name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CStarMatrix.instNonUnitalCStarAlgebra._proof_1 | Mathlib.Analysis.CStarAlgebra.CStarMatrix | [
"instHSMul",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"instSMulOfMul",
"HMul.hMul",
"NonUnitalNonAssocRing.toMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"Complex.instNormedField",
"NormedField.toF... | false |
Lean.Lsp.CodeActionContext.mk._flat_ctor | Lean.Data.Lsp.CodeActions | [
"Lean.Lsp.CodeActionContext.mk",
"Lean.Lsp.CodeActionTriggerKind",
"Array",
"Lean.Lsp.CodeActionKind",
"Lean.Lsp.Diagnostic",
"Lean.Lsp.CodeActionContext",
"Option"
] | false |
_private.Lean.Meta.Tactic.Apply.0.Lean.MVarId.iffOfEq._sparseCasesOn_1 | Lean.Meta.Tactic.Apply | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
_private.Mathlib.Topology.LocallyFinite.0.locallyFinite_option._simp_1_1 | Mathlib.Topology.LocallyFinite | [
"Finite",
"locallyFinite_of_finite",
"LocallyFinite",
"TopologicalSpace",
"True",
"eq_true",
"Eq",
"Set"
] | false |
RootPairing.Equiv.mul_eq_comp | Mathlib.LinearAlgebra.RootSystem.Hom | [
"CommRing",
"HMul.hMul",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"RootPairing.Equiv.comp",
"AddCommGroup",
"MulOne.toMul",
"MulOneClass.toMulOne",
"CommRing.toCommSemiring",
"RootPairing.Equiv.instMonoid",
"RootPairing.Equiv",
"Module",
"Eq",
"r... | true |
instCommRingFreeCommRing._proof_36 | Mathlib.RingTheory.FreeCommRing | [
"Mul.mk",
"instCommRingFreeCommRing._proof_30",
"One.mk",
"FreeCommRing",
"AddMonoid.toAddSemigroup",
"instCommRingFreeCommRing._aux_32",
"instCommRingFreeCommRing._aux_20",
"instCommRingFreeCommRing._aux_1",
"Add.mk",
"Neg.mk",
"HSub.hSub",
"AddMonoid.mk",
"Semigroup.mk",
"instCommRingFre... | false |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd.0.EulerSine.integral_sin_mul_sin_mul_cos_pow_eq._proof_1_1 | Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
SemiSimplexCategory.smallCategory._proof_2 | Mathlib.AlgebraicTopology.SimplexCategory.SemiSimplexCategory | [
"SemiSimplexCategory.Hom",
"id",
"RelEmbedding.refl",
"instOfNatNat",
"LE.le",
"instLEFin",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"SemiSimplexCategory",
"Eq.refl",
"RelEmbedding.trans",
"OfNat.ofNat",
"SemiSimplexCategory.len",
"Fin",
"Eq"
] | false |
Setoid.gi._proof_1 | Mathlib.Data.Setoid.Basic | [
"Pi.preorder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Eq.rec",
"Setoid",
"LE.le",
"Relation.EqvGen.setoid",
"Iff",
"Setoid.instPartialOrder",
"Setoid.eqvGen_mono",
"Iff.intro",
"Relation.EqvGen.rel",
"Prop.partialOrder",
"Eq",
"Setoid.r",
"Setoid.eqvGen_of_setoid"
] | false |
SetSemiring.instAddCommMonoid._proof_1 | Mathlib.Data.Set.Semiring | [
"SetSemiring.instAdd",
"instOfNatNat",
"SetSemiring",
"nsmulRec",
"Nat",
"SetSemiring.instZero",
"Zero.toOfNat0",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | false |
RootPairing.Equiv.mk'._proof_7 | Mathlib.LinearAlgebra.RootSystem.Hom | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"RootPairing.flip",
"RootPairing.isPerfPair_toLinearMap",
"RootPairing.toLinearMap",
"AddCommGroup",
"CommRing.toCommSemiring",
"LinearMap.IsPerfPair",
"Module",
"RootPairing"
] | false |
ClopenUpperSet.coe_toUpperSet | Mathlib.Topology.Sets.Order | [
"UpperSet",
"UpperSet.instSetLike",
"LE",
"ClopenUpperSet.toUpperSet",
"TopologicalSpace",
"SetLike.coe",
"Eq.refl",
"ClopenUpperSet",
"Eq",
"ClopenUpperSet.instSetLike",
"Set"
] | true |
_private.Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn.0.Summable.hasProdUniformlyOn_one_add._simp_1_1 | Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn | [
"UniformSpace",
"Finset",
"PartialOrder.toPreorder",
"Finset.partialOrder",
"TendstoUniformlyOn",
"Finset.prod",
"Filter.atTop",
"propext",
"hasProdUniformlyOn_iff_tendstoUniformlyOn",
"Eq",
"CommMonoid",
"HasProdUniformlyOn",
"Set"
] | false |
_private.Lean.Meta.Tactic.Grind.MatchCond.0.Lean.Meta.Grind.replaceLhs? | Lean.Meta.Tactic.Grind.MatchCond | [
"Unit.unit",
"Lean.Expr.isApp",
"Lean.Expr.cleanupAnnotations",
"Lean.mkApp4",
"Option.some",
"Lean.Expr",
"instDecidableEqBool",
"Option.get!",
"Lean.Expr.appArg",
"Lean.Expr.appFnCleanup",
"Lean.Expr.hasLooseBVars",
"dite",
"Lean.instInhabitedExpr",
"Bool.true",
"Option.none",
"Unit"... | true |
_private.Std.Data.ExtDHashMap.Basic.0.Std.ExtDHashMap.getKey._proof_3 | Std.Data.ExtDHashMap.Basic | [
"_private.Std.Data.ExtDHashMap.Basic.0.Std.ExtDHashMap.getKey._proof_2",
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Std.DHashMap.Equiv",
"Membership.mem",
"Eq.rec",
"Std.ExtDHashMap.mk",
"LawfulHashable",
"Std.DHashMap.Equiv.getKey_eq",
"_private.Std.Data.ExtDHashMap.Basic.0.Std.Ex... | false |
_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.applyReplacementFun.visitLambda._sparseCasesOn_1 | Mathlib.Tactic.Translate.Core | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
Filter.Tendsto.atBot_mul_atBot₀ | Mathlib.Order.Filter.AtTopBot.Ring | [
"NegZeroClass.toNeg",
"Filter.tendsto_neg_atBot_atTop",
"HMul.hMul",
"Ring.toNonAssocRing",
"IsOrderedRing",
"congrArg",
"PartialOrder.toPreorder",
"Function.comp",
"PartialOrder",
"Eq.mp",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZe... | true |
Affine.Simplex.map_mkOfPoint | Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | [
"AffineMap.instFunLike",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Affine.Simplex",
"instOfNatNat",
"AffineMap",
"Affine.Simplex.map",
"Nat",
"Affine.Simplex.mkOfPoint",
"AddTorsor",
"Function.Injective",
"Module",
"OfNat.ofNat",
"Ring.toSemiring",
"Eq... | true |
_private.Mathlib.RingTheory.FractionalIdeal.Operations.0.FractionalIdeal.spanFinset_eq_zero._simp_1_7 | Mathlib.RingTheory.FractionalIdeal.Operations | [
"propext",
"Eq",
"forall_apply_eq_imp_iff₂"
] | false |
Subgroup.mem_sup_of_normal_left | Mathlib.Algebra.Group.Subgroup.Lattice | [
"Semigroup.toMul",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"_private.Mathlib.Algebra.Group.Subgroup.Lattice.0.Subgroup.mem_sup_of_normal_left.match_1_1",
"DivInvOneMonoid.toInvOneClass",
"CompleteLattice.toLattice",
"Monoid.toMulOneClass",
"congrArg",
"mul_assoc",
"Group",
"Group.toDivisionMono... | true |
CategoryTheory.Localization.SmallShiftedHom.shift | Mathlib.CategoryTheory.Localization.SmallShiftedHom | [
"CategoryTheory.MorphismProperty.IsCompatibleWithShift",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Localization.SmallHom.mk",
"CategoryTheory.Localization.SmallHom.shift",
"CategoryTheory.Functor",
"CategoryTheory.Localization.SmallHom",
"AddMonoid.toAddSemigroup",
"CategoryTheory.Functor.cat... | true |
ContinuousAlternatingMap._sizeOf_1 | Mathlib.Topology.Algebra.Module.Alternating.Basic | [
"ContinuousMultilinearMap._sizeOf_inst",
"AddMonoid.toAddZeroClass",
"ContinuousMultilinearMap",
"AddZeroClass.toAddZero",
"Ne",
"instOfNatNat",
"AddCommMonoid",
"ContinuousAlternatingMap.rec",
"TopologicalSpace",
"AddZero.toZero",
"instHAdd",
"MultilinearMap.toFun",
"ContinuousMultilinearMa... | false |
lp.inftyStarRing._proof_1 | Mathlib.Analysis.Normed.Lp.lpSpace | [
"HMul.hMul",
"lp.nonUnitalRing",
"Pi.instStarMulForall",
"instAddCommGroupPreLp",
"AddCommGroup.toAddGroup",
"AddSubgroup.toAddGroup",
"Membership.mem",
