name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Batteries.RBNode.max? | Batteries.Data.RBMap.Basic | [
"Batteries.RBNode",
"Batteries.RBNode.brecOn",
"Batteries.RBNode.max?._f",
"Option"
] | true |
Real.differentiable_fourierChar_neg_bilinear_right | Mathlib.Analysis.Fourier.FourierTransformDeriv | [
"ContinuousLinearMap.comp",
"instInnerProductSpaceRealComplex",
"Differentiable",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Real.pi",
"RCLike.... | true |
CategoryTheory.Functor.WellOrderInductionData.Extension._sizeOf_inst | Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.WellOrderInductionData",
"Opposite",
"LinearOrder",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Preorder.smallCategory",
"Bot.bot",
"Opposite.op",
"... | false |
USize.toUInt32_le._simp_1 | Init.Data.UInt.Lemmas | [
"instLEUSize",
"instModUSize",
"instHMod",
"LE.le",
"HMod.hMod",
"USize.toUInt32_le",
"USize.toUInt32",
"propext",
"instLEUInt32",
"UInt32",
"OfNat.ofNat",
"Eq",
"USize",
"USize.instOfNat"
] | false |
WeierstrassCurve.Projective.negAddY_of_X_eq' | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Mathlib.Meta.NormNum.isNat_add",
"CommRing",
"Mathlib.Meta.NormNum.instAddMonoidWithOne",
"Mathlib.Tact... | true |
NormedCommRing.mul_comm | Mathlib.Analysis.Normed.Ring.Basic | [
"NormedCommRing.toNormedRing",
"Semigroup.toMul",
"NormedRing.toRing",
"HMul.hMul",
"NormedCommRing",
"Semiring.toMonoid",
"Monoid.toSemigroup",
"Ring.toSemiring",
"Eq",
"instHMul"
] | true |
ContinuousOn.comp_fract'' | Mathlib.Topology.Algebra.Order.Floor | [
"Set.instSProd",
"OrderTopology",
"Continuous",
"SProd.sprod",
"Int.fract",
"LinearOrder",
"Set.univ",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"IsStrictOrderedRing",
"instTopologicalSpaceProd",
"Function.comp",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"... | true |
Std.ExtDHashMap.Const.getKey?_ofList_of_contains_eq_false | Std.Data.ExtDHashMap.Lemmas | [
"List.map",
"List.contains",
"LawfulHashable",
"Prod.fst",
"Std.ExtDHashMap.getKey?",
"Option.none",
"List",
"Std.ExtDHashMap.Const.ofList",
"EquivBEq",
"Bool",
"Hashable",
"Prod",
"Bool.false",
"BEq",
"Eq",
"Std.DHashMap.Const.getKey?_ofList_of_contains_eq_false",
"Option"
] | true |
Lean.Grind.instCommRingInt | Init.GrindInstances.Ring.Int | [
"instPowNat",
"Lean.Grind.instCommRingInt._proof_4",
"instSMulOfMul",
"HMul.hMul",
"Int.mul_assoc",
"Int.add_assoc",
"Int.one_mul",
"Lean.Grind.Semiring.mk",
"Int.add_left_neg",
"Int.instNegInt",
"SMul.mk",
"Int.sub_eq_add_neg",
"Int",
"Int.instNatPow",
"Int.pow_succ",
"Int.pow_zero",
... | true |
Finset.sups_eq_empty._simp_1 | Mathlib.Data.Finset.Sups | [
"Finset.hasSups",
"Finset",
"Finset.sups_eq_empty",
"Finset.instEmptyCollection",
"propext",
"Or",
"EmptyCollection.emptyCollection",
"Eq",
"SemilatticeSup",
"HasSups.sups",
"DecidableEq"
] | false |
Submodule.localized_fg | Mathlib.RingTheory.Localization.Finiteness | [
"Submodule",
"Submodule.localized._proof_3",
"Semiring.toModule",
"LocalizedModule",
"OreLocalization.instAlgebra",
"Submodule.localized._proof_2",
"CommSemiring.toSemiring",
"Algebra.id",
"Localization",
"localizedModuleIsLocalizedModule",
"Submodule.FG",
"AddCommMonoid",
"MulZeroOneClass.t... | true |
_private.Lean.Meta.Hint.0.Lean.Meta.Hint.readableDiff.wordDiff.match_8 | Lean.Meta.Hint | [
"Lean.Diff.Action",
"String",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
Lean.Parser.initFn._@.Lean.Parser.Extension.4243742150._hygCtx._hyg.4 | Lean.Parser.Extension | [
"Lean.Option",
"IO",
"Lean.Option.Decl.mk",
"Lean.KVMap.instValueBool",
"Lean.Option.register",
"Bool",
"Lean.Name.mkStr2",
"Bool.false",
"Lean.Name.mkStr4"
] | false |
QuaternionAlgebra.basisOneIJK._proof_1 | Mathlib.Algebra.Quaternion | [
"Finite",
"instOfNatNat",
"Finite.of_fintype",
"Fin.fintype",
"Nat",
