |
Lean.Grind.Field.mk.noConfusion | Init.Grind.Ring.Field | [
"instHDiv",
"Inv",
"HMul.hMul",
"Lean.Grind.Field.noConfusion",
"id",
"HDiv.hDiv",
"Div",
"Int.instNegInt",
"Ne",
"Int",
"Lean.Grind.Semiring.toMul",
"Nat.cast",
"Lean.Grind.Field",
"Lean.Grind.Semiring.ofNat",
"instHAdd",
"Lean.Grind.Field.mk",
"heq_of_eq",
"Inv.inv",
"HPow.hPow... | false |
Valued.valueGroup₀_equiv_extensionValuation | Mathlib.Topology.Algebra.Valued.ValuedField | [
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Valued.valueGroup₀_equiv_extensionValuation._proof_2",
"Valued.valueGroup₀_equiv_extensionValuation._proof_1",
"ValuationClass.toMonoidWithZeroHomClass",
"MulZeroClass.toMul",
"Monoid.toMulOneClass",
... | true |
CStarMatrix.instTopologicalSpace._aux_1 | Mathlib.Analysis.CStarAlgebra.CStarMatrix | [
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"PseudoMetricSpace.toUniformSpace",
"CStarMatrix",
"TopologicalSpace",
"NonUnitalSeminormedRing.toPseudoMetricSpace",
"instTopologicalSpaceMatrix",
"NonUnitalCStarAlgebra",
"NonUnitalNormedRing.toNonUnitalSeminormedRing",
"UniformSpace.toTopologicalSpac... | false |
PrimeSpectrum.piLocalizationToMaximal_bijective | Mathlib.RingTheory.Spectrum.Maximal.Localization | [
"MaximalSpectrum.asIdeal",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"OreLocalization.instAlgebra",
"PrimeSpectrum.isPrime",
"CommSemiring.toSemiring",
"AlgHom",
"Localization.AtPrime",
"AlgHom.funLike",
"PrimeSpectrum.PiLocalization",
"Algebra.id",
"Localization",
"Add... | true |
Lean.Elab.Command.ElabHeaderResult.indFVar | Lean.Elab.MutualInductive | [
"Lean.Expr",
"Lean.Elab.Command.ElabHeaderResult"
] | true |
Lean.Order.ReverseImplicationOrder.instCompleteLattice | Init.Internal.Order.Basic | [
"Lean.Order.ReverseImplicationOrder",
"Lean.Order.CompleteLattice",
"Lean.Order.ReverseImplicationOrder.instOrder",
"Lean.Order.ReverseImplicationOrder.instCompleteLattice._proof_1",
"Lean.Order.CompleteLattice.mk"
] | true |
BoxIntegral.Prepartition.iUnion_disjUnion | Mathlib.Analysis.BoxIntegral.Partition.Basic | [
"Real",
"Finset.instUnion",
"BoxIntegral.Prepartition",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Iff.of_eq",
"congrArg",
"BoxIntegral.Box.toSet",
"Finset",
"Set.iUnion_union_distrib",
"BoxIntegral.Prepartition.mem_boxes._simp_1",
"Classical.propDecidable",
"Disjoint",
"Membership.... | true |
CFC.exp_log | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic | [
"Eq.mpr",
"IsSelfAdjoint",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"NormedRing.toRing",
"spectrum",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"Real.instZero",
"congrArg",
"cfc",
"ContinuousOn.log",
"Norme... | true |
Primrec.option_guard | Mathlib.Computability.Primrec.Basic | [
"Iff.mpr",
"Eq.mpr",
"Option.guard",
"PrimrecRel",
"congrArg",
"DecidableRel",
"Option.some",
"id",
"PrimrecRel.comp",
"instDecidableEqBool",
"Primrec.const",
"Primrec",
"Bool.true",
"funext",
"Option.none",
"Primrec.option_some_iff",
"Primcodable",
"Bool",
"decide_eq_true_eq",
... | true |
Subsemigroup.centerCongr_symm_apply_coe | Mathlib.GroupTheory.Submonoid.Center | [
"MulEquiv.instEquivLike",
"Subsemigroup.centerCongr",
"Subsemigroup.center.commSemigroup",
"Mul",
"Membership.mem",
"Subtype",
"CommMagma.toMul",
"Subsemigroup",
"CommSemigroup.toCommMagma",
"MulEquiv",
"Eq.refl",
"MulEquiv.symm",
"Subsemigroup.instSetLike",
