name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Data.WSeq.Basic.0.Stream'.Seq.BisimO.match_1.splitter | Mathlib.Data.WSeq.Basic | [
"Unit.unit",
"Stream'.Seq",
"False",
"Option.some.noConfusion",
"Option.ctorIdx",
"False.elim",
"Option.casesOn",
"Nat.shiftRight",
"noConfusion_of_Nat",
"Option.some",
"_private.Mathlib.Data.WSeq.Basic.0.Stream'.Seq.BisimO.match_1.splitter._sparseCasesOn_3",
"Nat.hasNotBit",
"Prod.mk",
"i... | true |
Std.Rci.rec | Init.Data.Range.Polymorphic.PRange | [
"Std.Rci.mk",
"Std.Rci"
] | false |
CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.instRingEmbeddingRing._aux_4 | Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.Opposite | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Functor",
"CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.EmbeddingRing",
"Opposite",
"CategoryTheory.CategoryStruct.opposite",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Abelian",
"AddZeroClass.toAddZero",
"NonUnitalSemi... | false |
MultilinearMap.freeFinsuppEquiv._proof_4 | Mathlib.LinearAlgebra.Multilinear.Finsupp | [
"CommSemiring.toSemiring",
"RingHomInvPair",
"CommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
supIrred_ofDual | Mathlib.Order.Irreducible | [
"Equiv.instEquivLike",
"OrderDual.ofDual",
"Iff.rfl",
"InfIrred",
"Equiv",
"Iff",
"OrderDual",
"SemilatticeSup",
"DFunLike.coe",
"OrderDual.instSemilatticeInf",
"EquivLike.toFunLike",
"SupIrred"
] | true |
NonUnitalSeminormedRing.rec | Mathlib.Analysis.Normed.Ring.Basic | [
"Norm.norm",
"NonUnitalSeminormedRing",
"Real.instLE",
"Real",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocRing.toMul",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"Norm",
"LE.le",
"instHAdd",
"AddSemigroup.toAd... | false |
_private.Mathlib.RingTheory.Polynomial.Resultant.Basic.0.Polynomial.isUnit_resultant_iff_isCoprime.match_1_4 | Mathlib.RingTheory.Polynomial.Resultant.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"Exists",
"Distrib.toAdd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Polynomial",
"instDistribOfSemiring",
"AddMonoidWithOne.toOne",
"instHAdd",
"CommRing.toCommSemiring",
"Exists.casesOn",
"Di... | false |
Lean.Parser.Command.declaration._regBuiltin.Lean.Parser.Command.axiom.formatter_105 | Lean.Parser.Command | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Lean.Parser.Command.axiom.formatter",
"Unit",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
AddCommGrpCat.ofHom_hom | Mathlib.Algebra.Category.Grp.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"AddCommGrpCat.carrier",
"AddCommGrpCat",
"AddCommGrpCat.of",
"AddCommGrpCat.Hom.hom",
"CategoryTheory.Category.toCategoryStruct",
"AddCommGrpCat.ofHom",
"AddCommGrpCat.str",
"Eq",
"rfl"
] | true |
CategoryTheory.Grothendieck.functorFrom_obj | Mathlib.CategoryTheory.Grothendieck | [
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.Grothendieck.fiber",
"CategoryTheory.Grothendieck.base",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.eqToHom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Grot... | true |
CategoryTheory.Free.of | Mathlib.Algebra.Category.ModuleCat.Adjunctions | [
"CategoryTheory.Free"
] | true |
Mathlib.Tactic.Widget.StringDiagram.IdNode | Mathlib.Tactic.Widget.StringDiagram | [
"Mathlib.Tactic.Widget.StringDiagram.IdNode.mk"
] | true |
Topology.IsConstructible.preimage_of_isOpenEmbedding | Mathlib.Topology.Constructible | [
"IsRetrocompact",
"Topology.IsOpenEmbedding.continuous",
"TopologicalSpace",
"Set.preimage",
"Topology.IsOpenEmbedding",
"IsRetrocompact.preimage_of_isOpenEmbedding",
"IsOpen",
"Topology.IsConstructible.preimage",
"Topology.IsConstructible",
"Set"
] | true |
Hashable.noConfusion | Init.Prelude | [
"UInt64",
"HEq.refl",
"Hashable.casesOn",
"Hashable.noConfusionType",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Hashable",
"Eq"
] | false |
ProbabilityTheory.HasGaussianLaw.toLp_prodMk | Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic | [
"WithLp",
"ContinuousLinearEquiv.symm",
"Real",
"MeasureTheory.Measure",
"Prod.normedSpace",
"WithLp.instProdNormedAddCommGroup",
"Prod.normedAddCommGroup",
"WithLp.prodContinuousLinearEquiv",
"NormedSpace",
"WithLp.instProdTopologicalSpace",
"WithLp.instProdNormedSpace",
"AddCommGroup.toAddCo... | true |
Std.ExtTreeMap.minKey?_insertIfNew_le_self | Std.Data.ExtTreeMap.Lemmas | [
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.ExtTreeMap",
"Option.get",
"Std.ExtTreeMap.inner",
"Bool",
"Std.ExtTreeMap.insertIfNew",
"Ordering.isLE",
"Std.ExtDTreeMap.minKey?_insertIfNew_le_self",
"Std.ExtTreeMap.minKey?",
"Eq",
"Std.ExtTreeMap.isSome_minKey?_insertIfNew"
] | true |
convexIndependent_iff_notMem_convexHull_diff | Mathlib.Analysis.Convex.Independent | [
"Set.mem_singleton",
"Eq.mpr",
"ChainCompletePartialOrder.instOfCompleteLattice",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Set.diff_singleton_eq_self",
"ConvexIndependent.mem_convexHull_iff",
"Membership.mem",
"PartialOrder",
"AddComm... | true |
Qq.QuotedDefEq.unsafeIntro | Qq.Typ | [
"Qq.QuotedDefEq",
"Lean.Expr.sort",
"Lean.Level",
"Qq.Quoted",
"Qq.QuotedDefEq.unsafeIntro"
] | true |
_private.Batteries.Data.Char.AsciiCasing.0.Char.not_isLower_of_isUpper._simp_1_2 | Batteries.Data.Char.AsciiCasing | [
"UInt32.toNat",
"LE.le",
"instLENat",
"Nat",
"propext",
"instLEUInt32",
"UInt32",
"Eq",
"UInt32.le_iff_toNat_le"
] | false |
TopCat.isInitialPEmpty._proof_2 | Mathlib.Topology.Category.TopCat.Limits.Basic | [
"Inhabited.default",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"ContinuousMap.mk",
"TopCat.ext",
"ContinuousMap",
"instTopologicalSpacePEmpty",
"PEmpty",
"PEmpty.elim",
"TopCat.str",
"TopCat.carrier",
"TopCat.ofHom... | false |
Nat.boddDiv2 | Mathlib.Data.Nat.Bits | [
"Nat.brecOn",
"Nat.boddDiv2._f",
"Nat",
"Bool",
"Prod"
] | true |
CategoryTheory.Functor.closedIhom_map_app | Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Groupoid | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.prodFunctorToFunctorProd",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.C... | true |
RelSeries.subsingleton_of_length_eq_zero | Mathlib.Order.RelSeries | [
"Eq.mpr",
"Equiv.instEquivLike",
"SetRel",
"congrArg",
"HEq.refl",
"AddMonoid.toAddZeroClass",
"finCongr",
"setOf",
"Nat.instAddMonoid",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.casesOn",
"id",
"Equiv",
"RelSeries.length",
"instOfNatNat",
"RelSeries",
"zero_add",
"Fin.subs... | true |
_private.Mathlib.RepresentationTheory.Rep.Iso.0.Rep.instHasBinaryBiproducts._simp_3 | Mathlib.RepresentationTheory.Rep.Iso | [
"Monoid",
"Representation",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"Representation.IntertwiningMap.instAdd",
"Rep.of",
"Rep.ofHom_add",
"Rep.instCategory",
"AddCommGroup",
"instHAdd",
"Rep",
"Rep.instAddHom",
"HAdd.hAdd",
"Rep.ofHom",
"S... | false |
MDifferentiableAt.prodMap' | Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | [
"Prod.normedSpace",
"Prod.normedAddCommGroup",
"NormedSpace",
"instTopologicalSpaceProd",
"MDifferentiableAt",
"instTopologicalSpaceModelProd",
"Prod.map",
"Prod.fst",
"TopologicalSpace",
"ModelWithCorners",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"prodChartedSpac... | true |
Equiv.nonUnitalNonAssocSemiring._proof_2 | Mathlib.Algebra.Ring.TransferInstance | [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"Equiv",
"Distrib.toAdd",
"instHAdd",
"HAdd.hAdd",
"NonUnitalNonAssocSemiring.toDistrib",
"Equiv.symm",
"NonUnitalNonAssocSemiring",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
Filter.bot_div | Mathlib.Order.Filter.Pointwise | [
"instHDiv",
"Filter.instDiv",
"Filter.map₂_bot_left",
"HDiv.hDiv",
"Div",
"Bot.bot",
"Eq",
"Filter",
"Filter.instBot"
] | true |
Real.Angle.two_nsmul_eq_pi_iff | Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real",
"instHSMul",