"OfNat.ofNat",
"Fin"
] | false |
EuclideanGeometry.orthogonalProjection_orthogonalProjection_of_le | Mathlib.Geometry.Euclidean.Projection | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Submodule",
"AffineSubspace.direction_le",
"NormedRing.toRing",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"SetLike.le_def",
"P... | true |
Std.Net.SocketAddressV6.noConfusionType | Std.Net.Addr | [
"Std.Net.SocketAddressV6.casesOn",
"Std.Net.IPv6Addr",
"UInt16",
"Std.Net.SocketAddressV6",
"Eq"
] | false |
_private.Mathlib.Algebra.Homology.HomotopyCategory.SpectralObject.0.HomotopyCategory.spectralObjectMappingCone._simp_4 | Mathlib.Algebra.Homology.HomotopyCategory.SpectralObject | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.map",
"CategoryTheory.Functor.map_comp_assoc",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheor... | false |
Finmap.lookup_insert | Mathlib.Data.Finmap | [
"congrArg",
"Finmap.lookup.congr_simp",
"Option.some",
"AList.insert",
"AList.lookup_insert",
"Finmap.lookup",
"Finmap.induction_on",
"AList",
"True",
"eq_self",
"Finmap.insert_toFinmap",
"of_eq_true",
"Finmap.insert",
"congrFun'",
"Eq",
"AList.toFinmap",
"Finmap",
"Eq.trans",
"O... | true |
Monoid.CoprodI.Word.of_smul_def | Mathlib.GroupTheory.CoprodI | [
"Monoid",
"instHSMul",
"MonoidHom.instFunLike",
"Monoid.CoprodI.of",
"Equiv.instEquivLike",
"HMul.hMul",
"MonoidHom",
"Monoid.toMulOneClass",
"Monoid.CoprodI.Word.Pair.mk",
"Equiv",
"MulOne.toMul",
"Monoid.CoprodI.Word.equivPair",
"Monoid.CoprodI.Word",
"Monoid.CoprodI",
"Monoid.instCopr... | true |
Isometry.extensionHom | Mathlib.Topology.MetricSpace.Completion | [
"Isometry.extensionHom._proof_1",
"UniformSpace.Completion.extensionHom",
"CompleteSpace",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"PseudoMetricSpace.toUniformSpace",
"RingHom",
"IsUniformAddGroup",
"NonAssocRing.toNonUnitalNonAssocRing",
"IsTopologicalRing",
"PseudoMetricSpace",
... | true |
LinearEquiv.funCongrLeft_apply | Mathlib.Algebra.Module.Equiv.Basic | [
"Pi.Function.module",
"Pi.addCommMonoid",
"Equiv.instEquivLike",
"LinearMap.instFunLike",
"Equiv",
"LinearMap",
"AddCommMonoid",
"LinearEquiv.funCongrLeft",
"LinearMap.funLeft",
"RingHomInvPair.ids",
"LinearEquiv",
"Semiring",
"LinearEquiv.instEquivLike",
"Module",
"RingHom.id",
"Semir... | true |
Lean.Elab.Command.CtorView.ctorIdx | Lean.Elab.MutualInductive | [
"Lean.Elab.Command.CtorView",
"Nat"
] | false |
CategoryTheory.kernelCokernelCompSequence.snakeInput_L₂_X₃ | Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.SnakeInput.L₂",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.kernelCokernelCompSequence.snakeInput",
"CategoryTheory.Abelian",
"CategoryTheory.Preadditive.preadditiveHasZeroMorphisms",
"Eq.refl",
"Categor... | true |
_private.Mathlib.Data.Finset.Erase.0.Finset.coe_erase._proof_1_1 | Mathlib.Data.Finset.Erase | [
"Lean.Grind.of_eq_eq_true",
"Set.ext",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Finset",
"False.elim",
"Classical.byContradiction",
"Lean.Grind.and_eq_of_eq_true_left",
"Membership.mem",
"Exists",
"Eq.mp",
"Set.i... | false |
Submodule.starProjection_unit_singleton | Mathlib.Analysis.InnerProductSpace.Projection.Basic | [
"NormedCommRing.toNormedRing",
"one_pow",
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Submodule",
"complete_of_proper",
"RingHom.instRingHomClass",
"MulOne.toOne",
"Real",
"instHSMul",
"NormedRing.toRing",
"RCLike.toNormedAlgebra",
"A... | true |
ProbabilityTheory.multivariateGaussian._proof_3 | Mathlib.Probability.Distributions.Gaussian.Multivariate | [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"fact_one_le_two_ennreal",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_conti... | false |
_private.Lean.Meta.RecursorInfo.0.Lean.Meta.mkRecursorInfoCore | Lean.Meta.RecursorInfo | [