"Subtype.val",
"Eq",
"DFunL... | true |
TopologicalSpace.ext_iff_nhds | Mathlib.Topology.Neighborhoods | [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"nhds",
"id",
"TopologicalSpace.ext",
"LE.le",
"iff_self",
"TopologicalSpace",
"funext",
"Iff",
"congrFun",
"implies_congr",
"congr",
"True",
"Iff.intro",
"propext",
"of_eq_true",
"Filter.prin... | true |
Lean.KeyedDeclsAttribute.AttributeEntry.mk.sizeOf_spec | Lean.KeyedDeclsAttribute | [
"Lean.KeyedDeclsAttribute.AttributeEntry.mk",
"instOfNatNat",
"Lean.KeyedDeclsAttribute.AttributeEntry",
"instHAdd",
"HAdd.hAdd",
"Lean.KeyedDeclsAttribute.OLeanEntry._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"Bool",
"instAddNat",
"Eq.refl",
"SizeOf",
"OfNat.ofNat",
"Lean.KeyedDeclsAttribute.... | true |
Stream'.cons.match_1 | Mathlib.Data.Stream.Defs | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
HomologicalComplex.truncGEXIsoOpcycles | Mathlib.Algebra.Homology.Embedding.TruncGE | [
"ComplexShape.Embedding.BoundaryGE",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.HasHomology",
"HomologicalComplex.truncGE",
"HomologicalComplex.opcycles",
"HomologicalComplex",
"CategoryTheory.Iso",
"ComplexShape",
"CategoryTheory.Iso.trans",
"ComplexShape.Embedding.IsTruncGE",
... | true |
CircleDeg1Lift.strictMono_iff_injective | Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | [
"Real.partialOrder",
"Real",
"StrictMono",
"Monotone.strictMono_iff_injective",
"CircleDeg1Lift.instFunLikeReal",
"Iff",
"CircleDeg1Lift.monotone",
"Function.Injective",
"DFunLike.coe",
"CircleDeg1Lift",
"Real.instPreorder",
"Real.linearOrder"
] | true |
AddEquiv.toIntLinearEquiv_refl | Mathlib.Algebra.Module.Equiv.Basic | [
"AddEquiv.toIntLinearEquiv",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"Int",
"RingHomInvPair.ids",
"AddEquiv.refl",
"LinearEquiv",
"LinearEquiv.refl",
"AddCommSemigroup.toAddCommMagma",
"Module",
"AddCommMonoid.toAddCommSemigroup",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
... | true |
_private.Mathlib.AlgebraicTopology.DoldKan.NCompGamma.0.AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero._proof_1_10 | Mathlib.AlgebraicTopology.DoldKan.NCompGamma | [
"Lean.RArray.leaf",
"False",
"of_decide_eq_true",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Lean.RArray.branch",
"id",
"False.casesOn",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.Linear.Expr.num",
"Fin.val",
"Bool.true",
"instHAdd",
"AddSemigroup.toA... | false |
AddEquiv.isSimpleAddGroup | Mathlib.GroupTheory.Subgroup.Simple | [
"Equiv.nontrivial",
"AddMonoid.toAddZeroClass",
"AddEquiv.toAddMonoidHom",
"AddZeroClass.toAddZero",
"IsSimpleAddGroup.isSimpleAddGroup_of_surjective",
"AddEquiv.surjective",
"AddGroup",
"AddGroup.toSubNegMonoid",
"AddEquiv",
"AddZero.toAdd",
"IsSimpleAddGroup.toNontrivial",
"IsSimpleAddGroup"... | true |
CategoryTheory.Limits.WidePullbackShape.equivalenceOfEquiv._proof_6 | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Functor.comp",
"Option.some",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Functor.id",
"Equiv",
"CategoryTheory.Limits.WidePullbackShape.Hom.term",
"Cat... | false |
WithTop.orderIsoSumLexPUnit_toLex | Mathlib.Data.Sum.Order | [
"Sum.Lex.LE",
"Equiv.instEquivLike",
"Lex",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"WithTop.orderIsoSumLexPUnit",
"Sum",
"Equiv",
"OrderIso",
"Sum.inl",
