name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Server.RequestCancellation.ctorIdx | Lean.Server.RequestCancellation | [
"Lean.Server.RequestCancellation",
"Nat"
] | false |
IO.Error.instToString | Init.System.IOError | [
"ToString",
"IO.Error",
"ToString.mk",
"IO.Error.toString"
] | true |
CategoryTheory.Bicategory.Adjunction.isAbsoluteLeftKan._proof_1 | Mathlib.CategoryTheory.Bicategory.Kan.Adjunction | [
"Mathlib.Tactic.Bicategory.evalWhiskerLeft_nil",
"Mathlib.Tactic.Bicategory.evalWhiskerRight_id",
"Mathlib.Tactic.Bicategory.naturality_rightUnitor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.whiskerLeftIso",
"Mathlib.Tactic.Bicategory.eval_whiskerLeft",
"Categ... | false |
DerivedCategory.singleFunctorsPostcompQIso | Mathlib.Algebra.Homology.DerivedCategory.Basic | [
"CategoryTheory.Abelian.toPreadditive",
"instCategoryDerivedCategory",
"HomologicalComplex.instCategory",
"DerivedCategory.instCommShiftHomologicalComplexIntUpHomFunctorQuotientCompQhIso",
"DerivedCategory",
"CategoryTheory.SingleFunctors.instCategory",
"HasDerivedCategory._proof_1",
"DerivedCategory.... | true |
MonoidWithZeroHom.snd.eq_1 | Mathlib.Algebra.GroupWithZero.ProdHom | [
"GroupWithZero.toMonoidWithZero",
"Units.coeHom",
"Equiv.instEquivLike",
"MonoidHom",
"Monoid.toMulOneClass",
"MonoidWithZeroHom.snd",
"GroupWithZero",
"Prod.instMulOneClass",
"Units",
"WithZero.instMulZeroOneClass",
"Equiv",
"MonoidHom.comp",
"WithZero.lift'",
"MulZeroOneClass.toMulOneCla... | true |
_private.Mathlib.Analysis.SpecialFunctions.Pow.NNReal.0.ENNReal.rpow_zero._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Pow.NNReal | [
"NNReal",
"Option.none",
"ENNReal.none_eq_top",
"ENNReal",
"instTopENNReal",
"Top.top",
"Eq.symm",
"Eq",
"Option"
] | false |
Std.DHashMap.Equiv.casesOn | Std.Data.DHashMap.Basic | [
"Std.DHashMap.Equiv.rec",
"Std.DHashMap.Equiv",
"Std.DHashMap.Equiv.mk",
"Std.DHashMap.Raw.Equiv",
"Std.DHashMap.inner",
"Hashable",
"BEq",
"Std.DHashMap"
] | false |
Units.instMul | Mathlib.Algebra.Group.Units.Defs | [
"Units.instMul._proof_1",
"Monoid",
"Units.val",
"Mul.mk",
"HMul.hMul",
"Monoid.toMulOneClass",
"Units.instMul._proof_2",
"Mul",
"Units",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Units.mk",
"Units.inv",
"instHMul"
] | true |
CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeTop | Mathlib.CategoryTheory.MorphismProperty.Limits | [
"CategoryTheory.MorphismProperty",
"trivial",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.IsPullback",
"CategoryTheory.MorphismProperty.IsStableUnderBaseChange",
"BooleanAlgebra.toTop",
"CategoryTheory.Morphism... | true |
AlgebraNorm.ctorIdx | Mathlib.Analysis.Normed.Unbundled.AlgebraNorm | [
"SeminormedCommRing",
"SeminormedCommRing.toCommRing",
"Algebra",
"AlgebraNorm",
"CommRing.toCommSemiring",
"Nat",
"Ring.toSemiring",
"Ring"
] | false |
CategoryTheory.MorphismProperty.LeftFraction₃.mk.inj | Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.LeftFraction₃.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"And",
"And.intro",
"eq_of_heq",
"CategoryTheory.MorphismProperty.LeftFraction₃",
"HEq",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Morp... | true |
Set.iUnion_subset_iff._simp_1 | Mathlib.Data.Set.Lattice | [
"Set.iUnion_subset_iff",
"HasSubset.Subset",
"propext",
"Eq",
"Set.iUnion",
"Set.instHasSubset",
"Set"
] | false |
Subalgebra.copy._proof_4 | Mathlib.Algebra.Algebra.Subalgebra.Basic | [
"Subalgebra.instSetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.toAddZeroClass",