"Pure.pure",
"Lean.getConstInfo",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"_private.Lean.Meta.RecursorInfo.0.Lean.Meta.getNumParams",
"Lean.ConstantInfo.type",
"_private.Lean.Meta.RecursorInfo.0.Lean.Meta.mkRecursorInfoCore.match_1",
"Lean.ConstantInfo.level... | true |
_private.Mathlib.Algebra.Category.CoalgCat.Basic.0.CoalgCat.Hom.toCoalgHom_injective.match_1_3 | Mathlib.Algebra.Category.CoalgCat.Basic | [
"CoalgCat.toModuleCat",
"CommRing",
"Coalgebra.toCoalgebraStruct",
"CoalgCat",
"CoalgHom",
"AddCommGroup.toAddCommMonoid",
"CoalgCat.Hom.casesOn",
"CoalgCat.instCoalgebra",
"CommRing.toCommSemiring",
"ModuleCat.isAddCommGroup",
"CoalgCat.Hom.toCoalgHom'",
"CoalgCat.Hom.mk",
"ModuleCat.carrie... | false |
FiniteDimensional.LinearEquiv.quotEquivOfQuotEquiv._proof_2 | Mathlib.LinearAlgebra.FiniteDimensional.Lemmas | [
"AddCommGroup.toAddCommMonoid",
"Membership.mem",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"Subtype",
"DivisionRing.toRing",
"Submodule.module",
"Module.Free",
"Subspace",
"Submodule.addCommGroup",
"Submodule.setLike",
"DivisionSemiring.toSemiring",
"Module.Free.of_divisionRing",
... | false |
_private.Mathlib.Topology.Sets.VietorisTopology.0.TopologicalSpace.vietoris.isTopologicalBasis._simp_1_8 | Mathlib.Topology.Sets.VietorisTopology | [
"Membership.mem",
"propext",
"Set.image",
"Eq",
"Set.instMembership",
"Set.forall_mem_image",
"Set"
] | false |
_private.Init.Data.Array.Lemmas.0.Array.set_push._proof_1_2 | Init.Data.Array.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Array.push",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Array.set",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Opti... | false |
ISize.toInt8_or | Init.Data.SInt.Bitwise | [
"instHOrOfOrOp",
"congrArg",
"instOrOpISize",
"Int8",
"BitVec.instOrOp",
"BitVec",
"Int8.toBitVec_inj",
"instOfNatNat",
"instOrOpInt8",
"System.Platform.numBits",
"HOr.hOr",
"Nat",
"congr",
"ISize.toBitVec_or",
"True",
"ISize.toBitVec",
"eq_self",
"Iff.mp",
"BitVec.signExtend",
... | true |
Plausible.Testable.varTestable.match_1 | Plausible.Testable | [
"Plausible.TestResult",
"Plausible.SampleableExt.proxy",
"Sigma.mk",
"Sigma.casesOn",
"Plausible.SampleableExt.interp",
"Plausible.SampleableExt",
"Sigma"
] | false |
SeminormedCommGroup.to_isUniformGroup | Mathlib.Analysis.Normed.Group.Uniform | [
"Prod.pseudoEMetricSpaceMax",
"LipschitzWith.prod_snd",
"instHDiv",
"SeminormedCommGroup.toPseudoMetricSpace",
"PseudoMetricSpace.toUniformSpace",
"LipschitzWith.prod_fst",
"Distrib.toAdd",
"HDiv.hDiv",
"NNReal",
"Prod.fst",
"LipschitzWith.uniformContinuous",
"instDistribOfSemiring",
"Group.... | true |
ProbabilityTheory.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero | Mathlib.Probability.Moments.SubGaussian | [
"Pure.pure",
"MeasureTheory.ae",
"Unit.unit",
"Real",
"MeasureTheory.Measure",
"instCountablePUnit",
"ProbabilityTheory.HasSubgaussianMGF_iff_kernel",
"Real.instZero",
"congrArg",
"Filter.Eventually",
"standardBorelSpace_of_discreteMeasurableSpace",
"Eq.mp",
"ProbabilityTheory.Kernel.instFun... | true |
RingHom.congr_arg | Mathlib.Algebra.Ring.Hom.Defs | [
"RingHom",
"NonAssocSemiring",
"RingHom.instFunLike",
"Eq",
"DFunLike.coe",
"DFunLike.congr_arg"
] | true |
IndiscreteTopology.casesOn | Mathlib.Topology.Order | [
"IndiscreteTopology.mk",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"TopologicalSpace.instCompleteLattice",
"CompleteLattice.toBoundedOrder",
"IndiscreteTopology",
"IndiscreteTopology.rec",
"TopologicalSpace",
"OrderTop.toTop",
"Bounded... | false |
Lean.Elab.Tactic.BVDecide.Frontend.Normalize.shiftLeft | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Simproc | [
"Pure.pure",
"_private.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Simproc.0.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.bv_and.match_1",