"BiheytingAlgebra.toCoheytingAlgebra",
"WithTop.some",
"LE",
"PUnit.instBiheytingAlgebra",
"ins... | true |
_private.Std.Data.DHashMap.Internal.Model.0.Std.DHashMap.Internal.Raw₀.Const.insertListₘ.match_1.eq_1 | Std.Data.DHashMap.Internal.Model | [
"Unit.unit",
"Std.DHashMap.Internal.Raw₀.Const.insertListₘ.match_1",
"List.cons",
"List",
"Unit",
"Eq.refl",
"Prod",
"Eq",
"List.nil"
] | true |
BitVec.rotateRight | Init.Data.BitVec.Basic | [
"BitVec",
"Nat.instMod",
"instHMod",
"HMod.hMod",
"Nat",
"BitVec.rotateRightAux"
] | true |
nhdsSet | Mathlib.Topology.Defs.Filter | [
"Filter.instSupSet",
"nhds",
"TopologicalSpace",
"Set.image",
"Filter",
"SupSet.sSup",
"Set"
] | true |
Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.cooper₂.injEq | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Eq.propIntro",
"Lean.Meta.Grind.Arith.Cutsat.CooperSplit",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.cooper₂.inj",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.cooper₂",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
Lean.Meta.KExprMap.insert | Lean.Meta.KExprMap | [
"Pure.pure",
"Lean.AssocList.nil",
"Lean.AssocList.cons",
"Lean.Meta.KExprMap.mk",
"Lean.Meta.State",
"Lean.instBEqHeadIndex",
"Lean.Meta.KExprMap.map",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Applicative.toPure",
"Lean.PersistentHashMap.insert",
"Lean.Expr.toHeadIndex",
"Lean.ins... | true |
CharTwo.sum_sq | Mathlib.Algebra.CharP.Two | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoidHom.instAddMonoidHomClass",
"CommSemiring.toSemiring",
"Finset",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"map_sum",
"Monoid.toPow",
"CommSemiring",
"NonUnitalNonAssocSe... | true |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.ediv_lt_ediv_iff_of_dvd_of_pos_of_neg._simp_1_1 | Init.Data.Int.DivMod.Lemmas | [
"False",
"eq_false",
"Int.ne_of_lt",
"Int",
"Int.instLTInt",
"LT.lt",
"Eq"
] | false |
Std.Do._aux_Std_Do_PostCond___unexpand_Std_Do_ExceptConds_imp_1 | Std.Do.PostCond | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
HasFibers.Fib.isoMk._proof_1 | Mathlib.CategoryTheory.FiberedCategory.HasFibers | [
"HasFibers",
"CategoryTheory.Functor",
"CategoryTheory.Functor.IsHomLift",
"CategoryTheory.CategoryStruct.id",
"HasFibers.category",
"CategoryTheory.Iso",
"HasFibers.Fib",
"HasFibers.ι",
"CategoryTheory.IsHomLift.lift_id_inv",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Iso.hom",... | false |
Lean.Core.mkFreshUserName | Lean.CoreM | [
"_private.Lean.CoreM.0.Lean.Core.mkFreshNameImp",
"Lean.Core.CoreM",
"Lean.Name"
] | true |
CategoryTheory.PreZeroHypercover.inv_inv_h₀_comp_f | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.Hom.h₀",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.IsIso.inv_comp_eq._simp_2",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.PreZeroHypercover.Hom.w₀",
"CategoryTheory.Iso",
"CategoryTheory.PreZeroHypercover.X",
"C... | true |
_private.Mathlib.CategoryTheory.Limits.Preserves.Creates.Opposites.0.CategoryTheory.Limits.createsLimitOfRightOp._proof_1 | Mathlib.CategoryTheory.Limits.Preserves.Creates.Opposites | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.ReflectsLimit",
"CategoryTheory.CreatesColimit.toReflectsColimit",
"CategoryTheory.Limits.reflectsLimit_of_rightOp",
"CategoryTheory.CreatesColimit",
"CategoryTheory.Category.opposite",
"CategoryTheory.Functor.rightOp",