"neg_div",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.pi",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"DivisionCommMonoid.toDivisionMonoid... | true |
BitVec.ofBoolListLE._sunfold | Init.Data.BitVec.Basic | [
"BitVec",
"BitVec.ofBoolListLE",
"instOfNatNat",
"BitVec.ofNat",
"BitVec.concat",
"List",
"Unit",
"Nat",
"Bool",
"OfNat.ofNat",
"List.length",
"BitVec.ofBoolListBE.match_1"
] | false |
Plausible.Gen.listOf | Plausible.Gen | [
"Pure.pure",
"ReaderT",
"Monad.toApplicative",
"ULift",
"ReaderT.instMonad",
"Applicative.toPure",
"Except.instMonad",
"Array.toList",
"Array",
"List",
"Nat",
"Monad.toBind",
"StdGen",
"Bind.bind",
"StateT.instMonad",
"Except",
"Plausible.Gen",
"Plausible.Gen.arrayOf",
"Plausible... | true |
IsTrans.comap | Mathlib.Logic.Relation | [
"Function.onFun",
"IsTrans.mk",
"IsTrans",
"trans_of"
] | true |
Order.succ_eq_succ_iff._simp_2 | Mathlib.Order.SuccPred.Basic | [
"Preorder.toLT",
"Order.succ",
"NoMaxOrder",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Order.succ_eq_succ_iff",
"propext",
"SuccOrder",
"Eq",
"instDistribLatticeOfLinearOrder",
"Lattice.toSemilatticeInf"
] | false |
RatFunc.algEquivOfTranscendental._proof_11 | Mathlib.FieldTheory.RatFunc.AsPolynomial | [
"Subalgebra.instSetLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IntermediateField.algebraAdjoinAdjoin.instAlgebraSubtypeMemSubalgebraAdjoinAdjoin",
"IntermediateField.instSMulMemCl... | false |
MeasureTheory.meas_le_ae_eq_meas_lt | Mathlib.MeasureTheory.Integral.Layercake | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"Preorder.toLT",
"MeasureTheory.NoAtoms",
"LinearOrder",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Filter.EventuallyEq",
"Ne",
"LE.le",
"Set.Countable.measure_zero",
"Mea... | true |
AddConstEquiv.instEquivLike._proof_2 | Mathlib.Algebra.AddConstMap.Equiv | [
"Equiv.right_inv",
"AddConstEquiv",
"Equiv.toFun",
"AddConstEquiv.toEquiv",
"Function.RightInverse",
"Equiv.invFun",
"Add"
] | false |
_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.StructInstState.mk.noConfusion | Lean.Elab.StructInst | [
"Lean.NameMap",
"Lean.FVarIdMap",
"Lean.NameSet",
"Lean.MVarId",
"Lean.Expr",
"id",
"Lean.FVarId",
"Array",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.StructInstState.noConfusion",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.StructInstState",
"Bool",
"Lean.Name",... | false |
PNat.gcdB' | Mathlib.Data.PNat.Xgcd | [
"PNat.XgcdType.y",
"PNat.XgcdType.zp",
"instHAdd",
"HAdd.hAdd",
"Nat.succPNat",
"Nat",
"instAddNat",
"PNat.xgcd",
"PNat"
] | true |
retractionKerCotangentToTensorEquivSection.match_3 | Mathlib.RingTheory.Smooth.Kaehler | [
"LinearMap.id",
"RingHom.instRingHomClass",
"Ideal.Algebra.kerSquareLift",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"instAddCommGroupKaehlerDifferential",
"Algebra.algebraMap",
"CommSemiring.toSe... | false |
Int8.ofIntLE_bitVecToInt._proof_1 | Init.Data.SInt.Lemmas | [
"Int8.minValue",
"BitVec",
"Int8.toInt",
"BitVec.le_toInt",
"instOfNatNat",
"Int",
"LE.le",
"Nat",
"BitVec.toInt",
"OfNat.ofNat",
"Int.instLEInt"
] | false |
MeasureTheory.lintegral_comp_eq_lintegral_meas_lt_mul | Mathlib.MeasureTheory.Integral.Layercake | [
"MeasureTheory.ae",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real.instLE",
"Real",
"Set.Ioi",
"MeasureTheory.Measure",
"Preorder.toLT",
"HMul.hMul",
"MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul",
"AEMeasurable",
"Real.instZero",
"ENNReal.ofReal",
"Real.instRCLike",
"Measur... | true |
CategoryTheory.Monad.forget_map | Mathlib.CategoryTheory.Monad.Algebra | [
"CategoryTheory.Monad",
"CategoryTheory.Monad.forget",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Functor.map",
"CategoryTheory.Monad.Algebra.Hom.f",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Monad.... | true |
LinearMap.range_domRestrict_eq_range_iff | Mathlib.LinearAlgebra.Span.Basic | [
"Eq.mpr",
"Submodule",
"Submodule.mem_top._simp_1",
"LinearMap.range_domRestrict_le_range",