"Submonoid.toSubsemigroup",
"Algebra",
"Membership.mem",
"AddZeroClass.toAddZero",
"MulOne.toMul",
"Subalgebra.toSubsemiring",
"NonAssocSemiring.toMulZeroOneClass",
"AddCommMonoidWithOne.toAddMonoidW... | false |
Lean.Kernel.Diagnostics.mk.noConfusion | Lean.Environment | [
"Lean.PHashMap",
"Lean.Kernel.Diagnostics.mk",
"id",
"Lean.Kernel.Diagnostics.noConfusion",
"Nat",
"Bool",
"Lean.Name",
"Eq",
"Lean.Name.instBEq",
"Lean.Kernel.Diagnostics",
"Lean.instHashableName"
] | false |
OrderDual.instNonAssocRing._proof_3 | Mathlib.Algebra.Order.Ring.Synonym | [
"OrderDual.instNonAssocSemiring",
"AddMonoid.toZero",
"instOfNatNat",
"NonAssocRing",
"NatCast.natCast",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"OrderDual",
"NonAssocSemiring.toNatCast",
... | false |
Lean.Server.GoToKind.ctorIdx | Lean.Server.GoTo | [
"Lean.Server.GoToKind.casesOn",
"Nat",
"Lean.Server.GoToKind"
] | false |
Matrix.IsAdjMatrix.toGraph_compl_eq | Mathlib.Combinatorics.SimpleGraph.AdjMatrix | [
"Nontrivial",
"MulOne.toOne",
"False",
"NeZero.one",
"Equiv.instEquivLike",
"eq_false",
"Matrix.IsAdjMatrix.compl",
"congrArg",
"and_self",
"Matrix",
"Compl.compl",
"Matrix.IsAdjMatrix.zero_or_one",
"SimpleGraph.Adj",
"Matrix.of",
"SimpleGraph.irrefl._simp_1",
"not_true_eq_false",
"M... | true |
CategoryTheory.Abelian.SpectralObject.leftHomologyDataShortComplex._proof_9 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.Exact.fIsKernel",
"CategoryTheory.Abelian.SpectralObject.cycles",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.Abelian.SpectralObject.δToCycles",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limi... | false |
RootPairing.RootPositiveForm.form_apply_root_ne_zero | Mathlib.LinearAlgebra.RootSystem.RootPositive | [
"Eq.mpr",
"CommRing",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"LinearMap.BilinForm",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"LinearMap.inst... | true |
Std.IterM.forIn_toList | Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop | [
"Std.IterM.toList_eq_match_step",
"Pure.pure",
"Eq.mpr",
"Std.IterM.DefaultConsumers.forIn'_eq_match_step.match_3",
"bind_congr",
"Std.IterStep",
"List.foldlM",
"congrArg",
"Std.Shrink",
"instForInOfForIn'",
"List.foldlM_cons",
"Monad.toApplicative",
"Std.PlausibleIterStep",
"Std.IteratorL... | true |
Simps.AutomaticProjectionData.recOn | Mathlib.Tactic.Simps.NotationClass | [
"Simps.AutomaticProjectionData.mk",
"Simps.AutomaticProjectionData.rec",
"Bool",
"Lean.Name",
"Simps.AutomaticProjectionData"
] | false |
List.Cursor.pos_at | Std.Do.Triple.SpecLemmas | [
"Eq.mpr",
"_private.Std.Do.Triple.SpecLemmas.0.List.Cursor.pos_at._proof_1_3",
"congrArg",
"List.Cursor.pos",
"List.Cursor.at",
"id",
"List.length_take",
"List",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"congrFun'",
"instDecidableEqNat",
"instLTNat",
"Eq",
"List.length",
"Not",
... | true |
Lean.getPPPiBinderNamesHygienic | Lean.PrettyPrinter.Delaborator.Options | [
"Lean.KVMap.instValueBool",
"Lean.Options.get",
"Lean.Option.defValue",
"Bool",
"Lean.pp.piBinderNames.hygienic",
"Lean.Options",
"Lean.Option.name"
] | true |
Finset.sum_range_diag_flip | Mathlib.Algebra.BigOperators.Intervals | [
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"le_add_iff_nonneg_right",
"Nat.zero_le",
"lt_of_le_of_lt",
"Nat.instOrderedSub",
"Preorder.toLT",
"Nat.instIsOrderedAddMonoid",
"and_true",
"congrArg",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Finset",
"and_imp",
"AddMonoid.toAddZeroClass",