"CategoryTheory.Fun... | false |
IsLocalization.algEquivOfAlgEquiv._proof_4 | Mathlib.RingTheory.Localization.Basic | [
"RingEquiv.toEquiv",
"IsLocalization",
"CommSemiring.toSemiring",
"Algebra",
"RingEquiv.map_add'",
"Distrib.toAdd",
"Equiv.toFun",
"IsLocalization.ringEquivOfRingEquiv",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"Submonoid.map",
"instMulZeroOneClassOfSemiring",
"CommSemiring"... | false |
LinearPMap.HasCore.recOn | Mathlib.Topology.Algebra.Module.LinearPMap | [
"Submodule",
"CommRing",
"ContinuousSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"LinearPMap.closure",
"LinearPMap.HasCore.mk",
"AddZeroCl... | false |
AlexDisc._sizeOf_inst | Mathlib.Topology.Order.Category.AlexDisc | [
"AlexDisc",
"SizeOf.mk",
"SizeOf",
"AlexDisc._sizeOf_1"
] | false |
CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct | Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"LinearOrder",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Preorder.smallCategory",
"B... | true |
NONote.instMul._proof_1 | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.NF",
"ONote.instMul",
"HMul.hMul",
"ONote.mul_nf",
"NONote",
"Subtype.val",
"ONote",
"NONote.NF",
"instHMul"
] | false |
String.Pos.toSlice_lt_toSlice_iff | Init.Data.String.Basic | [
"String.toSlice",
"String",
"Iff.rfl",
"String.Pos.toSlice",
"Iff",
"String.instLTPos",
"LT.lt",
"String.instLTPos_1",
"String.Pos",
"String.Slice.Pos"
] | true |
_private.Mathlib.Algebra.Module.ZLattice.Basic.0.ZLattice.comap_equiv._simp_6 | Mathlib.Algebra.Module.ZLattice.Basic | [
"Subtype",
"Subtype.ext_iff",
"propext",
"Subtype.val",
"Eq"
] | false |
Diffeomorph.prodCongr_symm | Mathlib.Geometry.Manifold.Diffeomorph | [
"Diffeomorph.symm",
"Prod.normedSpace",
"Prod.normedAddCommGroup",
"NormedSpace",
"instTopologicalSpaceProd",
"instTopologicalSpaceModelProd",
"Diffeomorph",
"TopologicalSpace",
"ModelWithCorners",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"prodChartedSpace"... | true |
ProbabilityTheory.integrable_condCDF | Mathlib.Probability.Kernel.Disintegration.CondCDF | [
"Unit.unit",
"NormedCommRing.toSeminormedCommRing",
"Real",
"MeasureTheory.Measure",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.Integrable",
"StieltjesFunction.toFun",
"SeminormedAddGroup.toContinuousENorm",
"MeasurableSpace",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"ProbabilityTh... | true |
_private.Batteries.Data.List.Lemmas.0.List.getElem_filter_eq_getElem_getElem_findIdxs_sub._proof_1_4 | Batteries.Data.List.Lemmas | [
"Lean.Grind.Nat.lt_eq",
"Eq.mp",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"List.filter",
"LT.lt",
"Bool",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"List.length",
"_private.Batteries.Data.List.Lemmas.0.List.getElem_filter_eq_getElem_getElem_findIdxs_sub._pr... | false |
Lean.Grind.IntModule | Init.Grind.Module.Basic | [
"Lean.Grind.IntModule.mk"
] | true |
CategoryTheory.epi_comp' | Mathlib.CategoryTheory.Category.Basic | [
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.epi_comp",
"inferInstance",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
List.isChain_split | Mathlib.Data.List.Chain | [
"_private.Mathlib.Data.List.Chain.0.List.isChain_split._proof_1_3",
"List.IsChain",
"List.cons",
"instHAppendOfAppend",
"_private.Mathlib.Data.List.Chain.0.List.isChain_split._proof_1_2",
"List",