"instPowNat",
"Unit.unit",
"bne",
"Lean.Meta.getNatValue?",
"Lean.Meta.Simp.Result.mk",
"Lean.Expr.isApp",
"ReaderT",
"Lean.Meta.Simp.Step",
"Lean.Meta.Stat... | true |
_private.Mathlib.Analysis.Calculus.DifferentialForm.Basic.0.extDeriv_smul._simp_1_1 | Mathlib.Analysis.Calculus.DifferentialForm.Basic | [
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"Set.univ",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"extDeriv",
"instOfNatNat",
"Field.toSemifield",
"extDerivWithin_univ",
"instHAdd",
"Semifield.toDivisionSemiring",
"SeminormedAddCommGroup.toPseudoMe... | false |
Bialgebra.ofAlgHom._proof_20 | Mathlib.RingTheory.Bialgebra.Basic | [
"MulOne.toOne",
"AlgHom.algHomClass",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"MonoidHomClass.toOneHomClass",
"Algebra.id",
"RingHomClass.toMonoidWithZeroHomClass",
"NonAssocSemiring.toMulZeroOneClass",
"MonoidWithZeroHomClass.toMonoidHomClass",
"MulZeroOneClass.toMul... | false |
Finset.sym_eq_empty | Mathlib.Data.Finset.Sym | [
"False",
"Finset",
"False.elim",
"Ne",
"instOfNatNat",
"Finset.instEmptyCollection",
"Nat.casesAuxOn",
"iff_of_false",
"And.casesOn",
"instHAdd",
"And",
"Iff",
"Nat.succ_ne_zero",
"And.left",
"HAdd.hAdd",
"Finset.eq_empty_of_sym_eq_empty",
"Nat",
"And.intro",
"Iff.intro",
"Sym"... | true |
MulHom.eqOn_closure | Mathlib.Algebra.Group.Subsemigroup.Basic | [
"Iff.mpr",
"MulHom",
"PartialOrder.toPreorder",
"MulHom.eqLocus",
"Subsemigroup.instPartialOrder",
"Preorder.toLE",
"Mul",
"HasSubset.Subset",
"Subsemigroup.closure_le",
"Set.EqOn",
"LE.le",
"SetLike.coe",
"Subsemigroup",
"MulHom.funLike",
"Subsemigroup.instSetLike",
"DFunLike.coe",
... | true |
SimpleGraph.UnitDistEmbedding.bot._proof_1 | Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic | [
"False",
"Real",
"SimpleGraph.Adj",
"Bot.bot",
"Function.Embedding",
"SimpleGraph",
"Real.instOne",
"MetricSpace",
"implies_congr",
"SimpleGraph.bot_adj._simp_1",
"True",
"of_eq_true",
"One.toOfNat1",
"Eq.refl",
"SimpleGraph.completeAtomicBooleanAlgebra",
"MetricSpace.toPseudoMetricSpa... | false |
Setoid.prodQuotientEquiv_apply | Mathlib.Data.Setoid.Basic | [
"Setoid.prodQuotientEquiv",
"Equiv.instEquivLike",
"Setoid.prodQuotientEquiv.match_1",
"Quotient.map₂",
"Equiv",
"Prod.mk",
"Setoid",
"Quotient",
"Eq.refl",
"Prod",
"Setoid.prod",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike",
"Setoid.prodQuotientEquiv._proof_1"
] | true |
AddMonoidHom.instIsCentralScalar | Mathlib.Algebra.GroupWithZero.Action.Hom | [
"instHSMul",
"instZeroAddMonoidHom",
"MulOpposite",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddMonoidHom.ext",
"AddZero.toZero",
"AddZeroClass",
"IsCentralScalar.mk",
"IsCentralScalar",
"DistribSMul",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"AddMonoidHom.instSMulZeroClassO... | true |
_private.Mathlib.Order.WithBot.0.WithBot.forall_coe_lt._simp_1_1 | Mathlib.Order.WithBot | [
"WithBot.some",
"WithBot",
"Bot.bot",
"WithBot.forall",
"And",
"propext",
"Eq",
"WithBot.bot"
] | false |
summable_jacobiTheta₂_term_fderiv_iff | Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable | [
"instInnerProductSpaceRealComplex",
"Filter.eventually_ne_atBot",
"Filter.instMembership",
"Iff.mpr",
"IsModuleTopology.toContinuousSMul",
"Real.instIsOrderedRing",
"Norm.norm",
"Int.cast",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCo... | true |
ContinuousCohomology.Iobj._proof_7 | Mathlib.Algebra.Category.ContinuousCohomology.Basic | [
"TopModuleCat.instCategory",
"CommRing",
"AddMonoid.toAddSemigroup",
"Group",
"AddCommGroup.toAddGroup",
"DivInvMonoid.toMonoid",
"TopModuleCat.instTopologicalSpaceCarrier",
"IsTopologicalAddGroup.toContinuousAdd",
"TopModuleCat.toModuleCat",
"Group.toDivInvMonoid",
"TopologicalSpace",
"TopMod... | false |
USize.size_sub_one_mod_uint32Size | Init.Data.UInt.Lemmas | [