"lp.instStarAddMonoid",
"NonUnitalRing.toNonUnitalNonAssocRing",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonUnitalNo... | false |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.ChebyshevGauss.0.Polynomial.Chebyshev.sumZeroes_T_of_not_dvd._simp_1_12 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.ChebyshevGauss | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
instNonemptyTypeName | Init.Dynamic | [
"TypeName",
"Nonempty.elim",
"_private.Init.Dynamic.0.TypeName.mk'",
"TypeNameData",
"Nonempty.intro",
"Nonempty",
"Subtype.val",
"Subtype.property"
] | true |
ArchimedeanClass.instSMulNat._proof_1 | Mathlib.Algebra.Order.Ring.Archimedean | [
"Eq.mpr",
"MulOne.toOne",
"CommRing",
"Nat.recAux",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"pow_succ",
"LinearOrder",
"IsStrictOrderedRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"id",
"MulOne.toMul",
"instOfNatNat",
"Archim... | false |
CategoryTheory.Limits.pushout.inl_of_epi | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono | [
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.PushoutCocone.epi_inl_of_is_pushout_of_epi",
"CategoryTheory.Limits.colimit.isColimit",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.Limits.WidePushoutShape... | true |
CategoryTheory.Functor.OplaxRightLinear.rec | Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MonoidalCategory.MonoidalRightActionStruct.actionHomRight",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.MonoidalRightActionStruct.actionUnitIso",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.Mon... | false |
CategoryTheory.Abelian.SpectralObject.fromOpcycles._proof_1 | Mathlib.Algebra.Homology.SpectralObject.Cycles | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Abelian.SpectralObject.H",
"CategoryTheory.Abelian.SpectralObject.opcycles._proof_2",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"HSub.hSub",
"CategoryTheo... | false |
Concept.casesOn | Mathlib.Order.Concept | [
"upperPolar",
"Concept",
"Concept.rec",
"Concept.mk",
"lowerPolar",
"Eq",
"Set"
] | false |
AlgebraicGeometry.Proj.toLocallyRingedSpace | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf | [
"SetLike",
"AlgebraicGeometry.Proj.toSheafedSpace",
"CommRing",
"AlgebraicGeometry.SheafedSpace",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"CommRingCat",
"AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.IsFraction._proof_1",
"AlgebraicGeometry.LocallyRingedSpace.mk",
"Nat.instA... | true |
EuclideanSpace.equiv | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"NormedCommRing.toNormedRing",
"Pi.Function.module",
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"NormedRing.toRing",
"Pi.topologicalSpace",
"AddCommGroup.toAddCommMonoid",
"PseudoMetricSpace.toUniformSpace",
"W... | true |
PFunctor.Approx.CofixA.noConfusion | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor",
"PFunctor.A",
"HEq.refl",
"PFunctor.B",
"PFunctor.Approx.CofixA.noConfusionType",
"PFunctor.Approx.CofixA.casesOn",
"PFunctor.Approx.CofixA",
"Nat",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq"
] | false |
List.take_succ_cons | Init.Data.List.Basic | [
"instOfNatNat",
"List.cons",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Eq",
"List.take",
"rfl"
] | true |
Lean.Compiler.LCNF.Code.del.elim | Lean.Compiler.LCNF.Basic | [
"Lean.Compiler.LCNF.Code.ctorElim",
"PULift.up",
"Lean.FVarId",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Code.ctorIdx",
"Lean.Compiler.LCNF.Code",
"Lean.Compiler.LCNF.Code.del",
"Lean.Compiler.LCNF.Purity.impure",
"Nat",
"Eq.symm",
"Eq"
] | false |
