name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier | Mathlib.Algebra.Category.ModuleCat.Basic | [
"CategoryTheory.IsIso",
"Equiv.right_inv",
"LinearEquiv.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CategoryTheory.Iso.toEquiv",
"AddCommGroup.toAddCommMonoid",
"LinearEquiv.toModuleIso",
"LinearMap.instFunLike",
"inferInstance",
"ModuleCat.instConcreteCategoryLi... | true |
_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.comm_ring_aux₁._proof_2 | Mathlib.RingTheory.WittVector.Basic | [
"Nat.instMulZeroClass",
"Nat.Prime",
"Equiv.instEquivLike",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"Nat.instOne",
"AddMonoidAlgebra.commRing",
"Rat",
"invertibleOfPos",
"Rat.commSemiring",
"Fact",
"Equiv",
"MvPolynomial.invertibleCoeNat",
"Field.toSemifield",
"Nat.Prime.one_lt... | false |
continuousMultilinearCurryRightEquiv._proof_6 | Mathlib.Analysis.Normed.Module.Multilinear.Curry | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"I... | false |
_private.Init.Data.ByteArray.Lemmas.0.ByteArray.append_inj_left._simp_1_1 | Init.Data.ByteArray.Lemmas | [
"Array",
"ByteArray.ext_iff",
"ByteArray.data",
"propext",
"ByteArray",
"UInt8",
"Eq"
] | false |
Real.artanh_le_artanh_iff | Mathlib.Analysis.SpecialFunctions.Artanh | [
"Real.instLE",
"Real",
"Real.strictMonoOn_artanh",
"Membership.mem",
"LE.le",
"Real.instOne",
"Iff",
"Real.instNeg",
"One.toOfNat1",
"Real.artanh",
"StrictMonoOn.le_iff_le",
"OfNat.ofNat",
"Set.instMembership",
"Set.Ioo",
"Neg.neg",
"Real.instPreorder",
"Real.linearOrder",
"Set"
] | true |
_private.Mathlib.RingTheory.Extension.Cotangent.LocalizationAway.0.Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHom._simp_1_1 | Mathlib.RingTheory.Extension.Cotangent.LocalizationAway | [
"Semiring.toModule",
"Membership.mem",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Submodule.setLike",
"Ideal.comap",
"propext",
"Semiring",
"Ideal.mem_comap",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"SetLike.instMembe... | false |
_private.Mathlib.Analysis.SpecialFunctions.Exp.0.Complex.exp_sub_sum_range_isBigO_pow._simp_1_3 | Mathlib.Analysis.SpecialFunctions.Exp | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
_private.Mathlib.CategoryTheory.Functor.TypeValuedFlat.0.CategoryTheory.FunctorToTypes.fromOverFunctorElementsEquivalence._proof_16 | Mathlib.CategoryTheory.Functor.TypeValuedFlat | [
"CategoryTheory.categoryOfElements",
"CategoryTheory.Over",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.elementsMk",
"CategoryTheory.Over.Hom.left",
"TypeCat.inst... | false |
Polynomial.eval_monomial_one_add_sub | Mathlib.Algebra.Polynomial.Eval.Degree | [
"one_pow",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Distrib.leftDistribClass",
"Eq.mpr",
"Finset.mul_sum",
"Polynomial.eval",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.cast_succ",
"MulOne.toOne",
"Semigroup.toMul",
"CommRing",
"Nat.choose",
"NonUnitalCommRing.toNon... | true |
CategoryTheory.ShortComplex.LeftHomologyMapData.ofZeros._proof_6 | 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 |
Lean.Grind.LinearOrder.trichotomy | Init.Grind.Ordered.Order | [
"Std.le_total",
"congrArg",
"Eq.mp",
"LE.le",
"Std.IsLinearOrder.toIsPartialOrder",
"Std.IsLinearOrder",
"Std.LawfulOrderLT",
"LE",
"Lean.Grind.PartialOrder.le_iff_lt_or_eq",
"Or.casesOn",
"LT.lt",
"propext",
"Eq.refl",
"Or.inl",
"Or",
"Eq.symm",
"Eq",
"Std.instTotalLeOfIsLinearPre... | true |
PowerBasis.liftEquiv._proof_5 | Mathlib.RingTheory.PowerBasis | [
"PowerBasis",
"CommRing",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"PowerBasis.gen",
"Algebra",
"PowerBasis.lift",
"Algebra.id",
"Subtype",
"PowerBasis.liftEquiv._proof_1",
"minpoly",
"Polynomial",
"CommRing.toCommSemiring",
"Polynomial.semi... | false |
_private.Init.Data.Int.Linear.0.Int.Linear.dvd_le_tight' | Init.Data.Int.Linear | [