"UInt32.size",
"congrArg",
"HSub.hSub",
"Nat.instMod",
"instHMod",
"instSubNat",
"instOfNatNat",
"Or.casesOn",
"Bool.true",
"HMod.hMod",
"USize.size_eq",
"instHSub",
"eq_true_of_decide",
"Nat",
"True",
"eq_self",
"Bool",
"of_eq_true",
"Eq.refl",
"congrFun'",
"instDecidableEqN... | true |
Std.Time.instInhabitedDuration._proof_2 | Std.Time.Duration | [
"Rat.instOfNat",
"of_decide_eq_true",
"Std.Time.Internal.Bounded.LE.mk",
"Rat",
"Int.decLe",
"Std.Time.instInhabitedDuration._proof_1",
"GE.ge",
"id",
"Int.instNegInt",
"Std.Time.Second.Offset",
"Int",
"LE.le",
"Bool.true",
"And",
"instOfNat",
"Std.Time.Second.instOfNatOffset",
"Bool... | false |
CategoryTheory.Pseudofunctor.mk._flat_ctor | Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | [
"CategoryTheory.Pseudofunctor.map₂_right_unitor._autoParam",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.PrelaxFunctorStruct.mk",
"CategoryTheory.Bicategory.rightUnitor",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Iso",
"... | false |
toLex_mul | Mathlib.Algebra.Order.Group.Synonym | [
"Equiv.instEquivLike",
"HMul.hMul",
"Lex",
"Mul",
"Equiv",
"instMulLex",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike",
"instHMul",
"toLex"
] | true |
Multiset.cons_inter_distrib | Mathlib.Data.Multiset.UnionInter | [
"Multiset.mem_cons._simp_1",
"Multiset.instInter",
"congrArg",
"true_or",
"Membership.mem",
"Multiset",
"Multiset.cons",
"Multiset.cons_inter_of_pos",
"Multiset.erase_cons_head",
"Inter.inter",
"Multiset.instMembership",
"True",
"Multiset.erase",
"eq_self",
"of_eq_true",
"congrFun'",
... | true |
Lean.Lsp.instBEqCompletionItem | Lean.Data.Lsp.LanguageFeatures | [
"BEq.mk",
"Lean.Lsp.CompletionItem",
"BEq",
"Lean.Lsp.instBEqCompletionItem.beq"
] | true |
Set.range_inr | Mathlib.Data.Set.Image | [
"Set.ext",
"Sum.isRight",
"False",
"Sum.ctorIdx",
"congrArg",
"Sum.inr.injEq",
"False.elim",
"setOf",
"noConfusion_of_Nat",
"Bool.false_eq_true",
"Membership.mem",
"Exists",
"Sum.casesOn",
"Sum",
"Sum.inl",
"Set.mem_range._simp_1",
"iff_self",
"Bool.true",
"funext",
"exists_fal... | true |
ContinuousOn.enorm | Mathlib.Analysis.Normed.Group.Continuity | [
"Continuous.continuousOn",
"Set.mapsTo_univ",
"Set.univ",
"ContinuousENorm.continuous_enorm",
"ContinuousENorm",
"ContinuousOn.comp",
"TopologicalSpace",
"ENorm.enorm",
"ContinuousENorm.toENorm",
"ENNReal",
"ContinuousOn",
"ENNReal.instTopologicalSpace",
"Set"
] | true |
_private.Mathlib.Order.PiLex.0.Pi.colex_le_iff_of_unique._simp_1_2 | Mathlib.Order.PiLex | [
"Inhabited.default",
"Preorder.toLT",
"Pi.Colex.lt_iff_of_unique",
"Colex",
"Unique",
"LT.lt",
"propext",
"Unique.instInhabited",
"Pi.instLTColexForall",
"Eq",
"Preorder",
"LT"
] | false |
CategoryTheory.EffectiveEpiFamilyStruct.mk._flat_ctor | Mathlib.CategoryTheory.EffectiveEpi.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.EffectiveEpiFamilyStruct",
"CategoryTheory.EffectiveEpiFamilyStruct.mk",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | false |
CategoryTheory.CommSq.isLimitEquivIsLimitKernelFork._proof_10 | Mathlib.Algebra.Homology.CommSq | [
"CategoryTheory.CommSq.isLimitEquivIsLimitKernelFork._proof_9",
"NegZeroClass.toNeg",
"CategoryTheory.CommSq.isLimitEquivIsLimitKernelFork._proof_13",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.CommSq.isLimitEquivIsLimitKernelFork._proof_5",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver... | false |
_private.Init.Data.String.Slice.0.String.Slice.SplitIterator.instIteratorIdSubslice.match_5.eq_1 | Init.Data.String.Slice | [
"String.Slice.Subslice",
"String.Slice.Pattern.SearchStep",
"String.Slice",
"Std.IterM.mk",
"String.Slice.SplitIterator.operating",
"String.Slice.SplitIterator.instIteratorIdSubslice.match_5",
"String.Slice.Pattern.ToForwardSearcher",
"Id",
"String.Slice.SplitIterator",