"P... | true |
String.Slice.Pattern.Char.instToForwardSearcherCharDefaultForwardSearcher | Init.Data.String.Pattern.Char | [
"String.Slice.Pattern.ToForwardSearcher",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher",
"Char",
"String.Slice.Pattern.Char.instForwardPatternChar",
"String.Slice.Pattern.ToForwardSearcher.defaultImplementation"
] | true |
Lean.Parser.Term.liftMethod | Lean.Parser.Do | [
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.leadingNode",
"Lean.Parser.Term.leftArrow",
"instHAndThenOfAndThen",
"instOfNatNat",
"Lean.Parser.withAntiquot",
"Bool.true",
"Unit",
"Nat",
"Lean.Parser.withCache",
"OfNat.ofNat",
"Lean.Parser.mkAntiquot",
"Bool.false",
"Lean.Name.... | true |
DiscreteUniformity.mk | Mathlib.Topology.UniformSpace.DiscreteUniformity | [
"UniformSpace",
"instBotUniformSpace",
"Bot.bot",
"DiscreteUniformity.mk",
"DiscreteUniformity",
"Eq"
] | true |
Representation.finsupp | Mathlib.RepresentationTheory.Basic | [
"Monoid",
"Pi.Function.module",
"MulOne.toOne",
"Representation.finsupp._proof_4",
"Representation",
"MonoidHom.instFunLike",
"Pi.addCommMonoid",
"Finsupp.module",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"OneHom.mk",
"AddMonoid.toAddZeroClass",
"Module.End.instSemiring",
"Repres... | true |
Std.DTreeMap.minKey?_eq_some_iff_mem_and_forall | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Ord.mk",
"Option.some",
"Membership.mem",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.instMembership",
"Bool.true",
"And",
"Iff",
"Std.LawfulEqCmp",
"Std.DTreeMap.wf",
"Std.DTreeMap.minKey?",
"Bool",
"Std.DTreeMap.Internal.Impl.minKey?_eq_some_iff_m... | true |
ConditionallyCompletePartialOrderSup.noConfusionType | Mathlib.Order.ConditionallyCompletePartialOrder.Defs | [
"ConditionallyCompletePartialOrderSup.casesOn",
"PartialOrder.toPreorder",
"Preorder.toLE",
"DirectedOn",
"PartialOrder",
"SupSet",
"LE.le",
"BddAbove",
"Set.Nonempty",
"IsLUB",
"ConditionallyCompletePartialOrderSup",
"HEq",
"SupSet.sSup",
"Set"
] | false |
instMonadEIO._aux_11 | Init.System.IO | [
"Unit.unit",
"EST",
"EST.bind",
"IO.RealWorld",
"EIO",
"Unit"
] | false |
ProofWidgets.Penrose.DiagramState.casesOn | ProofWidgets.Component.PenroseDiagram | [
"ProofWidgets.Html",
"String",
"Std.HashMap",
"instHashableString",
"instBEqOfDecidableEq",
"ProofWidgets.Penrose.DiagramState.rec",
"instDecidableEqString",
"ProofWidgets.Penrose.DiagramState.mk",
"Prod",
"ProofWidgets.Penrose.DiagramState"
] | false |
_private.Mathlib.RingTheory.SimpleModule.Basic.0.IsSemisimpleModule.sSup_simples_le._simp_1_1 | Mathlib.RingTheory.SimpleModule.Basic | [
"Submodule",
"isSimpleModule_iff_isAtom",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"Membership.mem",
"AddCommGroup",
"Subtype",
"IsSimpleModule",
"Submodule.instPartialOrder",
"Submodule.module",
"Submodule.addCommGroup",
"Submodule.setLike",
"propext",
"IsAtom",
"Submo... | false |
Set.finite_iff_finite_of_encard_eq_encard | Mathlib.Data.Set.Card | [
"Eq.mpr",
"Set.encard",
"instTopENat",
"congrArg",
"Iff.rfl",
"Set.Finite",
"Set.encard_lt_top_iff",
"id",
"Iff",
"ENat",
"LT.lt",
"propext",
"instLTENat",
"Top.top",
"Eq.symm",
"Eq",
"Set"
] | true |
LipschitzOnWith.prodMk | Mathlib.Topology.EMetricSpace.Lipschitz | [
"Prod.edist_eq",
"Eq.mpr",
"Prod.pseudoEMetricSpaceMax",
"ENNReal.ofNNReal",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"NonUnitalCommSemiring.toCommSemigroup",
"ENNReal.instIsOrderedMonoid"... | true |
Lean.Meta.Hint.tryThisDiffWidget | Lean.Meta.Hint | [