"Int.instDiv",
"Dvd.dvd",
"instHDiv",
"Lean.Omega.Int.add_le_zero_iff_le_neg",
"HMul.hMul",
"congrArg",
"Int.le_ediv_of_mul_le",
"Int.add_assoc",
"HSub.hSub",
"Eq.mp",
"HDiv.hDiv",
"Int.instNegInt",
"Int.add_sub_cancel",
"Int.sub_eq_add_neg",
"Int",
"LE.le",
"Int.instDvd",
"Int.ins... | true |
TensorPower.gsemiring._proof_6 | Mathlib.LinearAlgebra.TensorPower.Basic | [
"PiTensorProduct.instModule",
"Semiring.toModule",
"AddMonoid.toAddSemigroup",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"TensorPower.mulEquiv._proof_2",
"TensorPower.gMul._proof_3",
"LinearMap.instFunLike",
"Nat.instAddMonoid",
"LinearMap.compr₂",
"PiTensorProduct.instAddCommMon... | false |
AlgCat | Mathlib.Algebra.Category.AlgCat.Basic | [
"CommRing",
"_private.Mathlib.Algebra.Category.AlgCat.Basic.0.AlgCat.mk"
] | true |
UniformSpace.Completion.mapRingHom._proof_1 | Mathlib.Topology.Algebra.UniformRing | [
"UniformSpace",
"AddGroupWithOne.toAddGroup",
"IsUniformAddGroup",
"UniformSpace.Completion.uniformSpace",
"UniformSpace.Completion.isUniformAddGroup",
"UniformSpace.Completion.addGroup",
"Ring",
"Ring.toAddGroupWithOne",
"UniformSpace.Completion"
] | false |
Partition.mk.noConfusion | Mathlib.Order.Partition.Basic | [
"sSupIndep",
"Lattice.toSemilatticeSup",
"Partition.noConfusion",
"CompleteLattice.toLattice",
"HEq.refl",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"id",
"Bot.bot",
"h... | false |
Lean.Meta.Grind.Arith.Linear.IneqCnstr.ctorIdx | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"Nat",
"Lean.Meta.Grind.Arith.Linear.IneqCnstr"
] | false |
SimpleGraph.deleteEdges_univ | Mathlib.Combinatorics.SimpleGraph.DeleteEdges | [
"SimpleGraph.deleteEdges",
"Lattice.toSemilatticeSup",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"SimpleGraph.fromEdgeSet",
"Set.univ",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Bot.bot",
"SimpleGraph.fromEdgeSet_univ",
"CompleteDistribLattice.toCofram... | true |
IO.FileRight.noConfusion | Init.System.IO | [
"IO.FileRight.noConfusionType",
"IO.FileRight",
"IO.FileRight.casesOn",
"IO.AccessRight",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | false |
USize.neg_ne_zero | Init.Data.UInt.Lemmas | [
"congrArg",
"BitVec",
"BitVec.neg_eq_zero_iff._simp_1",
"Ne",
"instOfNatNat",
"BitVec.ofNat",
"BitVec.instNeg",
"iff_self",
"System.Platform.numBits",
"USize.toBitVec",
"Iff",
"Nat",
"USize.toBitVec_neg",
"congr",
"True",
"instNegUSize",
"USize.eq_iff_toBitVec_eq._simp_1",
"of_eq_t... | true |
Ideal.span_singleton_prime | Mathlib.RingTheory.Ideal.Maximal | [
"False",
"Dvd.dvd",
"Semiring.toModule",
"HMul.hMul",
"eq_false",
"MulZeroClass.toMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"semigroupDvd",
"Prime",
"Ideal.span_singleton_eq_top._simp_1",
"IsUnit",
"CommSemiring.toCommMonoidWithZero",
"Membershi... | true |
CategoryTheory.Limits.ChosenPullback.LiftStruct.f | Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.ChosenPullback.LiftStruct",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.ChosenPullback.pullback",
"CategoryTheory.Limits.ChosenPullback",
"CategoryTheory.Category"
] | true |
Ideal.span_singleton_mul_left_mono | Mathlib.RingTheory.Ideal.Operations | [
"IsDomain",
"False",
"Semiring.toModule",
"HMul.hMul",
"eq_false",
"MulZeroClass.toMul",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Set.instSingletonSet",
"mul_eq_mul_right_iff._simp_1",
"Ideal.IsTwoSided",
"Ne",
"Submodule.instPartialOrder",
... | true |
Lean.Order.Array.monotone_foldlM | Init.Internal.Order.Lemmas | [
"Eq.mpr",
"Array.forIn'._proof_2",
"Decidable.casesOn",
"congrArg",
"HSub.hSub",
"Decidable",
"Array.foldlM.loop",
"dif_pos",
"id",
"instSubNat",
"LE.le",
"instLENat",
"Lean.Order.Array.monotone_foldlM_loop",
"dif_neg",
"dite",
"Array",
"Array.foldlM",
"funext",