"Unit",
"Std.Iter",
"Eq... | true |
Lean.Lsp.InitializeResult | Lean.Data.Lsp.InitShutdown | [
"Lean.Lsp.InitializeResult.mk"
] | true |
UpperSet.erase_inf_Ici | Mathlib.Order.UpperLower.Closure | [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"UpperSet",
"congrArg",
"UpperSet.instSetLike",
"upperClosure_singleton",
"upperClosure",
"Preorder.toLE",
"Membership.mem",
"UpperSet.Ici",
"Set.instSingletonSet",
"id",
"UpperSet.erase",
"HasSubset.Subset",
"LE.le",
"UpperSet.instMin",
"SetLike.... | true |
_private.Mathlib.Data.List.Sym.0.List.mem_sym2_cons_iff._simp_1_7 | Mathlib.Data.List.Sym | [
"eq_comm",
"propext",
"Eq"
] | false |
_private.Init.Data.BitVec.Lemmas.0.BitVec.getLsbD_replicate._proof_1_2 | Init.Data.BitVec.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"HMul.hMul",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.LinearCombo... | false |
_private.Mathlib.Data.Stream.Init.0.Stream'.getElem?_take.match_1_1 | Mathlib.Data.Stream.Init | [
"False",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"instOfNatNat",
"Nat.le.step",
"instHAdd",
"HAdd.hAdd",
"Nat.le",
"Nat",
"LT.lt",
"Nat.ctorIdx",
"instAddNat",
"Nat.zero",
"Eq.refl",
"HEq",
"Nat.le.refl",
"instLTNat",
"Nat.le.casesOn",
"OfNat.ofNat",
"Nat.succ",
"Eq... | false |
ContinuousMap.instSMul | Mathlib.Topology.ContinuousMap.Algebra | [
"instHSMul",
"ContinuousMap.mk",
"ContinuousMap",
"SMul",
"ContinuousMap.instSMul._proof_1",
"Function.hasSMul",
"SMul.mk",
"ContinuousConstSMul",
"TopologicalSpace",
"HSMul.hSMul",
"ContinuousMap.instFunLike",
"DFunLike.coe"
] | true |
_private.Mathlib.FieldTheory.RatFunc.Luroth.0.RatFunc.Luroth.algEquiv._proof_1 | Mathlib.FieldTheory.RatFunc.Luroth | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"IsScalarTower",
"Polynomial.algebraOfAlgebra",
"Algebra.toModule",
"Algebra.id",
"MulOne.toMul",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemirin... | false |
Submodule.map_smul | Mathlib.Algebra.Module.Submodule.Map | [
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"le_refl",
"instHSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"Submodule.comap_smul",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semifield",
"id",
"Ne",
"Submodule.instPartialOrder",
"LE.le",
"LinearMap",
"smulCommClass_self",... | true |
_private.Mathlib.ModelTheory.Definability.0.Set.Definable.preimage_map.match_1_2 | Mathlib.ModelTheory.Definability | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
QuadraticAlgebra.mker_norm_eq_unitary | Mathlib.Algebra.QuadraticAlgebra.Basic | [
"QuadraticAlgebra.instStarRing",
"MonoidHom.instMonoidHomClass",
"CommRing",
"MonoidHom.instFunLike",
"QuadraticAlgebra",
"MonoidHom.mker",
"MonoidHom",
"CommSemiring.toSemiring",
"QuadraticAlgebra.norm_eq_one_iff_mem_unitary",
"unitary",
"QuadraticAlgebra.instCommSemiring",
"Submonoid.ext",
... | true |
MeasureTheory.IntegrableAtFilter._auto_1 | Mathlib.MeasureTheory.Integral.IntegrableOn | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
ProbabilityTheory.condIndepFun_iff_compProd_map_prod_eq_compProd_prod_map_map | Mathlib.Probability.Independence.Conditional | [
"StandardBorelSpace",
"ProbabilityTheory.IsZeroOrMarkovKernel.isFiniteKernel",
"MeasureTheory.Measure",
"MeasurableSpace.instLE",
"ProbabilityTheory.Kernel.map",
"Measurable",
"MeasureTheory.Measure.trim",
"Prod.mk",
"LE.le",
"ProbabilityTheory.condExpKernel",
"MeasurableSpace",
"Iff",
"Prob... | true |
_private.Init.Data.Format.Basic.0.Std.Format.State.column | Init.Data.Format.Basic | [
"_private.Init.Data.Format.Basic.0.Std.Format.State",
"Nat"
] | true |
MonoidHom.compLeft.eq_1 | Mathlib.Algebra.Group.Pi.Lemmas | [
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom",
"OneHom.mk",
"MonoidHom.compLeft._proof_1",
"Function.comp",
"MonoidHom.mk",
"MonoidHom.compLeft",
"Pi.mulOneClass",