Lean.KVMap.Value.ctorIdx | Lean.Data.KVMap | [
"Nat",
"Lean.KVMap.Value"
] | false |
List.findFinIdx?.go.match_1 | Init.Data.List.Basic | [
"List.cons",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"List.casesOn",
"instAddNat",
"Eq",
"List.length",
"List.nil"
] | false |
GrpCat.of.eq_1 | Mathlib.Algebra.Category.Grp.Basic | [
"GrpCat",
"Group",
"GrpCat.mk",
"Eq.refl",
"Eq",
"GrpCat.of"
] | true |
isClosed_empty._simp_1 | Mathlib.Topology.Basic | [
"isClosed_empty",
"IsClosed",
"TopologicalSpace",
"True",
"eq_true",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Set"
] | false |
_private.Mathlib.Dynamics.TopologicalEntropy.NetEntropy.0.Dynamics.netMaxcard_infinite_iff._simp_1_3 | Mathlib.Dynamics.TopologicalEntropy.NetEntropy | [
"Exists",
"Subtype.exists",
"Subtype",
"Subtype.mk",
"propext",
"Eq"
] | false |
CategoryTheory.Limits.colimitConstInitial._proof_6 | Mathlib.CategoryTheory.Limits.Shapes.Terminal | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.instHasColimitObjFunctorConstInitial",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.Limits.Cocone.mk",
"CategoryTheory.Li... | false |
_private.Init.Data.String.OrderInstances.0.String.Pos.instToIntCoOfNatIntHAddCastUtf8ByteSize._proof_2 | Init.Data.String.OrderInstances | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Lean.Omega.Int.le_of_not_lt",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"String",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"String.utf8ByteS... | false |
EReal.coe_ennreal_ne_zero | Mathlib.Data.EReal.Basic | [
"EReal",
"Iff.not",
"Ne",
"instZeroEReal",
"EReal.coe_ennreal_eq_zero",
"Iff",
"ENNReal.toEReal",
"ENNReal",
"Zero.toOfNat0",
"ENNReal.instZero",
"OfNat.ofNat",
"Eq"
] | true |
Vector.range'_inj._simp_1 | Init.Data.Vector.Range | [
"Vector",
"instOfNatNat",
"Vector.range'",
"Nat",
"propext",
"Or",
"Vector.range'_inj",
"OfNat.ofNat",
"Eq"
] | false |
_private.Mathlib.Data.List.Lookmap.0.List.lookmap_congr.match_1_1 | Mathlib.Data.List.Lookmap | [
"Membership.mem",
"List.cons",
"List",
"List.instMembership",
"List.casesOn",
"Eq",
"List.nil",
"Option"
] | false |
_private.Mathlib.Topology.Compactness.Lindelof.0.IsLindelof.elim_nhds_subcover._simp_1_3 | Mathlib.Topology.Compactness.Lindelof | [
"Set.mem_image",
"Membership.mem",
"Exists",
"And",
"propext",
"Set.image",
"Eq",
"Set.instMembership",
"Set"
] | false |
IsOrderedCancelAddMonoid.le_of_add_le_add_right._default | Mathlib.Algebra.Order.Monoid.Defs | [
"Preorder.toLE",
"id",
"LE.le",
"AddCommMonoid",
"instHAdd",
"IsOrderedCancelAddMonoid._proof_1",
"HAdd.hAdd",
"AddCommSemigroup.toAddCommMagma",
"AddCommMonoid.toAddCommSemigroup",
"Preorder",
"AddCommMagma.toAdd"
] | false |
UniformSpace.Completion.commRing | Mathlib.Topology.Algebra.UniformRing | [
"UniformSpace",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"UniformSpace.Completion.commRing._proof_4",
"AddGroupWithOne.toAddGroup",
"IsUniformAddGroup",
"IsTopologicalRing",
"UniformSpace.Completion.ring",
"NonUnitalNonAssocCommRing.toNonUnitalNo... | true |
IsRelPrime.of_mul_left_left | Mathlib.Algebra.Divisibility.Units | [
"dvd_mul_of_dvd_left",
"Dvd.dvd",
"HMul.hMul",
"Monoid.toMulOneClass",
"semigroupDvd",
"IsRelPrime",
"MulOne.toMul",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"Monoid.toSemigroup",
"CommMonoid",
"instHMul"
] | true |
Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.elim.sizeOf_spec | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof._sizeOf_inst",
"instOfNatNat",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstr",
"instHAdd",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstr._sizeOf_inst",