"Lattice.toSemilatticeSup",
"map_sub",
"eq_top_iff",
"SemilinearMapClass.distribMulActionSemiHomClass",
"sub_self",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Submodule.co... | true |
Lean.Parser.Command.grindPattern.parenthesizer | Lean.Meta.Tactic.Grind.Parser | [
"Lean.Parser.optional.parenthesizer",
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.Parser.ident.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.an... | true |
_private.Mathlib.Order.Interval.Set.Disjoint.0.Set.Ioo_disjoint_Ioo._simp_1_1 | Mathlib.Order.Interval.Set.Disjoint | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Set.instInter",
"Set.instDistribLattice",
"Set.disjoint_iff_inter_eq_empty",
"Inter.inter",
"Set.instBoundedOrder",
"BoundedOrder.toOrderBot",
"propext",
"Set.instEmptyCollec... | false |
_private.Init.Data.List.Sort.Basic.0.List.merge._unary._proof_2 | Init.Data.List.Sort.Basic | [
"invImage",
"Nat.lt_add_left_iff_pos._simp_1",
"instSizeOfDefault",
"PSigma.casesOn",
"id",
"Prod.mk",
"instOfNatNat",
"sizeOfWFRel",
"Nat.lt_add_one._simp_1",
"List.cons",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"List._sizeOf_inst",
"LT.lt",
"True",
"SizeOf.sizeOf",
"PSigma.mk",... | false |
_private.Mathlib.Data.ENat.Basic.0.ENat.WithBot.lt_add_one_iff._simp_1_2 | Mathlib.Data.ENat.Basic | [
"WithBot.some",
"WithBot",
"WithBot.instLT",
"Bot.bot",
"LT.lt",
"True",
"WithBot.bot_lt_coe",
"eq_true",
"Eq",
"WithBot.bot",
"LT"
] | false |
RelIso.casesOn | Mathlib.Order.RelIso.Basic | [
"Equiv.instEquivLike",
"RelIso.mk",
"Equiv",
"RelIso",
"Iff",
"RelIso.rec",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
TensorProduct.AlgebraTensorModule.rightComm._proof_8 | Mathlib.LinearAlgebra.TensorProduct.Tower | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"SMulCommClass.symm",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"TensorProduct.instSMul._proof_1",
"TensorPr... | false |
Lean.Elab.WF.GuessLex.withUserNames | Lean.Elab.PreDefinition.WF.GuessLex | [
"Pure.pure",
"Subarray",
"Lean.Meta.instMonadLCtxMetaM",
"instForInOfForIn'",
"instMonadControlTOfPure",
"Lean.Expr.fvarId!",
"Lean.Meta.State",
"Std.Stream.next?",
"Array.instMembership",
"ForInStep.done",
"inferInstance",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Prod.mk",
"Fo... | true |
Subgroup.coe_square | Mathlib.Algebra.Group.Subgroup.Even | [
"Monoid.toMulOneClass",
"setOf",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Subgroup",
"CommGroup",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"SetLike.coe",
"IsSquare",
"Subgroup.square",
"CommGroup.toGroup",
"Eq",
"Subgroup.instSetLike",
"rfl",
"Set"
] | true |
Lean.Meta.Grind.Arith.Cutsat.instHashableExpr_lean.hash | Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof | [
"UInt64",
"Lean.Meta.Grind.Arith.Cutsat.instHashableExpr_lean.hash._f",
"Int.Linear.Expr",
"Int.Linear.Expr.brecOn"
] | true |
Aesop.UnfoldRule.mk.injEq | Aesop.Rule | [
"Eq.propIntro",
"Aesop.UnfoldRule.mk.inj",
"Lean.injEq_helper",
"Aesop.UnfoldRule",
"And",
"Aesop.UnfoldRule.mk",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Eq",
"Option"
] | true |
String.Slice.Pattern.Model.IsValidSearchFrom.matched_of_eq | Init.Data.String.Lemmas.Pattern.Basic | [
"String.Slice.Pattern.Model.IsValidSearchFrom",
"HEq.refl",
"String.Slice.Pattern.Model.IsValidSearchFrom.matched",
"String.Slice.Pattern.SearchStep",
"String.Slice",
"Eq.casesOn",
"List.cons",
"List",
"String.Slice.Pattern.SearchStep.matched",
"Eq.ndrec",
"Eq.refl",
"HEq",
"String.Slice.Pat... | true |
EReal.mul_div_left_comm | Mathlib.Data.EReal.Inv | [
"CommMonoidWithZero.toCommMonoid",
"Eq.mpr",
"EReal.instDivInvMonoid",
"instHDiv",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"congrArg",
"EReal",
"id",
"HDiv.hDiv",
"EReal.mul_div",
"CommMagma.toMul",
"EReal.instCommMonoidWithZero",
"CommSemigroup.toCommMagma",
"DivInvMonoid.toDiv",
"... | true |