"MulOneClass.toMulOne",
"Eq.refl",
"MulOneClass",
"Eq",
"DFunLike.coe",
"MonoidHom.compLeft._proof_2"
] | true |
SimpleGraph.Hom.ofLE | Mathlib.Combinatorics.SimpleGraph.Maps | [
"SimpleGraph.Adj",
"id",
"LE.le",
"SimpleGraph",
"SimpleGraph.Hom",
"RelHom.mk",
"SimpleGraph.instLE"
] | true |
Lean.getPPAnalysisHole | Lean.PrettyPrinter.Delaborator.TopDownAnalyze | [
"Lean.Name.mkStr3",
"Lean.KVMap.instValueBool",
"Lean.Options.get",
"Bool",
"Bool.false",
"Lean.Options"
] | true |
Hyperreal.epsilon_lt_of_neg | Mathlib.Analysis.Real.Hyperreal | [
"Hyperreal.instField",
"Real",
"Preorder.toLT",
"Real.instArchimedean",
"Real.instZero",
"PartialOrder.toPreorder",
"Real.instLT",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Hyperreal.instLinearOrder",
"Real.commRing",
"Field.toCommRing",
"Hyperreal.instIsStrictOrderedRing... | true |
Valued.tendsto_zero_pow_of_le_exp_neg_one | Mathlib.Topology.Algebra.Valued.WithZeroMulInt | [
"Int.instAddCommGroup",
"Eq.mpr",
"Int.instAddCommMonoid",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Multiplicative.linearOrder",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"WithZero.exp_lt_exp",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneM... | true |
AlgebraicGeometry.IsAffineHom.isAffine_preimage | Mathlib.AlgebraicGeometry.Morphisms.Affine | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.IsAffineHom",
"TopologicalSpace.Opens.instPartialOrder",
"CommRingCat",
"PartialOrd... | true |
CategoryTheory.MonoidalCategory.MonoidalRightAction.monoidalOppositeRightAction_actionHom_mop_mop | Mathlib.CategoryTheory.Monoidal.Action.Opposites | [
"CategoryTheory.MonoidalOpposite.mop",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MonoidalOpposite",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalRightActionStruct.actionObj",
"CategoryTheory.monoidalCategoryMop",
"CategoryTheory.MonoidalCate... | true |
Int8.toInt16_mod | Init.Data.SInt.Lemmas | [
"Int.tmod",
"Int8.toInt_mod",
"Int16",
"Int8.toInt_toInt16",
"congrArg",
"Int8.toInt16",
"Int8",
"Int8.toInt",
"instModInt8",
"instHMod",
"Int",
"HMod.hMod",
"Int16.toInt_mod",
"congr",
"True",
"instModInt16",
"eq_self",
"Int16.toInt",
"of_eq_true",
"Int16.toInt.inj",
"Eq",
... | true |
_private.Mathlib.MeasureTheory.Measure.Typeclasses.SFinite.0.MeasureTheory.Measure.countable_meas_pos_of_disjoint_iUnion₀._simp_1_3 | Mathlib.MeasureTheory.Measure.Typeclasses.SFinite | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"not_lt",
"LT.lt",
"propext",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
Lean.Parser.instBEqRecoveryContext | Lean.Parser.Basic | [
"Lean.Parser.RecoveryContext",
"BEq.mk",
"Lean.Parser.instBEqRecoveryContext.beq",
"BEq"
] | true |
Prod.normedCommRing._proof_13 | Mathlib.Analysis.Normed.Ring.Basic | [
"SubNegMonoid.sub_eq_add_neg",
"AddMonoid.toAddSemigroup",
"NormedCommRing",
"NonUnitalNonAssocRing.toAddCommGroup",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"Prod.nonUnitalNormedRing",
"NormedCommRing.toNonUnitalNormedCommRing",
"SubNegMonoid.toSub",
"Non... | false |
AddCommMonoid.uniqueNatModule._proof_1 | Mathlib.Algebra.Module.NatInt | [
"Eq.mpr",
"instHSMul",
"DistribMulAction.toDistribSMul",
"HEq.refl",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"AddZeroClass.toAddZero",
"inferInstance",
"Eq.casesOn",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"AddZero.toZero",
"nat_smul_eq_nsmul",
"Nat",
"Semiring.toMonoid"... | false |
WithBot.map₂_eq_bot_iff | Mathlib.Order.WithBot | [
"WithBot",
"Bot.bot",
"Option.map₂_eq_none_iff",
"Iff",
"Or",
"Eq",
"WithBot.map₂",
"WithBot.bot"
] | true |
cfcₙ_realPart | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.RealImaginaryPart | [
"cfcₙ",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"instTrivialStarReal",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"instSMulOfMul",