"HAdd.hAdd",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.elim",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof",
"Nat",
... | true |
_private.Mathlib.Data.TwoPointing.0.TwoPointing.nonempty_two_pointing_iff.match_1_1 | Mathlib.Data.TwoPointing | [
"Nonempty.intro",
"Nonempty.casesOn",
"TwoPointing",
"Nonempty"
] | false |
Mathlib.Tactic.Bicategory.Context.level₁ | Mathlib.Tactic.CategoryTheory.Bicategory.Datatypes | [
"Mathlib.Tactic.Bicategory.Context",
"Lean.Level"
] | true |
toDual_min | Mathlib.Order.Lattice | [
"OrderDual.toDual",
"Equiv.instEquivLike",
"LinearOrder",
"DistribLattice.toLattice",
"Equiv",
"SemilatticeInf.toMin",
"OrderDual.instMaxOfMin",
"Max.max",
"OrderDual",
"Eq",
"DFunLike.coe",
"instDistribLatticeOfLinearOrder",
"Min.min",
"rfl",
"Lattice.toSemilatticeInf",
"EquivLike.toF... | true |
_aux_Init_Control_Basic___unexpand_andM_1 | Init.Control.Basic | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
CategoryTheory.Endofunctor.Algebra.comp_eq_comp | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Algebra.instCategoryStruct",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Endofunctor.Algebra.Hom",
"CategoryTheory.CategoryStruct.comp",
"Eq",
"rfl",
"CategoryTheory.Endofunctor.... | true |
CategoryTheory.MonoOver.isColimitCoconeOfHasStrongEpiMonoFactorisation._proof_1 | Mathlib.CategoryTheory.Subobject.MonoOver | [
"CategoryTheory.Limits.MonoFactorisation.I",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoOver.liftStructOfHasStrongEpiMonoFactorisati... | false |
CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv_assoc | Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv",
"Eq.mp",
"id",
"CategoryTheory.CartesianMonoidalCategory.lift",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.SemiCartesianMono... | true |
_private.Mathlib.Algebra.Group.Pointwise.Set.Basic.0.Set.prod_pow.match_1_1 | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
IsAddUnit.add_neg_cancel_right | Mathlib.Algebra.Group.Units.Basic | [
"NegZeroClass.toNeg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"IsAddUnit",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"AddUnits.add_neg_cancel_right",
"instHAdd",
"HAdd.hAdd",
"SubtractionMonoid",
"AddZero.toAdd"... | true |
CategoryTheory.Oplax.LaxTrans.Modification.naturality | Mathlib.CategoryTheory.Bicategory.Modification.Oplax | [
"CategoryTheory.Oplax.LaxTrans.Modification",
"CategoryTheory.Oplax.LaxTrans.instCategoryStructOplaxFunctor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Oplax.LaxTrans.Modification.app",
"CategoryTheory.Bicategory.whiskerRight",... | true |
StalkSkyscraperPresheafAdjunctionAuxs.counit | Mathlib.Topology.Sheaves.Skyscraper | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopCat.instCategoryPresheaf",
"CategoryTheory.Functor.category",
"Decidable",
"CategoryTheory.Functor.comp",
"TopologicalSpace.Opens",
"Membership.mem",
"CategoryTheory.Functor.id",
"TopCat.Presheaf",
"skyscrape... | true |
Int.Linear.Expr.toPoly'.go.eq_2 | Init.Data.Int.Linear | [
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.add",
"Int.Linear.Expr.toPoly'.go",
"Int.Linear.Expr.var",
"Eq.refl",
"Eq",
"Int.Linear.Poly"
] | true |
_private.Mathlib.RingTheory.Ideal.AssociatedPrime.Localization.0.Module.associatedPrimes.mem_associatedPrimes_of_comap_mem_associatedPrimes_of_isLocalizedModule.match_1_7 | Mathlib.RingTheory.Ideal.AssociatedPrime.Localization | [
"CommRing",
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Subtype",
"DistribSMul.toSMulZeroClass",
"Submonoid.smul",