"Lean.Widget.Module",
"UInt64",
"String",
"Lean.Widget.Module.mk",
"instHashableString",
"Subtype.mk",
"Hashable.hash",
"_private.Lean.Meta.Hint.0.Lean.Meta.Hint.tryThisDiffWidget._proof_1",
"Eq"
] | true |
NonarchAddGroupSeminorm.coe_iSup_apply | Mathlib.Analysis.Normed.Group.Seminorm | [
"Eq.mpr",
"Real",
"congrArg",
"Function.Surjective.iSup_congr",
"iSup",
"NonarchAddGroupSeminorm.funLike",
"PartialOrder.toPreorder",
"NonarchAddGroupSeminorm",
"Preorder.toLE",
"Membership.mem",
"Real.instSupSet",
"Set.Elem",
"id",
"NonarchAddGroupSeminorm.instSupSet",
"NonarchAddGroupS... | true |
Prod.mk_lt_mk_iff_right._gcongr_1 | Mathlib.Order.Basic | [
"Iff.mpr",
"Preorder.toLT",
"Prod.mk",
"Prod.mk_lt_mk_iff_right",
"LT.lt",
"Prod.instPreorder",
"Prod",
"Preorder"
] | false |
instIsSemisimpleModuleOfIsSimpleModule | Mathlib.RingTheory.SimpleModule.Basic | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"IsSimpleModule",
"IsSemisimpleModule",
"IsSimpleOrder.instComplementedLattice",
"IsSimpleModule.toIsSimpleOrder",
"Condit... | true |
_private.Mathlib.Tactic.Ring.Compare.0.Mathlib.Tactic.Ring.proveLE.match_4 | Mathlib.Tactic.Ring.Compare | [
"Option.ctorIdx",
"Option.some",
"Lean.Expr",
"Nat.hasNotBit",
"Prod.mk",
"Prod",
"Prod.casesOn",
"_private.Mathlib.Tactic.Ring.Compare.0.Mathlib.Tactic.Ring.proveLE._sparseCasesOn_4",
"Option"
] | false |
Orientation.kahler._proof_1 | Mathlib.Analysis.InnerProductSpace.TwoDim | [
"instInnerProductSpaceRealComplex",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Complex.instNormedAddCommGroup",
"Real.instRCLike",
"CommSemiring.toSemiring",
"NormedSpace.toModule",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"smulCommCl... | false |
_private.Mathlib.GroupTheory.DoubleCoset.0.DoubleCoset.mem_doubleCoset_of_not_disjoint._simp_1_1 | Mathlib.GroupTheory.DoubleCoset | [
"HMul.hMul",
"Mul",
"DoubleCoset.mem_doubleCoset",
"Membership.mem",
"Exists",
"And",
"propext",
"DoubleCoset.doubleCoset",
"Eq",
"Set.instMembership",
"instHMul",
"Set"
] | false |
Polynomial.modByMonic_eq_of_dvd_sub | Mathlib.Algebra.Polynomial.Div | [
"Nontrivial",
"Distrib.leftDistribClass",
"WithBot.instPreorder",
"Eq.mpr",
"Semigroup.toMul",
"CommRing",
"WithBot",
"Preorder.toLT",
"Dvd.dvd",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"AddMonoid.toAddSemigroup",
"AddGroupWithOne.toAdd... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.readyForRatAdd_insert._proof_1_4 | Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"Bool",
"instAddNat",
"instLTNat",
"Array.mk",
"Prod",
"OfNat.ofNat",
"Std.Tactic.BVDecide.LRAT.Internal.PosFin",
"Array.size",
"List.nil"
] | false |
Char.utf8Size_eq_one_iff | Init.Data.String.Decode | [
"UInt32.not_le._simp_1",
"Char.utf8Size._proof_3",
"Eq.mpr",
"False",
"congrArg",
"Char.utf8Size._proof_2",
"eq_false_of_decide",
"true_iff",
"Eq.mp",
"id",
"UInt32.ofNatLT",
"instOfNatNat",
"LE.le",
"Char.utf8Size._proof_1",
"false_iff",
"Char.utf8Size.fun_cases_unfolding",
"Char.va... | true |
Lean.Meta.Grind.TopSort.State.mk | Lean.Meta.Tactic.Grind.EqResolution | [
"Lean.Meta.Grind.TopSort.State",
"Lean.Meta.Grind.TopSort.State.mk",
"Lean.Expr.instBEq",
"Std.HashSet",
"Lean.Expr",
"Array",
"Lean.Expr.instHashable"
] | true |
LinearMap.coe_smul | Mathlib.Algebra.Module.LinearMap.Defs | [
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"RingHom",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"LinearMap.instSMul",
"Pi.instSMul",
"Semiring",
"DistribSMul",
"HSMul.h... | true |