LieHom.mk.congr_simp | Mathlib.Algebra.Lie.Basic | [
"LieHom",
"LieAlgebra.toModule",
"CommRing",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Bracket.bracket",
"Eq.rec",
"LinearMap.toAddHom",
"LieRingModule.toBracket",
"LinearMap",
"LieRing",
"CommRing.toCommSemiring",
"Eq.ndrec",
"Eq.refl",
"Lie... | true |
Std.DHashMap.Internal.Raw₀.erase_equiv_congr | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"_private.Std.Data.DHashMap.Internal.RawLemmas.0.Std.DHashMap.Internal.Raw₀.erase_equiv_congr._simp_1_1",
"Std.DHashMap.Internal.Raw.WF.out",
"Std.DHashMap.Raw",
"List.Perm.congr_right",
"Std.DHashMap.Raw.Equiv.impl",
"id",
"List.Perm",
"instOfNatNat",
"Std.DHash... | true |
ArchimedeanClass.instFieldFiniteResidueField._proof_31 | Mathlib.Algebra.Order.Ring.StandardPart | [
"Mul.mk",
"One.mk",
"IsLocalRing.instCommRingResidueField._proof_31",
"AddMonoid.toAddSemigroup",
"ArchimedeanClass.instFieldFiniteResidueField._aux_28",
"IsOrderedRing",
"ArchimedeanClass.FiniteResidueField._proof_1",
"LinearOrder",
"Add.mk",
"AddMonoidWithOne.natCast_succ._autoParam",
"Archime... | false |
Nat.mem_primeFactorsList_mul | Mathlib.Data.Nat.Factors | [
"and_or_left",
"Eq.mpr",
"Nat.instMulZeroClass",
"IsDomain.to_noZeroDivisors",
"Nat.Prime",
"Dvd.dvd",
"HMul.hMul",
"congrArg",
"Membership.mem",
"id",
"Nat.instIsDomain",
"Ne",
"instMulNat",
"instOfNatNat",
"_private.Mathlib.Data.Nat.Factors.0.Nat.mem_primeFactorsList_mul._simp_1_1",
... | true |
InnerProductSpace.Core.toNormedAddCommGroupOfTopology | Mathlib.Analysis.InnerProductSpace.Defs | [
"InnerProductSpace.Core",
"PreInnerProductSpace.Core.toInner",
"NormedCommRing.toSeminormedCommRing",
"Real",
"InnerProductSpace.Core.toCore",
"InnerProductSpace.Core.toNorm",
"AddMonoid.toAddSemigroup",
"Bornology.IsVonNBounded",
"Inner.inner",
"Real.instAddMonoid",
"ContinuousAt",
"DistribMu... | true |
finsum_sum_comm | Mathlib.Algebra.BigOperators.Finprod | [
"Eq.mpr",
"Mathlib.Tactic.Push.not_and_eq",
"Iff.of_eq",
"Classical.not_not",
"congrArg",
"Finset",
"finsum",
"AddMonoid.toAddZeroClass",
"Function.HasFiniteSupport",
"Set.mem_iUnion",
"Membership.mem",
"Mathlib.Tactic.Push.not_exists",
"Exists",
"AddZeroClass.toAddZero",
"id",
"Set.Fi... | true |
AddCommGrpCat.Colimits.Quot.ι_desc | Mathlib.Algebra.Category.Grp.Colimits | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"AddCommGrpCat.Colimits.Quot.desc._proof_1",
"AddCommGrpCat.instCategory",
"DFinsupp.sumAddHom_single",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"AddCommGrpCat.Colimits.instAddCommGroupQuo... | true |
CategoryTheory.ShortComplex.cyclesFunctorIso._proof_3 | Mathlib.Algebra.Homology.ShortComplex.PreservesHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Limits.kernel",
"CategoryTheory.Limits.HasCokernels.has_colimit",
"CategoryTheory.ShortComplex.HasLeftHomology.of_hasKernel_of_hasCokernel",
"CategoryThe... | false |
Lean.Grind.OrderedAdd.zsmul_le_zsmul | Init.Grind.Ordered.Module | [
"Lean.Grind.OrderedAdd.zsmul_nonneg",
"Iff.mpr",
"instHSMul",
"_private.Init.Grind.Ordered.Module.0.Lean.Grind.OrderedAdd.zsmul_le_zsmul._simp_1_1",
"congrArg",
"Lean.Grind.IntModule.zsmul_sub",
"Lean.Grind.IntModule.toNatModule",
"Lean.Grind.IntModule.zsmul",
"HSub.hSub",
"Eq.mp",
"Lean.Grind.A... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.contains_of_contains_union_of_contains_eq_false_left._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
Array.mem_flatten_of_mem | Init.Data.Array.Lemmas | [
"Iff.mpr",
"Array.flatten",
"Array.instMembership",
"Membership.mem",
"Exists",
"Array",
"And",
"Array.mem_flatten",
"And.intro",
"Exists.intro"
] | true |
CategoryTheory.ShortComplex.HomologyData.ofIsIsoLeftRightHomologyComparison' | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.IsIso",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.ShortComplex.RightHomologyData",
"CategoryTheory.ShortComplex.HomologyData.ofIsIsoLeftRightHomologyComparison'._proof_2",