"instHSub",
"Na... | true |
AlgebraicGeometry.Scheme.Cover.Hom.sigma_h₀ | Mathlib.AlgebraicGeometry.Cover.Sigma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.PreZeroHypercover.Hom.h₀",
"Inhabited.default",
"AlgebraicGeometry.Scheme",
"UnivLE",
"CategoryTheory.CategoryStruct.toQuiver",
"AlgebraicGeometry.Scheme.Cover.instUniqueI₀Sigma",
"Quiver.Hom",
"CategoryTheory.Precoverage.ZeroHypercover.instCategory... | true |
Plausible.Option.shrinkable.match_1 | Plausible.Shrinkable | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
Finset.subsetSum_nonempty._simp_1 | Mathlib.Combinatorics.Additive.SubsetSum | [
"Finset.subsetSum",
"Finset",
"AddCommMonoid",
"Finset.subsetSum_nonempty",
"True",
"Finset.Nonempty",
"eq_true",
"Eq",
"DecidableEq"
] | false |
LieIdeal.comap_mono | Mathlib.Algebra.Lie.Ideal | [
"LieHom",
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"Eq.mpr",
"Submodule",
"CommRing",
"LieRing.toAddCommGroup",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"Monotone",
"LinearMap.instFunLike",
"LieSubmodule.instPartialOrder",
... | true |
LocallyLipschitz.min_const | Mathlib.Topology.MetricSpace.Lipschitz | [
"Real",
"EMetricSpace.toPseudoEMetricSpace",
"LocallyLipschitz",
"PseudoEMetricSpace",
"Real.instMin",
"Real.metricSpace",
"MetricSpace.toEMetricSpace",
"LocallyLipschitz.const",
"Min.min",
"LocallyLipschitz.min"
] | true |
Function.locallyFinsuppWithin.mk.noConfusion | Mathlib.Topology.LocallyFinsupp | [
"Filter.instMembership",
"Function.locallyFinsuppWithin.mk",
"HEq.refl",
"Set.Finite",
"Membership.mem",
"Exists",
"nhds",
"id",
"HasSubset.Subset",
"Function.locallyFinsuppWithin.noConfusion",
"Set.instInter",
"Inter.inter",
"TopologicalSpace",
"And",
"heq_of_eq",
"Function.support",
... | false |
NormedSpace.normalize_smul_of_neg | Mathlib.Analysis.Normed.Module.Normalize | [
"AddGroup.toSubtractionMonoid",
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"SubtractionMonoid.toInvolutiveNeg",
"Real.partialOrder",
"neg_smul",
"Real",
"instH... | true |
_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.Code.instantiateValueLevelParams.instFunDecl | Lean.Compiler.LCNF.Basic | [
"Inhabited.default",
"Lean.Compiler.LCNF.FunDecl",
"Lean.Level",
"Lean.Compiler.LCNF.Purity.pure",
"List",
"Lean.Name",
"Inhabited",
"Inhabited.mk"
] | true |
CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf | Mathlib.CategoryTheory.Bicategory.Extension | [
"CategoryTheory.StructuredArrow.isoMk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.LeftExtension.whiskerOfCompIdIsoSelf._proof_2",
"CategoryTheory.Bicategory.rightUnitor",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.LeftE... | true |
CategoryTheory.Limits.Types.Pushout.Rel.rec | Mathlib.CategoryTheory.Limits.Types.Pushouts | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"Sum",
"Sum.inl",
"TypeCat.Fun",
"Sum.inr",
"CategoryTheory.Limits.Types.Pushout.Rel.inl_inr",
"CategoryTheory.types",
"CategoryTheory.Limits.Types.Pushout.Rel",
"CategoryTh... | false |
Sym.mem_map._simp_1 | Mathlib.Data.Sym.Basic | [
"Sym.mem_map",
"Membership.mem",
"Exists",
"And",
"Nat",
"Sym",
"propext",
"Sym.instMembership",
"Sym.map",
"Eq"
] | false |
Module.Baer | Mathlib.Algebra.Module.Injective | [
"Semiring.toModule",
"Ring.toNonAssocRing",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"LinearMap.instFunLike",
"Membership.mem",
"Exists",
"AddCommGroup",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Submodule.module",
"Ideal",
"LinearMap",
"NonAssocRin... | true |
OrderIso.arrowCongr._proof_4 | Mathlib.Order.Hom.Basic | [
"Preorder.toLE",
"RelIso.instRelHomClass",
"LE.le",
"RelIso",
"RelIso.instFunLike",
"RelHomClass",
"Preorder"
] | false |
_private.Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE.0.CategoryTheory.Triangulated.TStructure.from_truncGE_obj_ext._proof_1_3 | Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE | [
"Lean.RArray.leaf",
"False",
"Int.Linear.eq_eq_true",
"congrArg",
"Classical.byContradiction",
"HSub.hSub",
"Int.Linear.Expr.add",
"id",
"False.casesOn",
"instOfNatNat",
"Int",
"Bool.true",
"instHAdd",
"instHSub",
"instOfNat",
"HAdd.hAdd",
"Nat",
"True",
"Bool",
"Int.instAdd",
... | false |
TopologicalSpace.Compacts.t2Space_iff | Mathlib.Topology.Sets.VietorisTopology | [
"TopologicalSpace.Compacts.instSingleton",
"TopologicalSpace.Compacts.instT2Space",
"inferInstance",
"TopologicalSpace",
"Iff",
"T2Space",
"TopologicalSpace.Compacts.topology",
"Iff.intro",
"Singleton.singleton",
"TopologicalSpace.Compacts.isEmbedding_singleton",
"Topology.IsEmbedding.t2Space",
... | true |
LieModule.exists_forall_mem_corootSpace_smul_add_eq_zero | Mathlib.Algebra.Lie.Weights.Chain | [
"LieHom",
"LieAlgebra.toModule",
"LinearMap.trace",
"Nontrivial",
"Module.End.instRing",
"Iff.mpr",
"zero_le",
"LieSubalgebra.lieAlgebra",
"LieSubmodule.instSetLike",
"Eq.mpr",
"Int.instAddCommMonoid",
"Submodule",
"IsDomain",
"LieSubmodule.iSup_toSubmodule",
"CommRing",
"instHSMul",
... | true |
_private.Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy.0.CategoryTheory.SimplicialObject.Homotopy.ToChainHomotopy.comm_succ._proof_1_34 | Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | [
"Int.Linear.not_eq_norm_expr",
"Lean.RArray.leaf",
"False",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Lean.Grind.CommRing.Expr.var",
"congrArg",
"Classical.byContradiction",
"Nat.ToInt.add_congr",
"Nat.Linear.Expr.mulL",
"Lean.RArra... | false |
Std.DTreeMap.Internal.Impl.filterMap._unsafe_rec | Std.Data.DTreeMap.Internal.Operations | [
"Std.DTreeMap.Internal.Impl.minView._proof_9",
"Std.DTreeMap.Internal.Impl.BalancedTree.mk",
"Ord",
"Std.DTreeMap.Internal.Impl.link",
"Std.DTreeMap.Internal.Impl.filterMap.match_1",
"Std.DTreeMap.Internal.Impl.minView._proof_11",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.filt... | false |
Filter.EventuallyEq.congr_continuousWithinAt | Mathlib.Topology.ContinuousOn | [
"Eq.mpr",
"ContinuousWithinAt",
"congrArg",
"nhdsWithin",
"Iff.rfl",
"nhds",
"Filter.EventuallyEq",
"id",
"TopologicalSpace",
"Iff",
"Filter.Tendsto",
"propext",
"ContinuousWithinAt.eq_1",
"Filter.tendsto_congr'",
"Eq",
"Set"
] | true |
RingQuot.instCommRing | Mathlib.Algebra.RingQuot | [
"Ring.mk",
"Ring.toSub",
"RingQuot.instCommSemiring",
"CommRing",
"RingQuot.instCommRing._proof_1",
"Ring.toNeg",
"CommSemiring.toSemiring",
"RingQuot.instCommRing._proof_5",
"RingQuot.instCommRing._proof_3",
"RingQuot",
"RingQuot.instCommRing._proof_6",
"RingQuot.instCommRing._proof_8",
"Ri... | true |
lcm_comm' | Mathlib.Algebra.GCDMonoid.Basic | [
"GCDMonoid",
"GCDMonoid.toIsCancelMulZero",
"MulZeroClass.toMul",
"dvd_lcm_right",
"lcm_dvd",
"associated_of_dvd_dvd",
"IsCancelMulZero.toIsLeftCancelMulZero",
"CommMonoidWithZero.toMonoidWithZero",
"dvd_lcm_left",
"GCDMonoid.lcm",
"Associated",
"MonoidWithZero.toMulZeroOneClass",
"CommMonoi... | true |
Std.HashSet.fold_eq_foldl_toList | Std.Data.HashSet.Lemmas | [
"Std.HashSet.toList",
"Std.HashSet",
"Std.HashSet.fold",
"List.foldl",
"Unit",
"Std.HashSet.inner",
"Std.HashMap.fold_eq_foldl_keys",
"Hashable",
"BEq",
"Eq"
] | true |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.induct_rco_left._proof_1_2 | Init.Data.Range.Polymorphic.NatLemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"... | false |
IsNoetherian.mk._flat_ctor | Mathlib.RingTheory.Noetherian.Defs | [
"Submodule",
"Submodule.FG",
"AddCommMonoid",
"IsNoetherian",
"Semiring",
"Module",
"IsNoetherian.mk"
] | false |
Aesop.Goal.children | Aesop.Tree.Data | [
"Aesop.Goal",
"Aesop.RappRef",
"Aesop.Goal.elim",
"Aesop.Rapp",
"Array",
"Aesop.GoalData.children",
"Aesop.MVarCluster"
] | true |