"Continuous.continuousOn",
"CommRing.toNonUnitalCommRing",
"IsStarNormal",
"IsTopologicalRing.toIsTopologicalSemiring",
... | true |
Mathlib.Tactic.Ring.RatCoeff.hyp | Mathlib.Tactic.Ring.Common | [
"Mathlib.Tactic.Ring.RatCoeff",
"Lean.Expr",
"Lean.Expr.sort",
"Lean.Level",
"Qq.Quoted",
"Lean.Level.succ",
"Option"
] | true |
_private.Mathlib.Data.List.Chain.0.List.IsChain.induction._proof_1_6 | Mathlib.Data.List.Chain | [
"False",
"Lean.Grind.not_false",
"congrArg",
"False.elim",
"noConfusion_of_Nat",
"List.cons",
"List",
"True",
"Eq.substr",
"eq_false'",
"Eq",
"List.ctorIdx",
"Not",
"Eq.trans",
"True.intro",
"List.nil"
] | false |
summable_extend_zero | Mathlib.Topology.Algebra.InfiniteSum.Basic | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Pi.instZero",
"hasSum_extend_zero",
"AddCommMonoid",
"TopologicalSpace",
"AddZero.toZero",
"exists_congr",
"Function.extend",
"Iff",
"HasSum",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"Function.Injective",
"Summable",
"OfNat.o... | true |
BoxIntegral.integrable_zero | Mathlib.Analysis.BoxIntegral.Basic | [
"Real",
"BoxIntegral.Integrable",
"NormedSpace",
"BoxIntegral.hasIntegral_zero",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousLinearMap.addCommMonoid",
"AddCommGroup.toAddGroup",
"Real.semiring",
"SubtractionMonoid.toSubNegZeroMonoid",
... | true |
MeasureTheory.Measure.rnDeriv_of_not_haveLebesgueDecomposition | Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | [
"Eq.mpr",
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure",
"congrArg",
"Measurable",
"MeasureTheory.Measure.rnDeriv",
"ENNReal.measurableSpace",
"Classical.propDecidable",
"id",
"Pi.instZero",
"MeasureTheory.Measure.HaveLebesgueDecomposition",
"MeasureTheory.Measure.HaveLebesgueDe... | true |
CompHausLike.LocallyConstant.functorIso._proof_1 | Mathlib.Condensed.Discrete.LocallyConstant | [
"CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompHausLike.HasExplicitFiniteCoproducts",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"CompHausLike.LocallyConstan... | false |
Lean.Doc.PostponedName.rec | Lean.Elab.DocString.Builtin.Postponed | [
"Lean.Doc.PostponedName",
"Lean.Doc.PostponedName.mk",
"Lean.Name"
] | false |
_private.Mathlib.Data.Finset.Density.0.Finset.dens_union_add_dens_inter._simp_1_2 | Mathlib.Data.Finset.Density | [
"instHDiv",
"GroupWithZero.toDivInvMonoid",
"DivisionSemiring.toGroupWithZero",
"Distrib.toAdd",
"HDiv.hDiv",
"instDistribOfSemiring",
"DivisionSemiring",
"instHAdd",
"HAdd.hAdd",
"DivInvMonoid.toDiv",
"DivisionSemiring.toSemiring",
"Eq.symm",
"Eq",
"add_div"
] | false |
_private.Mathlib.Data.Matrix.Block.0.Matrix.blockDiagonal_diagonal._simp_1_1 | Mathlib.Data.Matrix.Block | [
"Prod.mk_inj",
"Prod.mk",
"And",
"propext",
"Prod",
"Eq"
] | false |
_private.Std.Sat.AIG.RefVecOperator.Map.0.PSigma.casesOn._arg_pusher | Std.Sat.AIG.RefVecOperator.Map | [
"PSigma.casesOn",
"PSigma.mk",
"Eq.refl",
"PSigma",
"Eq"
] | false |
Ideal.basisSpanSingleton.eq_1 | Mathlib.RingTheory.Ideal.Basis | [
"Submodule",
"IsDomain",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"LinearEquiv.restrictScalars",
"Submodule.addCommMonoid",
"Submodule.restrictScalars",
"Module.Basis.map"... | true |
_private.Lean.Data.Lsp.Internal.0.Lean.Lsp.instFromJsonOpenNamespace.fromJson.match_1 | Lean.Data.Lsp.Internal | [
"Unit.unit",
"String",
"dite",
"Unit",
"Eq.ndrec_symm",
"instDecidableEqString",
"Eq",
"Not"
] | false |
IsLocalizedModule.mk'_sub | Mathlib.Algebra.Module.LocalizedModule.Basic | [
"Eq.mpr",
"NegZeroClass.toNeg",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"IsLocalizedModule",
"sub_eq_add_neg",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddCommGroup",
"id",
"Subtype",
... | true |
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