_private.Mathlib.RingTheory.Ideal.Quotient.PowTransition.0.Submodule.factorPow_comp_powSMulQuotInclusion._proof_3 | Mathlib.RingTheory.Ideal.Quotient.PowTransition | [
"Int.Linear.not_eq_norm_expr",
"Lean.RArray.leaf",
"False",
"congrArg",
"Classical.byContradiction",
"Nat.ToInt.add_congr",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"Nat.Linear.ExprCnstr.eq_of_toNormPoly_eq",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"N... | false |
SimpleGraph.decidableMemCommonNeighbors._aux_1 | Mathlib.Combinatorics.SimpleGraph.Basic | [
"SimpleGraph.Adj",
"DecidableRel",
"Membership.mem",
"SimpleGraph.neighborSet",
"SimpleGraph.commonNeighbors",
"SimpleGraph",
"DecidablePred",
"SimpleGraph.neighborSet.memDecidable",
"instDecidableAnd",
"Set.instMembership",
"Set"
] | false |
Module.ringKrullDim_quotient_add_one_of_mem_nonZeroDivisors | Mathlib.RingTheory.KrullDimension.Regular | [
"Ideal.Quotient.commSemiring",
"CommRing",
"WithBot.some",
"WithBot",
"instCompleteLinearOrderENat",
"Semiring.toModule",
"instAddMonoidWithOneENat",
"CompleteLattice.instOmegaCompletePartialOrder",
"CommSemiring.toSemiring",
"CompletelyDistribLattice.toCompleteLattice",
"PartialOrder.toPreorder... | true |
Lean.Server.Test.Runner.RunnerState.method | Lean.Server.Test.Runner | [
"String",
"Lean.Server.Test.Runner.RunnerState"
] | true |
Aesop.TreeRef.recOn | Aesop.Tree.Traversal | [
"Aesop.TreeRef",
"Aesop.RappRef",
"Aesop.TreeRef.rapp",
"Aesop.GoalRef",
"Aesop.TreeRef.mvarCluster",
"Aesop.TreeRef.rec",
"Aesop.TreeRef.goal",
"Aesop.MVarClusterRef"
] | false |
CauSeq.const.congr_simp | Mathlib.Algebra.Order.CauSeq.Basic | [
"LinearOrder",
"IsStrictOrderedRing",
"SemilatticeInf.toPartialOrder",
"Eq.rec",
"DistribLattice.toLattice",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"IsAbsoluteValue",
"CauSeq",
"DivisionSemiring.toSemiring",
"Eq.refl",
"CauSeq.const",
"Ring.toSemiring",
"Eq",
"Field",
"Ri... | true |
HomologicalComplex.mapBifunctor₁₂.ι_eq | Mathlib.Algebra.Homology.BifunctorAssociator | [
"HomologicalComplex.mapBifunctor₁₂.ι",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"CategoryTheory.functorCategoryPreadditive",
"HomologicalComplex.ma... | true |
Std.Net.instDecidableEqIPv4Addr.decEq.match_1 | Std.Net.Addr | [
"Vector",
"Std.Net.IPv4Addr",
"instOfNatNat",
"Std.Net.IPv4Addr.casesOn",
"Nat",
"Std.Net.IPv4Addr.mk",
"OfNat.ofNat",
"UInt8"
] | false |
omegaToLiaRegressions | Mathlib.Tactic.TacticAnalysis.Declarations | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Mathlib.TacticAnalysis.Config",
"Lean.SourceInfo",
"Array.mkArray0",
"Lean.Syntax.atom",
"Float",
"Lean.TSyntax.mk",
"Lean.Syntax",
"IO.RealWorld",
"EIO",
"instMonadEIO",
"Applicative.toPure",
"Lean.Ela... | true |
CantorScheme.ClosureAntitone | Mathlib.Topology.MetricSpace.CantorScheme | [
"HasSubset.Subset",
"List.cons",
"TopologicalSpace",
"List",
"closure",
"Set.instHasSubset",
"Set"
] | true |
List.foldrM_filterMap | Init.Data.List.Monadic | [
"Pure.pure",
"Eq.mpr",
"List.foldrM_cons",
"congrArg",
"Monad.toApplicative",
"Option.casesOn",
"Option.some",
"List.foldrM",
"LawfulMonad.bind_pure_comp",
"LawfulApplicative.toLawfulFunctor",
"id",
"LawfulMonad",
"List.rec",
"List.filterMap.match_1",
"Applicative.toPure",
"List.cons",... | true |
Std.HashMap.Raw.getKey!_emptyWithCapacity | Std.Data.HashMap.RawLemmas | [
"Inhabited.default",
"Std.DHashMap.Raw.getKey!_emptyWithCapacity",
"Nat",
"Std.HashMap.Raw.emptyWithCapacity",
"Inhabited",
"Hashable",
"BEq",
"Eq",
"Std.HashMap.Raw.getKey!"