AddCommMonCat.forget_createsLimit.eq_1 | Mathlib.Algebra.Category.MonCat.Limits | [
"AddCommMonCat.forget_createsLimit",
"CategoryTheory.Functor",
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"AddCommMonCat.forget_createsLimit._proof_1",
"AddCommMonCat.instCategory",
"AddMonCat.forget_createsLimit",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryThe... | true |
WriterT.instLawfulMonad | Mathlib.Control.Monad.Writer | [
"Applicative.toSeqLeft",
"Pure.pure",
"Monoid",
"MulOne.toOne",
"Semigroup.toMul",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"LawfulMonad.bind_assoc",
"Monad.toApplicative",
"mul_assoc",
"LawfulMonad.bind_pure_comp",
"LawfulApplicative.toLawfulFunctor",
"WriterT.ext",
"id",
"Mul... | true |
Lean.Meta.LazyDiscrTree.buildPath | Lean.Meta.LazyDiscrTree | [
"Inhabited.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"Array",
"Lean.Meta.instInhabitedMetaM",
"Bool",
"Prod",
"Lean.Meta.LazyDiscrTree.Key"
] | true |
Lean.Meta.withLocalDeclD | Lean.Meta.Basic | [
"Lean.LocalDeclKind.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"MonadControlT",
"Lean.Meta.withLocalDecl",
"Lean.Name",
"Lean.BinderInfo.default",
"Monad"
] | true |
Complex.sin_eq_one_iff | Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex | [
"Int.cast",
"Eq.mpr",
"Complex.cos_eq_one_iff",
"instHDiv",
"Real.pi",
"HMul.hMul",
"Complex.cos",
"congrArg",
"AddMonoid.toAddZeroClass",
"Complex.sin",
"Nat.instAtLeastTwoHAddOfNat",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Complex.instDivInvMonoid",
"Exists",
"Complex.instMul",
"A... | true |
Polynomial.monic_normalize | Mathlib.Algebra.Polynomial.FieldDivision | [
"Polynomial.instNormalizationMonoid",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"IsDomain.to_noZeroDivisors",
"congrArg",
"CommSemiring.toSemiring",
"MonoidWithZeroHom.funLike",
"Polynomial.leadingCoeff_normalize",
"IsUnit",
"Divisio... | true |
Lean.Diff.Action.delete.sizeOf_spec | Lean.Util.Diff | [
"Lean.Diff.Action",
"Lean.Diff.Action._sizeOf_inst",
"Lean.Diff.Action.delete",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
Subrepresentation.instSetLike | Mathlib.RepresentationTheory.Subrepresentation | [
"SetLike",
"Monoid",
"Submodule",
"Representation",
"Subrepresentation.toSubmodule",
"Subrepresentation",
"AddCommMonoid",
"SetLike.mk",
"Subrepresentation.instSetLike._proof_1",
"SetLike.coe",
"Submodule.setLike",
"Semiring",
"Module"
] | true |
_private.Mathlib.RingTheory.Perfection.0.PreTilt.instCharP._proof_1 | Mathlib.RingTheory.Perfection | [
"Ideal.Quotient.commSemiring",
"CommRing",
"Nat.Prime",
"CommSemiring.toSemiring",
"ModP",
"AddGroupWithOne.toAddMonoidWithOne",
"IsUnit",
"Perfection.instCharP",
"Fact",
"Set.instSingletonSet",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"CommRing.toCommSemiring",
"PreTilt",
"Nat",
"Mod... | false |
AddMonoidAlgebra.cardinalMk_eq_max_lift_of_infinite' | Mathlib.Algebra.MonoidAlgebra.Cardinal | [
"Lattice.toSemilatticeSup",
"Cardinal",
"congrArg",
"Cardinal.lift",
"Cardinal.mk",
"SemilatticeSup.toMax",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"LinearOrder.toMax",
"Cardinal.instConditionallyCompleteLinearOrderBot",
"Max.max",
"True",
"eq_self",
"of_eq_true",
... | true |
CategoryTheory.ShortComplex.RightHomologyMapData.rightHomologyMap'_eq | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.ShortComplex.RightHomologyMapData.instSubsingleton",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.rightHomologyMapData",
"CategoryTheory.ShortComplex.RightHomologyMapData.φH",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.R... | true |
SimpleGraph.UnitDistEmbedding.iso | Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic | [
"SimpleGraph.UnitDistEmbedding.copy",
"SimpleGraph.Iso",
"SimpleGraph",
"SimpleGraph.UnitDistEmbedding",
"MetricSpace",