"And",
"Iff",
"List.twoStepInduction",
"List.instAppend",
"_private.Mathlib.Data.List.Chain.0.List.i... | true |
MeasureTheory.stronglyMeasurable_zero | Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic | [
"MeasureTheory.stronglyMeasurable_const",
"Zero.zero",
"Pi.instZero",
"MeasurableSpace",
"TopologicalSpace",
"Zero.toOfNat0",
"MeasureTheory.StronglyMeasurable",
"OfNat.ofNat",
"Zero"
] | true |
Order.Ideal.instInhabited | Mathlib.Order.Ideal | [
"Inhabited.default",
"Preorder.toLE",
"Order.Ideal.principal",
"Inhabited",
"Order.Ideal",
"Preorder",
"Inhabited.mk"
] | true |
_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.Extension.addEMatchAttr.match_1 | Lean.Meta.Tactic.Grind.EMatchTheorem | [
"Lean.Meta.Grind.EMatchTheoremKind.ctorIdx",
"Nat.hasNotBit",
"_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.Extension.addEMatchAttr._sparseCasesOn_1",
"Lean.Meta.Grind.EMatchTheoremKind",
"Lean.Meta.Grind.EMatchTheoremKind.eqBoth",
"Lean.Meta.Grind.EMatchTheoremKind.eqLhs",
"Bool",
... | false |
Subtype.semilatticeInf._proof_3 | Mathlib.Order.Lattice | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"inf_le_right",
"SemilatticeInf.toPartialOrder",
"Subtype",
"SemilatticeInf.toMin",
"LE.le",
"SemilatticeInf",
"Subtype.val",
"Min.min"
] | false |
IsLeftRegular.mul_left_eq_zero_iff | Mathlib.Algebra.GroupWithZero.Regular | [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"MulZeroClass",
"Eq.rec",
"id",
"MulZeroClass.mul_zero",
"IsLeftRegular",
"Iff",
"Iff.intro",
"Zero.toOfNat0",
"Eq.refl",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Eq.trans",
"MulZeroClass.toZero",
"instHMul"
] | true |
FreeGroup.lift._proof_1 | Mathlib.GroupTheory.FreeGroup.Basic | [
"cond",
"MulOne.toOne",
"FreeGroup.Red.Step",
"InvOneClass.toOne",
"List.prod_append",
"HMul.hMul",
"Semigroup.to_isAssociative",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"List.map",
"Quot.ind",
"Group",
"FreeGroup.Lift.aux",
"Group.toDivisionMonoid",
"Divis... | false |
Sym2.coe_lift₂_symm_apply | Mathlib.Data.Sym.Sym2 | [
"Equiv.instEquivLike",
"Sym2.mk",
"Sym2.lift₂",
"Equiv",
"Subtype",
"And",
"Equiv.symm",
"Subtype.val",
"Eq",
"DFunLike.coe",
"Sym2",
"rfl",
"EquivLike.toFunLike"
] | true |
Complex.instNNRatCast | Mathlib.Data.Complex.Basic | [
"Real.instNNRatCast",
"Real",
"NNRatCast",
"NNRatCast.mk",
"NNRat",
"Complex.ofReal",
"Complex",
"NNRat.cast"
] | true |
Booleanisation.instSemilatticeSup | Mathlib.Order.Booleanisation | [
"SemilatticeSup.mk",
"Booleanisation",
"Booleanisation.instPartialOrder",
"Booleanisation.instSup",
"Max.max",
"GeneralizedBooleanAlgebra",
"Booleanisation.instSemilatticeSup._proof_3",
"Booleanisation.instSemilatticeSup._proof_2",
"Booleanisation.instSemilatticeSup._proof_1",
"SemilatticeSup"
] | true |
LocallyFiniteOrder.mk.noConfusion | Mathlib.Order.Interval.Finset.Defs | [
"Preorder.toLT",
"HEq.refl",
"Finset",
"Preorder.toLE",
"Membership.mem",
"id",
"LE.le",
"LocallyFiniteOrder.noConfusion",
"And",
"heq_of_eq",
"Iff",
"Finset.instSetLike",
"LT.lt",
"LocallyFiniteOrder.mk",
"LocallyFiniteOrder",
"Eq.refl",
"HEq",
"Eq",
"SetLike.instMembership",
... | false |
GradedMonoid.GradeZero.monoid._proof_3 | Mathlib.Algebra.GradedMonoid | [
"instHSMul",
"HMul.hMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"GradedMonoid.mk_zero_smul",
"GradedMonoid.GMonoid",
"GradedMonoid.GMonoid.toGMul",