] | true |
CategoryTheory.Functor.HomObj.comp_app | Mathlib.CategoryTheory.Functor.FunctorHom | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.HomObj.app",
"CategoryTheory.types",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Functor.HomObj.comp",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.... | true |
Vector.exists_of_mem_flatMap | Init.Data.Vector.Lemmas | [
"Vector.instMembership",
"HMul.hMul",
"Vector",
"Membership.mem",
"Exists",
"instMulNat",
"And",
"Vector.mem_flatMap",
"Nat",
"Iff.mp",
"Vector.flatMap",
"instHMul"
] | true |
NumberField.recOn | Mathlib.NumberTheory.NumberField.Basic | [
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Rat.commSemiring",
"Field.toDivisionRing",
"Algebra.toModule",
"Rat.instDivisionRing",
"DivisionRing.toRing",
"NumberField.rec",
"Field.toSemifield",
"DivisionRing.toRatAlgebra",
"CharZero",
"FiniteDimensional",
"Semifield.toDivisionSemiring",
... | false |
nhds_le_nhdsSet | Mathlib.Topology.NhdsSet | [
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"nhds",
"LE.le",
"TopologicalSpace",
"Set.mem_image_of_mem",
"Set.image",
"le_sSup",
"CompleteLattice.toCompleteSemilatticeSup",
"nhdsSet",
"Set.instMembership",
"Filter",
"Filter.instPartia... | true |
Matroid.spanning_iff_compl_coindep | Mathlib.Combinatorics.Matroid.Closure | [
"Eq.mpr",
"Set.diff_subset_iff._simp_1",
"congrArg",
"Matroid.E",
"Iff.rfl",
"Matroid.spanning_iff_compl_coindep._auto_1",
"Set.instUnion",
"id",
"HasSubset.Subset",
"autoParam",
"SDiff.sdiff",
"Iff",
"Set.subset_union_right._simp_1",
"Matroid.Spanning",
"True",
"propext",
"Set.diff_... | true |
NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero | Mathlib.NumberTheory.NumberField.Units.DirichletTheorem | [
"NormedCommRing.toNormedRing",
"Real.instIsOrderedRing",
"Not.intro",
"NumberField.InfinitePlace.instFunLikeReal",
"Units.val",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real.instLE",
"Real",
"Mathlib.Meta.NormNum.instAddMonoidWithOne",
... | true |
Array.getElem_shrink._proof_2 | Init.Data.Array.Lemmas | [
"congrArg",
"_private.Init.Data.Array.Lemmas.0.Array.getElem_shrink._proof_1",
"Array.shrink",
"Eq.mp",
"Array",
"Array.size_shrink",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"Nat.decLt",
"instLTNat",
"Array.size",
"Not",
"Min.min",
"instMinNat"
] | false |
Module.Presentation.tautological.R.recOn | Mathlib.Algebra.Module.Presentation.Tautological | [
"Module.Presentation.tautological.R.rec",
"Module.Presentation.tautological.R",
"Module.Presentation.tautological.R.add",
"Module.Presentation.tautological.R.smul"
] | false |
List.Perm.length_eq | Init.Data.List.Perm | [
"congrArg",
"List.Perm",
"instOfNatNat",
"List.cons",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"of_eq_true",
"instAddNat",
"Eq.refl",
"congrFun'",
"List.Perm.rec",
"OfNat.ofNat",
"Eq",
"List.length",
"Eq.trans",
"List.nil"
] | true |
CategoryTheory.Limits.ChosenPullback.p₂ | Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.ChosenPullback.pullback",
"CategoryTheory.Limits.ChosenPullback",
"CategoryTheory.Category"
] | true |
CategoryTheory.ObjectProperty.prop_cokernel | Mathlib.CategoryTheory.ObjectProperty.Kernels | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ObjectProperty.prop_of_isColimit_cokernelCofork",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.cokernel",
"CategoryTheory.Limits.cokernel.condition",
"CategoryTheory.ObjectProperty.IsClosedUnderCokernels",
"Cat... | true |
_private.Init.Data.List.Attach.0.List.pmap_eq_pmapImpl.match_1_1 | Init.Data.List.Attach | [
"Subtype.casesOn",
"Subtype",
"Subtype.mk"
] | false |
Std.Rxi.Iterator.toList_eq_match | Init.Data.Range.Polymorphic.Lemmas | [
"Iff.mpr",
"Eq.mpr",
"_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Rxc.Iterator.toList_eq_match.match_1.splitter",
"Std.IterStep",
"Std.PRange.UpwardEnumerable",
"Std.Rxi.Iterator.isPlausibleStep_iff",
"congrArg",
"Std.Rxc.Iterator.toList_eq_match.match_1",
"Std.Rxi.Iterator.mk",
"Std.Rxi.ins... | true |
measurable_of_countable | Mathlib.MeasureTheory.MeasurableSpace.Basic | [