"MulZeroOneCla... | false |
deriv_div_const | Mathlib.Analysis.Calculus.Deriv.Mul | [
"DivInvMonoid.toInv",
"deriv_mul_const_field",
"instHDiv",
"NormedRing.toRing",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"deriv",
"NormedSpace.toModule",
"NormedDivisionRing.toNormedRing",
"PseudoMetricSpace.toUniformSpace",
"NormedDivisionRing.toDivisionRing",
"NormedRing.toNonUnita... | true |
exists_orderEmbedding_covby_of_forall_covby_finite_of_bot | Mathlib.Order.KonigLemma | [
"Eq.mpr",
"Preorder.toLT",
"Set.Ici",
"congrArg",
"IsStronglyAtomic",
"CovBy",
"Set.univ",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Set.Finite",
"OrderBot",
"Exists",
"PartialOrder",
"id",
"exists_orderEmbedding_covby_of_forall_covby_finite",
"instOfN... | true |
List.sectionsTR | Batteries.Data.List.Basic | [
"cond",
"List.sectionsTR.go",
"Array.toList",
"List.toArray",
"List.cons",
"Array",
"List",
"List.isEmpty",
"List.any",
"List.foldr",
"List.nil"
] | true |
CategoryTheory.Comma.preLeft_obj_hom | Mathlib.CategoryTheory.Comma.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.comp",
"CategoryTheory.Comma.hom",
"CategoryTheory.Comma",
"CategoryTheory.commaCategory",
"CategoryTheory.Comma.preLeft",
"Eq.refl... | true |
NumberField.place | Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings | [
"Nontrivial",
"Norm.norm",
"NumberField.place._proof_2",
"Real.partialOrder",
"Real",
"NormedDivisionRing.toNorm",
"IsAbsoluteValue.toAbsoluteValue",
"NormedDivisionRing.toDivisionRing",
"RingHom",
"DivisionRing.toDivisionSemiring",
"Real.semiring",
"Field.toSemifield",
"NumberField.place._p... | true |
hasSum_sq_fourierCoeffOn | Mathlib.Analysis.Fourier.AddCircle | [
"MeasureTheory.ae",
"Real.instIsOrderedRing",
"Norm.norm",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"Set.Ioc",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
... | true |
CoalgCat.rec | Mathlib.Algebra.Category.CoalgCat.Basic | [
"CommRing",
"CoalgCat",
"Coalgebra",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"CoalgCat.mk",
"CommRing.toCommSemiring",
"ModuleCat.isAddCommGroup",
"ModuleCat.carrier",
"CommRing.toRing",
"ModuleCat.isModule"
] | false |
coborder.eq_1 | Mathlib.Topology.LocallyClosed | [
"Compl.compl",
"Set.instCompl",
"TopologicalSpace",
"SDiff.sdiff",
"coborder",
"closure",
"Eq.refl",
"Eq",
"Set.instSDiff",
"Set"
] | true |
LLVM.IntPredicate.UGT | Lean.Compiler.IR.LLVMBindings | [
"UInt64.instOfNat",
"instAddUInt64",
"LLVM.IntPredicate",
"UInt64",
"_private.Lean.Compiler.IR.LLVMBindings.0.LLVM.IntPredicate.mk",
"LLVM.IntPredicate.NE",
"instHAdd",
"LLVM.IntPredicate.val",
"HAdd.hAdd",
"OfNat.ofNat"
] | true |
List.filterM_toArray' | Init.Data.Array.Monadic | [
"_private.Init.Data.Array.Monadic.0.List.filterM_toArray'._simp_1_1",
"congrArg",
"Monad.toApplicative",
"LawfulMonad",
"instOfNatNat",
"List.toArray",
"Array",
"Array.filterM",
"List",
"List.size_toArray",
"Nat",
"True",
"eq_self",
"Bool",
"of_eq_true",
"Eq.ndrec",
"Applicative.toFu... | true |
Lean.Elab.Tactic.BVDecide.Frontend.Normalize.VarState.noConfusion | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AC | [
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Op",
"Lean.Expr.instBEq",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.VarState.casesOn",
"Lean.Expr",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.VarState.noConfusionType",
"Std.HashMap",
"Array",
"Eq.ndrec",
"Eq.refl",
"Lean.Expr.instHashable",
... | false |
NonUnitalSubalgebra.nonUnitalNormedRing._proof_3 | Mathlib.Analysis.Normed.Ring.Basic | [
"Norm.norm",
"Real.instLE",
"Real",
"CommRing",
"NonUnitalSubalgebra",