"CategoryTheory.ShortComplex",
"CategoryTheory.Short... | true |
_private.Mathlib.Tactic.Linter.Header.0.Mathlib.Linter.Style.header.collectAtoms._unsafe_rec | Mathlib.Tactic.Linter.Header | [
"_private.Mathlib.Tactic.Linter.Header.0.Mathlib.Linter.Style.header.collectAtoms._unsafe_rec",
"Array.flatten",
"Lean.Syntax.getArgs",
"String",
"Lean.Syntax.isAtom",
"Lean.Syntax",
"Array.map",
"instDecidableEqBool",
"Lean.Syntax.getAtomVal",
"List.toArray",
"List.cons",
"Array",
"Bool.tru... | false |
Aesop.Nanos.mk | Aesop.Nanos | [
"Aesop.Nanos.mk",
"Aesop.Nanos",
"Nat"
] | true |
AlgebraicGeometry.functionField_isFractionRing_of_isAffineOpen | Mathlib.AlgebraicGeometry.FunctionField | [
"AlgebraicGeometry.irreducibleSpace_of_isIntegral",
"AlgebraicGeometry.IsIntegral",
"Iff.mpr",
"Eq.mpr",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"IsDomain.to_noZeroDivisors",
"AlgebraicGeometry.Scheme",
"Opposite",
"CommRingCat.carrier",
"Al... | true |
CategoryTheory.Functor.final_const_terminal | Mathlib.CategoryTheory.Filtered.Final | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.final_const_of_isTerminal",
"CategoryTheory.Limits.terminal",
"CategoryTheory.IsFiltered",
"CategoryTheory.Functor.const",
"CategoryTheory.Limits.terminalIsTerminal",
"CategoryTheory.Functor.Final",
"CategoryTheory.... | true |
CategoryTheory.Sieve.sSup_apply | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Membership.mem",
"Exists",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Sieve",
"iff_self",
"funext",
"And",
"Iff",
"True",
"exists_prop._simp_1",
"of_eq_true",
"CategoryTheory.Sieve.instCompleteLattice",
"CompleteS... | true |
AlgebraicGeometry.LocallyOfFinitePresentation.SpecMap_iff | Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation | [
"AlgebraicGeometry.Spec",
"RingHom.FinitePresentation",
"CommRingCat.Hom.hom",
"CommRingCat.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommRingCat",
"AlgebraicGeometry.Spec.map",
"CommRingCat.instCategory",
"CommRingCat.instCommRingObjForgetRingHomCarrier",
"Iff",
"Alge... | true |
Int.lt_of_add_lt_add_left | Init.Data.Int.Order | [
"congrArg",
"Int.neg_add_cancel_left",
"Eq.mp",
"Int.instNegInt",
"Int",
"Int.add_lt_add_left",
"Int.instLTInt",
"instHAdd",
"HAdd.hAdd",
"congr",
"LT.lt",
"Int.instAdd",
"Neg.neg"
] | true |
Polynomial.natDegree_eq_card_roots | Mathlib.Algebra.Polynomial.Splits | [
"IsDomain",
"CommRing",
"Polynomial.roots",
"CommSemiring.toSemiring",
"Polynomial",
"Polynomial.Splits.natDegree_eq_card_roots",
"CommRing.toCommSemiring",
"Nat",
"Multiset.card",
"Polynomial.Splits",
"Polynomial.natDegree",
"Eq"
] | true |
_private.Mathlib.RingTheory.Binomial.0.Ring.smeval_ascPochhammer_self_neg.match_1_1 | Mathlib.RingTheory.Binomial | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
Algebra.adjoin_singleton_natCast | Mathlib.Algebra.Algebra.Subalgebra.Lattice | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"Lattice.toSemilatticeSup",
"Algebra.adjoin_singleton_algebraMap",
"Algebra.algebraMap",
"CompleteLattice.toLattice",
"congrArg",
"CommSemiring.toSemiring",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Algebra.instCompleteLa... | true |
WithTop.LinearOrderedAddCommGroup.instLinearOrderedAddCommGroupWithTopOfIsOrderedAddMonoid.match_1 | Mathlib.Algebra.Order.AddGroupWithTop | [
"False",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"False.elim",
"PartialOrder.toPreorder",
"LinearOrderedAddCommMonoidWithTop.toOrderTop",
"Option.casesOn",
"AddCommGroup.toAddCancelCommMonoid",
"Preorder.toLE",
"WithTop.linearOrderedAddCommMonoidWithTop",
"Option.some",
"SemilatticeInf.... | false |
ProjectiveSpectrum.zeroLocus_iSup_homogeneousIdeal | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology | [
"SetLike",
"ProjectiveSpectrum.gc_homogeneousIdeal",
"CommRing",
"CommSemiring.toSemiring",
"iSup",
"Set.iInter",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Nat.instAddMonoid",