"SimpleGraph.Iso.toCopy",
"SimpleGraph.Iso.symm"
] | true |
List.compare_cons_cons | Init.Data.Ord.Basic | [
"List.compareLex_cons_cons",
"Ord",
"Ordering",
"Ordering.then",
"Ord.compare",
"List.cons",
"List",
"List.instOrd",
"Eq"
] | true |
TopologicalSpace.UpgradedIsCompletelyPseudoMetrizableSpace.toPseudoMetricSpace | Mathlib.Topology.Metrizable.CompletelyMetrizable | [
"TopologicalSpace.UpgradedIsCompletelyPseudoMetrizableSpace",
"PseudoMetricSpace"
] | true |
_private.Mathlib.Analysis.Normed.Affine.Simplex.0.Affine.Triangle.scalene_iff_dist_ne_and_dist_ne_and_dist_ne.match_1_1 | Mathlib.Analysis.Normed.Affine.Simplex | [
"instNeZeroNatHAdd_1",
"Affine.Simplex.points",
"Real",
"SeminormedAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"Fin.instOfNat",
"Ne",
"instOfNatNat",
"And.casesOn",
"instHAdd",
"And",
"PseudoMetricSpace",
"NormedAddTorsor.toAddTorsor",
"HAdd.hAdd",
"SeminormedAddCommGroup.toAddCommGro... | false |
StarAddMonoid.star_add | Mathlib.Algebra.Star.Basic | [
"AddMonoid.toAddSemigroup",
"StarAddMonoid.toInvolutiveStar",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"AddMonoid",
"StarAddMonoid",
"InvolutiveStar.toStar",
"Eq",
"Star.star"
] | true |
_private.Lean.Elab.DeclNameGen.0.Lean.Elab.Command.NameGen.winnowExpr.visit | Lean.Elab.DeclNameGen | [
"Inhabited.default",
"Lean.Core.instMonadLiftIOCoreM",
"instInhabitedOfMonad",
"IO.instMonadLiftSTRealWorldBaseIO",
"Lean.Expr.instBEq",
"Lean.Meta.State",
"IO",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.MonadCacheT",
"ReaderT.instMonadLift",
"Lean.MonadCacheT.instMonad",
"ST",... | true |
PSet.Mem | Mathlib.SetTheory.ZFC.PSet | [
"PSet.Func",
"Exists",
"PSet",
"PSet.Type",
"PSet.Equiv"
] | true |
Set.mul_add_subset | Mathlib.Algebra.Ring.Pointwise.Set | [
"Distrib.leftDistribClass",
"HMul.hMul",
"Set.image2_distrib_subset_left",
"Distrib.toAdd",
"HasSubset.Subset",
"instHAdd",
"Set.add",
"Distrib.toMul",
"HAdd.hAdd",
"Distrib",
"mul_add",
"Set.mul",
"Set.instHasSubset",
"instHMul",
"Set"
] | true |
CategoryTheory.Limits.lift_comp_kernelIsoOfEq_inv._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"Zero.toOfNat0",
"CategoryTheory.Category.toCategoryStruct",
"cong... | false |
Lean.Meta.instToFormatInstanceEntry.match_1 | Lean.Meta.Instances | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Lean.Meta.instToFormatInstanceEntry._sparseCasesOn_1",
"Lean.Name",
"Option"
] | false |
Ordinal.lt_bsup | Mathlib.SetTheory.Ordinal.Family | [
"Iff.mpr",
"Ordinal.instLinearOrder",
"Preorder.toLT",
"Ordinal.partialOrder",
"Iff.of_eq",
"congrArg",
"PartialOrder.toPreorder",
"_private.Mathlib.SetTheory.Ordinal.Family.0.Ordinal.lt_bsup._simp_1_2",
"Preorder.toLE",
"Exists",
"Ordinal.bsup",
"Eq.mp",
"LE.le",
"funext",
"Iff",
"_pr... | true |
PiTensorProduct.distribMulAction'._proof_3 | Mathlib.LinearAlgebra.PiTensorProduct | [
"Monoid",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"instHSMul",
"instSMulOfMul",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"id",
"DistribSMul.toSMulZeroC... | false |
_private.Lean.Elab.DocString.0.Lean.Doc.InternalState.footnotes | Lean.Elab.DocString | [
"String",
"Lean.Doc.InternalState",
"Std.HashMap",
"instHashableString",
"instBEqOfDecidableEq",
"_private.Lean.Elab.DocString.0.Lean.Doc.Ref",
"instDecidableEqString",
"Lean.ElabInline",
"Lean.Doc.Inline"
] | true |
Aesop.PhaseName.rec | Aesop.Rule.Name | [
"Aesop.PhaseName.safe",
"Aesop.PhaseName",
"Aesop.PhaseName.unsafe",
"Aesop.PhaseName.norm"
] | false |
_private.Init.Data.List.Find.0.List.filterMap.match_1.eq_2 | Init.Data.List.Find | [
"Option.some",
"List.filterMap.match_1",
"Option.none",
"Unit",
"Eq.refl",
"Eq",
"Option"
] | true |
CategoryTheory.IsPullback.isIso_fst_of_mono | Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | [
"CategoryTheory.IsIso",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsPullback",
"CategoryTheory.IsPullback.isIso_fst_of_mono._auto_1",
"CategoryTheory.Limits.PullbackCone.isIso_fst_of_mono_of_isLimit",
"autoParam",
"CategoryTheory.Category.toCatego... | true |
sq_eq_one | Mathlib.Algebra.Group.Torsion | [
"Monoid",
"MulOne.toOne",
"IsMulTorsionFree",
"Monoid.toMulOneClass",
"instOfNatNat",
"Monoid.toPow",
"pow_eq_one_iff_left",
"MulOneClass.toMulOne",
"Iff",
"_private.Mathlib.Algebra.Group.Torsion.0.sq_eq_one._proof_1_1",
"HPow.hPow",
"Nat",
"One.toOfNat1",
"instHPow",
"OfNat.ofNat",
"E... | true |
CategoryTheory.Abelian.SpectralObject.p_opcyclesToE | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.SpectralObject.E",
"CategoryTheory.Abelian.SpectralObject.cycles",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Abelian.SpectralObject.H",
"CategoryTheory.Abelian.SpectralObject.p_opcyclesToE._auto_1",
"PartialOrder.toPreorder",
"Categor... | true |
AlgebraicGeometry.Scheme.Pullback.pullbackP1Iso_inv_fst_assoc | Mathlib.AlgebraicGeometry.Pullbacks | [
"AlgebraicGeometry.Scheme.GlueData.ι",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AlgebraicGeometry.Scheme.Pullback.gluing",
"AlgebraicGeom... | true |
_private.Mathlib.Combinatorics.Graph.Basic.0.Graph.incidenceSet_subset_edgeSet.match_1_1 | Mathlib.Combinatorics.Graph.Basic | [
"Graph.incidenceSet",
"Membership.mem",
"Graph",
"Graph.IsLink",
"Exists.casesOn",
"Exists.intro",
"Set.instMembership",
"Set"
] | false |
Std.Http.CustomStatus.validUnknown._autoParam | Std.Internal.Http.Data.Status | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
inner_mul_inner_self_le | Mathlib.Analysis.InnerProductSpace.Basic | [
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"InnerProductSpace.Core.inner_mul_inner_self_le",
"Real.instLE",
"Real",
"SeminormedAddCommGroup",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Inner.inner",
"Real.instAddMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZe... | true |
_private.Batteries.Data.Vector.Basic.0.Vector.scanrMFast.loop._unary._proof_3 | Batteries.Data.Vector.Basic | [
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"instHSub",
"_private.Batteries.Data.Vector.Basic.0.Vector.scanrMFast._proof_2",
"USize.toNat",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"instLTNat",
"instSubUSize",
"OfNat.ofNat",
"Eq",
"Not",
"Nat.decLe",
"USize... | false |
Matrix.rank_mul_le_left | Mathlib.LinearAlgebra.Matrix.Rank | [
"Nontrivial",
"Eq.mpr",
"Pi.Function.module",
"Submodule",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"instReflLe",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"Submodule.addCommM... | true |
Complex.betaIntegral_eval_one_right | Mathlib.Analysis.SpecialFunctions.Gamma.Beta | [
"instInnerProductSpaceRealComplex",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"sub_pos",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"MulOne.toOne",
"le_refl",
"Real.partialOrder",
"Real",
"MeasureTheory.Measure",
"Preorder.... | true |
_private.Mathlib.Control.LawfulFix.0.Part.Fix.mem_iff._simp_1_2 | Mathlib.Control.LawfulFix | [
"Part",
"False",
"eq_false",
"Membership.mem",
"Part.instMembership",
"Part.none",
"Part.notMem_none",
"Eq"
] | false |
FreeAbelianGroup.map_add | Mathlib.GroupTheory.FreeAbelianGroup | [
"Equiv.instEquivLike",
"AddCommGroup.toAddCommMonoid",
"Monad.toApplicative",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Function.comp",
"AddZeroClass.toAddZero",
"Equiv",
"FreeAbelianGroup.instMonad",
"instAddCommGroupFreeAbelianGroup",
"instHAdd",
"FreeAbelianGroup.lift",
"Add... | true |
_private.Mathlib.Analysis.Meromorphic.NormalForm.0.meromorphicNFAt_prod._proof_1_1 | Mathlib.Analysis.Meromorphic.NormalForm | [