"HMul.hMul",
"NonUnitalNonAssocRing.toMul",
"CommSemiring.toSemiring",
"NonUnitalSeminormedRing.norm_mul_le",
"Membership.mem",
"NonUnitalRing.toNonUnitalNonAssocRing",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAsso... | false |
AbsolutelyContinuousOnInterval.hasBasis_totalLengthFilter | Mathlib.MeasureTheory.Function.AbsolutelyContinuous | [
"Set.ext",
"Real.instIsOrderedRing",
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorder.toLT",
"instNoMaxOrderOfNontrivial",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
"HEq.refl",
"Finset",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"setOf",
"dist_non... | true |
_private.Mathlib.CategoryTheory.Sites.Point.Skyscraper.0.CategoryTheory.GrothendieckTopology.Point.presheafToSheafCompSheafFiberIso._simp_2 | Mathlib.CategoryTheory.Sites.Point.Skyscraper | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.map",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Functor.map_comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Cate... | false |
Lean.Elab.Term.instInhabitedDiscr.default | Lean.Elab.Match | [
"Inhabited.default",
"Lean.Elab.Term.Discr",
"Lean.Syntax",
"Lean.Elab.Term.Discr.mk",
"Lean.Expr",
"Lean.instInhabitedExpr",
"instInhabitedOption",
"Option"
] | true |
Fin.inv_partialProd_mul_eq_contractNth | Mathlib.Algebra.BigOperators.Fin | [
"Iff.mpr",
"Fin.succAbove_of_le_castSucc",
"Fin.succAbove",
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"Preorder.toLT",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"inv_mul_cancel_left",
"Fin.succ",
"Monoid.toMulOneClass",
"instReflLe",
"congrArg",
"Nat.succ_le_of_lt",
"mul_a... | true |
_private.Lean.Elab.Tactic.Omega.Frontend.0.Lean.Elab.Tactic.Omega.formatErrorMessage.varNameOf | Lean.Elab.Tactic.Omega.Frontend | [
"instHDiv",
"String",
"instToStringChar",
"Char.toNat",
"HDiv.hDiv",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"ToString.toString",
"instAppendString",
"instHAppendOfAppend",
"instHAdd",
"instToStringNat",
"HMod.hMod",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Nat.instDiv",
"Nat.decLt",
"... | true |
Function.sometimes_spec | Mathlib.Logic.Function.Basic | [
"Eq.mpr",
"congrArg",
"id",
"Function.sometimes",
"Nonempty",
"Function.sometimes_eq",
"Eq"
] | true |
_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.card_mul_finset_lt_two._simp_1_5 | Mathlib.Combinatorics.Additive.VerySmallDoubling | [
"False",
"eq_false",
"pow_ne_zero",
"Ne",
"Monoid.toPow",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Nat",
"Zero.toOfNat0",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq",
"MonoidWithZero.toMonoid",
"MulZeroClass.toZero",
"IsReduced"
] | false |
IsFractional.map | Mathlib.RingTheory.FractionalIdeal.Operations | [
"IsLocalization.IsInteger",
"AlgHom.toLinearMap",
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SemilinearMapClass.toMulActionSemiHomClass",
"AlgHom.algHomClass",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
... | true |
_private.Lean.Meta.HaveTelescope.0.Lean.Meta.simpHaveTelescopeAux._sparseCasesOn_11 | Lean.Meta.HaveTelescope | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
Nat.Partition.ofComposition_parts | Mathlib.Combinatorics.Enumerative.Partition.Basic | [
"Composition.blocks",
"Nat.Partition.parts",
"Multiset",
"Composition",
"Multiset.ofList",
"Nat.Partition.ofComposition",
"Nat",
"Eq.refl",
"Eq"
] | true |
NNReal.sqrt_mul_le_half_add | Mathlib.Analysis.SpecialFunctions.ArithmeticGeometricMean | [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"NNReal.instCommSemiring",
"pow_pos",
"Semigroup.toMul",