"ProjectiveSpectrum.vanishingIdeal",
"AddSubmonoidClass",
"HomogeneousIdeal.completeLattice",... | true |
CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_one | Mathlib.CategoryTheory.ComposableArrows.Four | [
"instNeZeroNatHAdd_1",
"CategoryTheory.ComposableArrows.fourδ₁Toδ₀",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"CategoryTheory.CategoryStruct.id",
"Fin.instOfNat",
"Preorder.smallCategory",
"instOfNatNat",
"instHAdd",
"Fin.instPartialOrder",
"HAdd.hAdd"... | true |
SimpleGraph.replaceVertex.eq_1 | Mathlib.Combinatorics.SimpleGraph.Operations | [
"False",
"SimpleGraph.Adj",
"SimpleGraph.mk",
"SimpleGraph.replaceVertex",
"SimpleGraph",
"Eq.refl",
"SimpleGraph.replaceVertex._proof_4",
"Eq",
"SimpleGraph.replaceVertex._proof_2",
"DecidableEq",
"ite"
] | true |
Valuation.IsRankOneDiscrete.generator_eq_exp_neg_one_of_mem_range._proof_1 | Mathlib.RingTheory.Valuation.Discrete.RankOne | [
"Multiplicative.group",
"AddGroup.toSubtractionMonoid",
"inv_eq_zero._simp_1",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"False",
"GroupWithZero.toDivisionMonoid",
"WithZero.inv",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"DivisionMonoid.toDivInvOneMonoid",
"Int.instNegInt",
... | false |
Vector.ne_and_not_mem_of_not_mem_push | Init.Data.Vector.Lemmas | [
"Vector.instMembership",
"False",
"Vector.push",
"eq_false",
"Vector",
"congrArg",
"and_self",
"Vector.mem_push._simp_1",
"Membership.mem",
"Ne",
"instOfNatNat",
"instHAdd",
"And",
"not_or._simp_1",
"HAdd.hAdd",
"Nat",
"congr",
"True",
"of_eq_true",
"instAddNat",
"Or",
"imp... | true |
_private.Lean.Elab.Tactic.Grind.Lint.0.Lean.Elab.Tactic.Grind.getTheorems | Lean.Elab.Tactic.Grind.Lint | [
"Pure.pure",
"Lean.ModuleIdx",
"Lean.PersistentEnvExtensionState",
"Lean.Environment.header",
"Std.TreeSet.any",
"Lean.NameSet",
"Monad.toApplicative",
"Lean.Core.instMonadEnvCoreM",
"_private.Lean.Elab.Tactic.Grind.Lint.0.Lean.Elab.Tactic.Grind.getTheorems.match_1",
"Lean.Meta.Grind.grindExt",
... | true |
Lean.Elab.Term.Do.instInhabitedCode | Lean.Elab.Do.Legacy | [
"Inhabited",
"Lean.Elab.Term.Do.Code",
"Lean.Elab.Term.Do.instInhabitedCode.default",
"Inhabited.mk"
] | true |
Std.DHashMap.Internal.Raw.Const.get_eq._proof_1 | Std.Data.DHashMap.Internal.Raw | [
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"False",
"Decidable.casesOn",
"Std.DHashMap.Internal.Raw₀.contains",
"congrArg",
"False.elim",
"Std.DHashMap.Raw",
"Decidable",
"Bool.false_eq_true",
"Membership.mem",
"Eq.mp",
"id",
"instOfNatNat",
"dif_neg",
"dite",
"Subtype.mk",
"B... | false |
MonoidHom.injective_codRestrict._simp_2 | Mathlib.Algebra.Group.Submonoid.Operations | [
"SetLike",
"MonoidHom.instFunLike",
"SubmonoidClass.toMulOneClass",
"MonoidHom",
"MonoidHom.injective_codRestrict",
"Membership.mem",
"Subtype",
"MonoidHom.codRestrict",
"MulOneClass.toMulOne",
"propext",
"Function.Injective",
"SubmonoidClass",
"MulOneClass",
"Eq",
"DFunLike.coe",
"Set... | false |
List.mapFinIdx.go | Init.Data.List.MapIdx | [
"List.brecOn",
"List.mapFinIdx.go._f",
"Array",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"Eq",
"List.length",
"Array.size"
] | true |
SSet.Subcomplex.Pairing.RankFunction.Cell.mapToSucc.eq_1 | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | [
"SSet.Subcomplex.toSSet",
"Preorder.toLT",
"Opposite",
"Order.succ",
"SSet.Subcomplex.Pairing.RankFunction.filtration",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SSet.Subcomplex.Pairing.RankFunction.Cell.map",
"NoMaxOrder",
"LinearOrder",
"PartialOrder.toPreorder",
"CategoryTheo... | true |
MulDistribMulActionHom.map_mul | Mathlib.GroupTheory.GroupAction.Hom | [
"Monoid",
"MonoidHom.instFunLike",
"HMul.hMul",
"MonoidHom",
"Monoid.toMulOneClass",
"MulDistribMulActionHom.instFunLike",
"MulOne.toMul",
"MulDistribMulActionHom.instMulDistribMulActionSemiHomClassCoeMonoidHom",
"MulDistribMulActionSemiHomClass.toMonoidHomClass",
"map_mul",