"MeasurableSet",
"MeasurableSingletonClass",
"Measurable",
"Set.Countable.measurableSet",
"MeasurableSpace",
"Set.preimage",
"SetCoe.countable",
"Set.to_countable",
"Countable",
"Set"
] | true |
_private.Init.Data.List.Impl.0.List.takeWhileTR.go | Init.Data.List.Impl | [
"cond",
"List.brecOn",
"Array.push",
"Array.toList",
"_private.Init.Data.List.Impl.0.List.takeWhileTR.go.match_1",
"List.cons",
"Array",
"List",
"Bool",
"List.below",
"List.nil"
] | true |
Polynomial.X_pow_sub_one_separable_iff | Mathlib.FieldTheory.Separable | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"False",
"Polynomial.instOne",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NeZero.one",
"CommRing.toNonUnitalCommRing",
"sub_self",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"... | true |
Complex.ofReal_comp_pow | Mathlib.Data.Complex.Basic | [
"RingHom.instRingHomClass",
"Real",
"map_comp_pow",
"RingHom",
"Function.comp",
"Real.semiring",
"RingHomClass.toMonoidWithZeroHomClass",
"Pi.instPow",
"NonAssocSemiring.toMulZeroOneClass",
"MonoidWithZeroHomClass.toMonoidHomClass",
"Complex.ofReal",
"Complex.ofRealHom",
"Monoid.toPow",
"R... | true |
Matroid.Nonempty.casesOn | Mathlib.Combinatorics.Matroid.Basic | [
"Matroid.Nonempty.rec",
"Matroid.E",
"Set.Nonempty",
"Matroid",
"Matroid.Nonempty",
"Matroid.Nonempty.mk"
] | false |
List.forall_iff_forall_mem | Mathlib.Data.List.Basic | [
"List.brecOn",
"Eq.mpr",
"congrArg",
"Iff.rfl",
"Membership.mem",
"List.forall_cons",
"id",
"List.cons",
"List",
"And",
"Unit",
"Iff",
"List.instMembership",
"List.Forall",
"List.forall_mem_cons",
"True",
"propext",
"List.below",
"List.uniqueOfIsEmpty.match_1",
"iff_true_intro"... | true |
_private.Mathlib.LinearAlgebra.Eigenspace.Basic.0.Module.End.eigenspace_restrict_le_eigenspace._simp_1_1 | Mathlib.LinearAlgebra.Eigenspace.Basic | [
"SetLike",
"Membership.mem",
"SetLike.coe",
"SetLike.mem_coe",
"propext",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
PreOpposite.op'.inj | Mathlib.Algebra.Opposites | [
"eq_of_heq",
"HEq",
"PreOpposite",
"PreOpposite.op'",
"Eq",
"PreOpposite.op'.noConfusion"
] | true |
LieSubmodule.gi._proof_2 | Mathlib.Algebra.Lie.Submodule | [
"LieSubmodule.instSetLike",
"CommRing",
"CompleteLattice.instOmegaCompletePartialOrder",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"LieSubmodule",
"Preorder.toLE",
"AddCommGroup",
"LE.le",
"LieRing",
"CommRing.toCommSemiring",
"SetLike.coe",
"Lie... | false |
Std.TreeSet.foldrM_eq_foldrM_toList | Std.Data.TreeSet.Lemmas | [
"Std.TreeSet",
"Std.TreeSet.toList",
"Ordering",
"List.foldrM",
"Std.TreeSet.inner",
"LawfulMonad",
"Std.TreeSet.foldrM",
"Unit",
"Monad",
"Eq",
"Std.TreeMap.foldrM_eq_foldrM_keys"
] | true |
_private.Mathlib.CategoryTheory.Iso.0.CategoryTheory.Iso.cancel_iso_hom_right_assoc._simp_1_2 | Mathlib.CategoryTheory.Iso | [
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.cancel_mono",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | false |
CategoryTheory.Abelian.Ext.homEquiv₀_symm_apply | Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | [
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian",
"Equiv",
"instOfNatNat",
"CategoryTheory.HasExt",
"Nat",
"CategoryTheory.Abelian.Ext",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Equiv.symm",
"OfNat.ofNat",
"Eq",
"DFunL... | true |
AddCommute.map | Mathlib.Algebra.Group.Commute.Hom | [
"AddSemiconjBy.map",
"AddCommute",
"AddHomClass",
"DFunLike.coe",
"Add",
"FunLike"
] | true |
PNat.toPNat'_coe | Mathlib.Data.PNat.Defs | [
"PNat.val",
"Nat.succ_pred_eq_of_pos",
"Nat.toPNat'",
"instOfNatNat",
"Nat",
"LT.lt",
"instLTNat",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.JointlyFaithful | Mathlib.CategoryTheory.Functor.ReflectsIso.Jointly | [
"CategoryTheory.Functor",
"CategoryTheory.JointlyFaithful.mk",
"CategoryTheory.Category"
] | true |
WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_eq_zero | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | [
"WeierstrassCurve.Jacobian.Point.toAffine_of_Z_eq_zero",