"le_div_iff₀'",
"instHDiv",
"NNReal.sqrt_le_iff_le_sq",
"HMul.hMul",
"GroupWithZer... | true |
Set.mul_iUnion | Mathlib.Algebra.Group.Pointwise.Set.Lattice | [
"HMul.hMul",
"Mul",
"Set.image2_iUnion_right",
"Set.mul",
"Eq",
"Set.iUnion",
"instHMul",
"Set"
] | true |
CategoryTheory.Abelian.SpectralObject.spectralSequencePageSc'Iso._auto_1 | Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.Meta.InstanceEntry.ctorIdx | Lean.Meta.Instances | [
"Nat",
"Lean.Meta.InstanceEntry"
] | false |
FundamentalGroupoid.equiv_apply | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | [
"Equiv.instEquivLike",
"Equiv",
"FundamentalGroupoid.equiv",
"FundamentalGroupoid",
"FundamentalGroupoid.as",
"Eq.refl",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Lean.Grind.Field.noNatZeroDivisors.ofIsCharPZero | Init.Grind.Ring.Field | [
"Nat.mod_zero",
"Lean.Grind.Field.toCommRing",
"False",
"Lean.Grind.Semiring.nsmul_eq_ofNat_mul",
"instHSMul",
"HMul.hMul",
"eq_false",
"iff_false",
"congrArg",
"Lean.Grind.Semiring.mul_one",
"False.elim",
"Lean.Grind.IntModule.toNatModule",
"Lean.Grind.CommSemiring.toSemiring",
"Classical... | true |
Std.DTreeMap.Internal.Impl.minKey_insertIfNew | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"instDecidableEqOrdering",
"Std.DTreeMap.Internal.Impl.isEmpty_eq_isEmpty",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"beqOfOrd",
"Std.DTreeMap.Internal.Impl.Ordered.distinctKeys",
"Std.TransOrd",
... | true |
CategoryTheory.Limits.biprod_isZero_iff._simp_1 | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.HasBinaryBiproduct",
"CategoryTheory.Limits.biprod",
"And",
"propext",
"CategoryTheory.Limits.IsZero",
"CategoryTheory.Limits.biprod_isZero_iff",
"Eq",
"CategoryTheory.Category"
] | false |
CategoryTheory.bifunctorComp₁₂Functor_obj | Mathlib.CategoryTheory.Functor.Trifunctor | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.bifunctorComp₁₂FunctorObj",
"CategoryTheory.bifunctorComp₁₂Functor",
"Eq.refl",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Topology.ContinuousOn.0.ContinuousOn.iterate.match_1_1 | Mathlib.Topology.ContinuousOn | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
ENNReal.iInf_coe_eq_top | Mathlib.Data.ENNReal.Basic | [
"ENNReal.ofNNReal",
"iInf",
"WithTop.iInf_coe_eq_top",
"NNReal",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"IsEmpty",
"Iff",
"NNReal.instConditionallyCompleteLinearOrderBot",
"CompleteLinearOrder.toConditionallyCompleteLinearOrderBot",
"ENNReal",
"ConditionallyCompleteLi... | true |
MeasureTheory.measureReal_union' | Mathlib.MeasureTheory.Measure.Real | [
"Real",
"MeasureTheory.Measure",
"ChainCompletePartialOrder.instOfCompleteLattice",
"MeasurableSet",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"MeasurableSet.nullMeasurableSet",
"MeasureTheory.Measure.real",
"Disjoint",
"MeasureTheory.measureReal_union₀'",
"Set.instUnion",
"Ne",
"Chai... | true |
Matrix.diag_list_sum | Mathlib.Data.Matrix.Basic | [
"Matrix.diag",
"Matrix.add",
"AddMonoidHom.instAddMonoidHomClass",
"AddMonoid.toAddSemigroup",
"Matrix",
"List.map",
"AddMonoid.toAddZeroClass",
"List.sum",
"Matrix.diagAddMonoidHom",
"AddZeroClass.toAddZero",
"Pi.instZero",
"map_list_sum",
"AddZero.toZero",
"List",
"AddSemigroup.toAdd",... | true |
instDivColex.eq_1 | Mathlib.Algebra.Order.Group.Synonym | [
"Colex",
"Div",
"instDivColex",
"Eq.refl",
"Eq"
] | true |
_private.Init.Data.Nat.Basic.0.Nat.lt_trichotomy.match_1_3 | Init.Data.Nat.Basic | [
"GE.ge",
"instLENat",
"Or.casesOn",
"Nat",
"LT.lt",
"Or.inl",
"Or",
"instLTNat",
"Or.inr"
] | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.