"AddZero.toZero",
"GradedMonoid.GradeZero.smul",
"AddMonoid",
"GradedMonoid",
"AddZero.toAdd",
"Zero.toOfNat0",
"HSMul.hSMul",... | false |
Metric.Snowflaking.image_toSnowflaking_closedEBall | Mathlib.Topology.MetricSpace.Snowflaking | [
"Eq.mpr",
"Real.instLE",
"Real",
"Equiv.instEquivLike",
"Metric.Snowflaking.instPseudoEMetricSpace",
"Metric.Snowflaking.toSnowflaking",
"Real.instZero",
"congrArg",
"ENNReal.instPowReal",
"Real.instLT",
"id",
"Equiv",
"LE.le",
"PseudoEMetricSpace",
"Metric.Snowflaking.image_toSnowflakin... | true |
_private.Mathlib.LinearAlgebra.LinearIndependent.Lemmas.0.Fintype.linearIndependent_iff'._simp_1_3 | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | [
"funext_iff",
"propext",
"Eq"
] | false |
Polynomial.evalEval_multiset_prod | Mathlib.Algebra.Polynomial.Bivariate | [
"Polynomial.eval_multiset_prod",
"Polynomial.C",
"Polynomial.eval",
"Multiset.map",
"congrArg",
"CommSemiring.toSemiring",
"Multiset.prod",
"RingHom",
"Function.comp",
"Membership.mem",
"Multiset",
"Polynomial",
"Polynomial.evalEval",
"CommSemiring",
"Multiset.instMembership",
"RingHom... | true |
instRingCliffordAlgebra._proof_41 | Mathlib.LinearAlgebra.CliffordAlgebra.Basic | [
"CommRing",
"CliffordAlgebra.Rel",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"QuadraticForm",
"AddCommGroup",
"TensorAlgebra",
"Int",
"Nat.cast",
"autoParam",
"TensorAlgebra.instRing",
"CommRing.toCommSemiring",
"Nat",
"instRingCliffordAlgebra._aux_37"... | false |
«term_++_» | Init.Notation | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
MeasureTheory.Measure.hausdorffMeasure_mono | Mathlib.MeasureTheory.Measure.Hausdorff | [
"ENNReal.instCanonicallyOrderedAdd",
"LE.le.eq_or_lt",
"Real.partialOrder",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"le_rfl",
"congrArg",
"instIsBotZeroClass",
"zero_le._simp_1",
"le_top._simp_2",
"AddMonoid.toAddZeroClass",
"MeasureTheory.Measure.hausdorffMeasure"... | true |
Finmap.mk.injEq | Mathlib.Data.Finmap | [
"Eq.propIntro",
"Finmap.mk",
"Finmap.mk.inj",
"Multiset",
"Multiset.NodupKeys",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Sigma",
"Finmap"
] | true |
_private.Mathlib.CategoryTheory.ConnectedComponents.0.CategoryTheory.instIsConnectedComponent._proof_5 | Mathlib.CategoryTheory.ConnectedComponents | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Lean.Grind.nestedProof",
"HSub.hSub",
"Quotient.mk''",
"Membership.mem",
"instSubNat",
"instOfNatNat",
"CategoryTheory.Zigzag",
"Quotient.mk",
"List.cons",
"_private.Mathlib.CategoryTheory.ConnectedComponents.0.CategoryTheory.instIsConnectedCo... | false |
Homeomorph.subLeft._proof_1 | Mathlib.Topology.Algebra.Group.Basic | [
"Equiv.subLeft",
"Continuous",
"continuous_const",
"continuous_id'",
"IsTopologicalAddGroup.to_continuousSub",
"Equiv.toFun",
"SubNegMonoid.toSub",
"TopologicalSpace",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Continuous.sub",
"IsTopologicalAddGroup"
] | false |
_private.Mathlib.Analysis.Normed.Module.Ball.Pointwise.0.cthickening_thickening._simp_1_1 | Mathlib.Analysis.Normed.Module.Ball.Pointwise | [
"Real",
"Metric.mem_cthickening_iff",
"ENNReal.ofReal",
"Membership.mem",
"LE.le",
"Metric.infEDist",
"PseudoEMetricSpace",
"ENNReal.instLE",
"ENNReal",
"propext",
"Eq",
"Set.instMembership",
"Metric.cthickening",
"Set"
] | false |
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