"of_eq_false",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Lean.Grind.not_not",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"Lean.Grind.CommRing.Expr.mul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"eq_false",
"Lean.Grind.iff_eq",
"L... | false |
UpperHalfPlane.verticalStrip_anti_right | Mathlib.Analysis.Complex.UpperHalfPlane.Topology | [
"Real.instLE",
"Real",
"le_rfl",
"UpperHalfPlane.verticalStrip",
"HasSubset.Subset",
"LE.le",
"UpperHalfPlane",
"UpperHalfPlane.verticalStrip_mono",
"Real.instPreorder",
"Set.instHasSubset",
"Set"
] | true |
Finmap.liftOn.congr_simp | Mathlib.Data.Finmap | [
"Eq.rec",
"List.Perm",
"AList",
"Eq.ndrec",
"Finmap.liftOn",
"Eq.refl",
"Eq",
"Sigma",
"Finmap",
"AList.entries"
] | true |
_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.propagateUniversesToConstructors.match_1 | Lean.Elab.MutualInductive | [
"Unit.unit",
"Lean.Level.ctorIdx",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.propagateUniversesToConstructors._sparseCasesOn_1",
"Lean.Level.mvar",
"Lean.Level.param",
"Nat.hasNotBit",
"Lean.Level",
"Unit",
"Lean.Level.zero",
"Lean.Name",
"Lean.LMVarId"
] | false |
Filter.Germ.instAddGroupWithOne._proof_6 | Mathlib.Order.Filter.Germ.Basic | [
"AddGroupWithOne.toAddGroup",
"Int",
"Nat.cast",
"SubNegMonoid.zsmul",
"AddGroup.toSubNegMonoid",
"Filter.Germ",
"Nat",
"SubNegMonoid.toNeg",
"SubNegMonoid.zsmul_neg'",
"AddGroupWithOne",
"instNatCastInt",
"Int.negSucc",
"Nat.succ",
"Eq",
"Filter.Germ.instAddGroup",
"Filter",
"Neg.ne... | false |
SzemerediRegularity.bound | Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | [
"Real.instIsOrderedRing",
"SzemerediRegularity.stepBound",
"Real.partialOrder",
"Real",
"instHDiv",
"HMul.hMul",
"FloorRing.toFloorSemiring",
"SzemerediRegularity.initialBound._proof_2",
"Nat.instMonoid",
"Real.instDivInvMonoid",
"Real.semiring",
"HDiv.hDiv",
"Real.instFloorRing",
"Real.in... | true |
Lean.Doc.Parser.InList.mk.sizeOf_spec | Lean.DocString.Parser | [
"Lean.Doc.Parser.UnorderedListType._sizeOf_inst",
"Lean.Doc.Parser.OrderedListType._sizeOf_inst",
"Lean.Doc.Parser.OrderedListType",
"Sum",
"Sum._sizeOf_inst",
"instOfNatNat",
"instHAdd",
"Lean.Doc.Parser.InList.mk",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"instSizeOf... | true |
Lean.Parser.Command.declaration._regBuiltin.Lean.Parser.Command.computedFields.formatter_121 | Lean.Parser.Command | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Unit",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin",
"Lean.Parser.Command.computedFields.formatter"
] | false |
_private.Lean.Elab.DocString.0.Lean.Doc.ModuleDocstringState | Lean.Elab.DocString | [
"_private.Lean.Elab.DocString.0.Lean.Doc.ModuleDocstringState.mk"
] | true |
TrivSqZeroExt.inrCLM | Mathlib.Topology.Instances.TrivSqZeroExt | [
"TrivSqZeroExt.inr",
"TrivSqZeroExt",
"Semiring.toModule",
"CommSemiring.toSemiring",
"TrivSqZeroExt.inrCLM._proof_2",
"ContinuousLinearMap.mk",
"instTopologicalSpaceProd",
"TrivSqZeroExt.inrCLM._proof_3",
"TrivSqZeroExt.instTopologicalSpace",
"AddCommMonoid",
"ContinuousLinearMap",
"CommSemir... | true |
Lean.Grind.CommRing.Mon.mul.go.match_1.congr_eq_2 | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Power",
"False",
"Lean.Grind.CommRing.Mon.mult",
"id",
"heq_of_eq",
"absurd",
"Lean.Grind.CommRing.Mon.rec",
"Lean.Grind.CommRing.Mon.mul.go.match_1",
"Lean.Grind.CommRing.Mon.casesOn",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"Lean.Grind.CommRing.Mon",
"Lean... | true |
_private.Init.Data.String.Lemmas.Pattern.String.ForwardSearcher.0.String.Slice.Pattern.Model.ForwardSliceSearcher.prefixFunction_le_iff._simp_1_1 | Init.Data.String.Lemmas.Pattern.String.ForwardSearcher | [
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"propext",
"instAddNat",
"Nat.le_iff_lt_add_one",
"instLTNat",
"OfNat.ofNat",
"Eq"
] | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.