"Units.instMulAction",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"WeierstrassCurve.Affine.Point.instZero",
"CommSemiring.toSemiring",
"WeierstrassCurve.Jacobian.instMulActionForallFinOfNatNat",
"Weierstrass... | true |
strictConvexOn_of_deriv2_pos | Mathlib.Analysis.Convex.Deriv | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"Real.denselyNormedField",
"Real.instZero",
"Real.instZeroLEOneClass",
"congrArg",
"CommSemiring.toSemiring",
"IsTopologic... | true |
CategoryTheory.Monad.forgetCreatesColimits | Mathlib.CategoryTheory.Monad.Limits | [
"CategoryTheory.Limits.PreservesColimitsOfSize",
"CategoryTheory.Monad",
"CategoryTheory.Monad.forget",
"CategoryTheory.Monad.forgetCreatesColimits._proof_1",
"CategoryTheory.CreatesColimitsOfShape",
"inferInstance",
"CategoryTheory.CreatesColimitsOfSize.mk",
"CategoryTheory.Monad.toFunctor",
"Categ... | true |
Ring.instIsDomainNormalClosure | Mathlib.RingTheory.NormalClosure | [
"IsDomain",
"CommRing",
"Ring.NormalClosure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Module.IsTorsionFree",
"Algebra",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Ring.instCommRingNormalClosure",
... | true |
Rat.commRing._proof_11 | Mathlib.Algebra.Ring.Rat | [
"Rat",
"AddMonoid.toZero",
"AddCommGroup.toAddGroup",
"Int",
"SubNegMonoid.zsmul",
"AddGroup.toSubNegMonoid",
"instOfNat",
"Zero.toOfNat0",
"SubNegMonoid.zsmul_zero'",
"SubNegMonoid.toAddMonoid",
"OfNat.ofNat",
"Eq",
"Rat.addCommGroup"
] | false |
Lean.Level.PP.Result.maxNode.noConfusion | Lean.Level | [
"Lean.Level.PP.Result.maxNode",
"id",
"Lean.Level.PP.Result.noConfusion",
"List",
"Lean.Level.PP.Result",
"Eq"
] | false |
HahnEmbedding.Seed.mk.sizeOf_spec | Mathlib.Algebra.Order.Module.HahnEmbedding | [
"Submodule",
"StrictMono",
"Ring.toNonAssocRing",
"IsOrderedRing",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"HahnEmbedding.Seed._sizeOf_inst",
"PartialOrder.toPreorder",
"LinearMap.instFunLike",
"N... | true |
Std.HashMap.Raw.distinct_keys | Std.Data.HashMap.RawLemmas | [
"List.Pairwise",
"Std.HashMap.Raw.WF.out",
"Std.DHashMap.Raw.distinct_keys",
"Std.HashMap.Raw.WF",
"LawfulHashable",
"Std.HashMap.Raw",
"BEq.beq",
"EquivBEq",
"Std.HashMap.Raw.keys",
"Bool",
"Std.HashMap.Raw.inner",
"Hashable",
"Bool.false",
"BEq",
"Eq"
] | true |
AlgebraicGeometry.Scheme.Modules.fromTildeΓ._proof_6 | Mathlib.AlgebraicGeometry.Modules.Tilde | [
"Eq.mpr",
"RingHom.instRingHomClass",
"AlgebraicGeometry.Spec",
"CategoryTheory.Functor",
"Module.End.instMonoid",
"Opposite",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"PrimeSpectrum.basicOpen",
"ModuleCat",
"Monoid.to... | false |
Lean.Lsp.TextDocumentSyncOptions.noConfusion | Lean.Data.Lsp.TextSync | [
"Lean.Lsp.TextDocumentSyncKind",
"Lean.Lsp.TextDocumentSyncOptions",
"Lean.Lsp.TextDocumentSyncOptions.casesOn",
"Lean.Lsp.TextDocumentSyncOptions.noConfusionType",
"Lean.Lsp.SaveOptions",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Option"
] | false |
hasCardinalLT_iff_cardinal_mk_lt | Mathlib.SetTheory.Cardinal.HasCardinalLT | [
"Preorder.toLT",
"HasCardinalLT",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Cardinal.lift",
"Cardinal.mk",
"iff_self",
"Cardinal.partialOrder",
"Iff",
"congr",
"LT.lt",
"True",
"of_eq_true",
"congrFun'",
"Eq.trans",
"Cardinal.lift_id"
] | true |
FreeLieAlgebra.Rel.smulOfTower | Mathlib.Algebra.Lie.Free | [
"LieAlgebra.toModule",
"MonoidAlgebra.addCommMonoid",
"Monoid",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"MonoidAlgebra.distribMulAction",
"CommRing.toNonUnitalCommRing",
"FreeNonUnitalNonAsso... | true |
Associates.factors_subsingleton | Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet | [
"Eq.mpr",
"HEq.refl",
"Associates.instZero",
"Associates.factors_zero",
"Irreducible",
"inferInstance",
"Lean.Meta.FastSubsingleton.elim",
"Multiset",
"Eq.casesOn",
"Subtype",
"UniqueFactorizationMonoid",
"CommMonoidWithZero.toMonoidWithZero",
"Associated.setoid",
"WithTop.top",
"MonoidW... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.