"MulOneClass.toMulOn... | true |
_private.Aesop.Tree.Data.0.Aesop.GoalOrigin.originalGoalId?._sparseCasesOn_1 | Aesop.Tree.Data | [
"Aesop.GoalOrigin.rec",
"Nat.ne_of_beq_eq_false",
"Aesop.GoalId",
"Nat.shiftRight",
"Aesop.GoalOrigin.ctorIdx",
"Nat.hasNotBit",
"instOfNatNat",
"Nat.land",
"Nat",
"Aesop.GoalOrigin.subgoal",
"Bool",
"Eq.refl",
"Aesop.GoalOrigin.copied",
"OfNat.ofNat",
"Bool.false",
"Aesop.GoalOrigin.d... | false |
OrderIso.isCoatom_iff | Mathlib.Order.Atoms | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"OrderIso.isAtom_iff",
"OrderIso",
"OrderTop",
"IsCoatom",
"OrderIso.dual",
"Iff",
"instFunLikeOrderIso",
"OrderDual.instPartialOrder",
"OrderDual",
"DFunLike.coe",
"OrderDual.instOrderBotOfOrderTop"
] | true |
Std.DHashMap.Internal.Raw₀.Const.getD_diff_of_contains_right | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Bool.not",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Internal.Raw.WF.out",
"congrArg",
"List.map",
"List.contains",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.contains_eq_containsKey",
"Std.Internal.List.getVal... | true |
MeasureTheory.addContent_eq_add_disjointOfDiffUnion_of_subset | Mathlib.MeasureTheory.Measure.AddContent | [
"Eq.mpr",
"MeasureTheory.IsSetSemiring.pairwiseDisjoint_union_disjointOfDiffUnion",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Finset.instUnion",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Finset",
"Set.PairwiseDisjoint",
"AddMonoid.toAddZeroClass",
"Set.sUnion",
"M... | true |
_private.Mathlib.ModelTheory.Complexity.0.FirstOrder.Language.BoundedFormula.IsAtomic.realize_comp_of_injective._simp_1_4 | Mathlib.ModelTheory.Complexity | [
"FirstOrder.Language.Relations.boundedFormula",
"FirstOrder.Language.Term",
"Sum",
"FirstOrder.Language.BoundedFormula.Realize",
"FirstOrder.Language.Structure.RelMap",
"FirstOrder.Language.Structure",
"Nat",
"FirstOrder.Language.Relations",
"propext",
"FirstOrder.Language.BoundedFormula.realize_r... | false |
CategoryTheory.Limits.ChosenEndsOfShape.mk._flat_ctor | Mathlib.CategoryTheory.Limits.Chosen.End | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingMulticospan.instSmallCategory",
"CategoryTheory.Limits.multicospanIndexEnd",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Limits.multicospanShapeEnd",
"CategoryTheory.Limits.ChosenEndsOfShape",
... | false |
Std.DTreeMap.Internal.RcoSliceData.mk.injEq | Std.Data.DTreeMap.Internal.Zipper | [
"Std.Rco",
"Ord",
"Std.DTreeMap.Internal.RcoSliceData.mk",
"Eq.propIntro",
"Lean.injEq_helper",
"Std.DTreeMap.Internal.RcoSliceData",
"And",
"Std.DTreeMap.Internal.RcoSliceData.mk.inj",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | true |
Lean.instQuoteCharCharLitKind | Init.Meta.Defs | [
"Lean.Quote",
"Lean.charLitKind",
"Lean.Syntax.mkCharLit",
"Char",
"Lean.Quote.mk",
"Lean.SourceInfo.none"
] | true |
Function.FromTypes.uncurry_two_eq_uncurry | Mathlib.Data.Fin.Tuple.Curry | [
"Equiv.instEquivLike",
"Function.FromTypes.uncurry",
"Function.comp",
"Function.FromTypes",
"Fin.instOfNat",
"Equiv",
"instOfNatNat",
"Nat.instNeZeroSucc",
"Matrix.vecHead",
"Nat",
"Function.uncurry",
"Prod",
"OfNat.ofNat",
"Fin",
"Matrix.vecTail",
"Eq",
"DFunLike.coe",
"piFinTwoEq... | true |
DirectSum.lieAlgebraComponent._proof_1 | Mathlib.Algebra.Lie.DirectSum | [
"LieAlgebra.toModule",
"DirectSum.bracket_apply",
"CommRing",
"instAddCommMonoidDirectSum",
"LieRing.toAddCommGroup",
"DirectSum.instModule",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Bracket.bracket",
"LinearMap.instFunLike",
"Direct... | false |
CategoryTheory.PreOneHypercover.instUniqueLMulticospanShapeSigmaOfIsColimit._aux_1 | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.Limits.Cofan",
"CategoryTheory.PreOneHypercover",
"CategoryTheory.PreOneHypercover.toPreZeroHypercover",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.PreOneHyperco... | false |
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