name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
List.prev_getLast_cons' | Mathlib.Data.List.Cycle | [
"dite_cond_eq_true",
"List.getLast",
"False",
"congrArg",
"False.elim",
"noConfusion_of_Nat",
"Membership.mem",
"List.cons",
"List.getLast_cons",
"List",
"List.prev._proof_3",
"List.instMembership",
"List.prev",
"List.cons_ne_nil",
"congr",
"True",
"List.casesOn",
"eq_self",
"of_... | true |
Ioc_mem_nhdsLT_of_mem | Mathlib.Topology.Order.OrderClosed | [
"Filter.instMembership",
"Set.Ioc",
"LinearOrder",
"nhdsWithin",
"PartialOrder.toPreorder",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Ioo_mem_nhdsLT_of_mem",
"ClosedIicTopology",
"TopologicalSpace",
"Set.Ioo_subset_Ioc_self",
"Set.Iio",
"Set.instMember... | true |
Array.countP_set | Init.Data.Array.Count | [
"List.countP",
"congrArg",
"List.getElem_toArray._proof_1",
"Array.set",
"List.countP_toArray",
"HSub.hSub",
"List.countP_set",
"Eq.mp",
"Array.casesOn",
"instDecidableEqBool",
"List.set",
"instSubNat",
"instOfNatNat",
"List.toArray",
"Array",
"GetElem.getElem",
"Bool.true",
"List"... | true |
LieAlgebra.Basis.symm_f | Mathlib.Algebra.Lie.Basis | [
"CommRing",
"LieAlgebra.Basis.e",
"Finite",
"LieAlgebra.Basis.symm",
"LieAlgebra.Basis.f",
"LieRing",
"LieAlgebra.Basis",
"Eq.refl",
"LieAlgebra",
"Eq"
] | true |
CategoryTheory.Limits.biprod.map_eq_map' | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.BinaryBicone.fst",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Limits.BinaryBicone.inl_fst",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.BinaryBicone.toCone",
"CategoryTheory.Limits.I... | true |
Std.Time.Modifier.E.injEq | Std.Time.Format.Basic | [
"Eq.propIntro",
"Std.Time.Modifier.E",
"Std.Time.Modifier.E.inj",
"Eq.ndrec",
"Eq.refl",
"Std.Time.Text",
"Std.Time.Modifier",
"Eq"
] | true |
Representation.quotient._proof_2 | Mathlib.RepresentationTheory.Basic | [
"Monoid",
"Submodule",
"MonoidHom.instMonoidHomClass",
"Submodule.Quotient.addCommMonoid",
"Representation",
"MonoidHom.instFunLike",
"LinearMap.comp.congr_simp",
"HMul.hMul",
"Monoid.toMulOneClass",
"Submodule.Quotient.addCommGroup",
"LinearMap.ext",
"congrArg",
"AddCommGroup.toAddCommMonoi... | false |
Mathlib.Tactic.BicategoryLike.Normalize.Result._sizeOf_inst | Mathlib.Tactic.CategoryTheory.Coherence.PureCoherence | [
"Mathlib.Tactic.BicategoryLike.Normalize.Result._sizeOf_1",
"SizeOf.mk",
"Mathlib.Tactic.BicategoryLike.Normalize.Result",
"SizeOf"
] | false |
Aesop.Frontend.TacticConfig.rec | Aesop.Frontend.Tactic | [
"Lean.Meta.Simp.Config",
"Std.HashSet",
"Aesop.Frontend.TacticConfig",
"Lean.Syntax.Term",
"Array",
"Aesop.Options",
"Aesop.Frontend.RuleExpr",
"Aesop.RuleSetName",
"Aesop.Frontend.TacticConfig.mk",
"Lean.Name.instBEq",
"Option",
"Lean.instHashableName"
] | false |
SchwartzMap.toTemperedDistributionCLM._proof_3 | Mathlib.Analysis.Distribution.TemperedDistribution | [
"ContinuousLinearMap.comp",
"instInnerProductSpaceRealComplex",
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"MeasureTheory.Measure",
"SchwartzMap.instContinuousSMul",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"RCLike.... | false |
CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fst | Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | [
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"_private.Mathlib.CategoryTheory.Monoidal.Cartesian.Basic.0.CategoryTheory.CartesianMonoi... | true |
CategoryTheory.EnrichedCategory | Mathlib.CategoryTheory.Enriched.Basic | [
"CategoryTheory.EnrichedCategory.mk",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Category"
] | true |
Lean.Meta.isCoeDecl | Lean.Meta.Coe | [
"Lean.TagAttribute.hasTag",
"Lean.Meta.coeDeclAttr",
"Bool",
"Lean.Name",
"Lean.Environment"
] | true |
Matroid.eRk_singleton_eq | Mathlib.Combinatorics.Matroid.Rank.ENat | [
"instAddMonoidWithOneENat",
"Matroid.eRk_singleton_eq._auto_1",
"Matroid.E",
"Matroid.IsNonloop.eRk_eq",
"Membership.mem",
"Set.instSingletonSet",
"autoParam",
"Matroid.isNonloop_of_loopless",
"AddMonoidWithOne.toOne",
"Matroid.Loopless",
"ENat",
"Matroid.eRk",
"One.toOfNat1",
"Singleton.s... | true |
_private.Mathlib.Topology.Instances.AddCircle.Defs.0.AddCircle.coe_eq_zero_of_pos_iff._simp_1_1 | Mathlib.Topology.Instances.AddCircle.Defs | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"AddMonoid.toAddZeroClass",
"AddLeftMono",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
"SubNegZeroMonoid.toNegZeroClass",
"LE",
"neg_nonneg",
"AddGroup",
"AddGroup.toSubNegMonoid",
"propext",
"AddZero.toAd... | false |
FixedPoints.subring | Mathlib.Algebra.Algebra.Subalgebra.Operations | [
"Monoid",
"Ring.toNonAssocRing",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"Subsemigroup.mk",
"AddMonoid.toAddZeroClass",
"AddSubsemigroup.carrier",
"FixedPoints.subring._proof_3",
"AddZeroClass.toAddZero",
"MulOne.toMul",
"AddSubmonoid.toAddSubsemigroup",
"NonAssocSemiring.toMulZe... | true |
CategoryTheory.ExponentiableMorphism.instChosenPullbacksAlongHomMk | Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism | [
"CategoryTheory.ChosenPullbacksAlong",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Over.mk",
"CategoryTheory.Over.left",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ExponentiableMorphism.instChosenPullbacksAlongHomMk._aux_1",
"CategoryTheory.Over.hom",
"Ca... | true |
SlashInvariantForm.trace.eq_1 | Mathlib.NumberTheory.ModularForms.NormTrace | [
"SlashInvariantForm",
"Real",
"Subgroup.subgroupOf",
"Fintype.ofFinite",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Pi.addCommMonoid",
"Finset.univ",
"outParam",
"Matrix",
"instDecidableEqFin",
"Complex.instNormedField",
"Membership.mem",
"Real.semiring",
"SlashInvariantFormClass",
... | true |
LieModule.genWeightSpace_neg_add_chainBot | Mathlib.Algebra.Lie.Weights.Chain | [
"Eq.mpr",
"NegZeroClass.toNeg",
"IsDomain",
"CommRing",
"LieModule.Weight.instFunLike",
"Pi.instNeg",
"LieSubmodule.instBot",
"LieRing.toAddCommGroup",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"neg_eq_zero._simp_1",
"LieRing.IsNilpotent",
"Module.IsTorsionFree... | true |
Homeomorph.secondCountableTopology | Mathlib.Topology.Homeomorph.Lemmas | [
"Homeomorph.isInducing",
"SecondCountableTopology",
"Topology.IsInducing.secondCountableTopology",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Homeomorph",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Basis.piTensorProduct._proof_1 | Mathlib.LinearAlgebra.PiTensorProduct.Basis | [
"CommSemiring.toSemiring",
"RingHomInvPair",
"CommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
Equiv.sumEmbeddingEquivProdEmbeddingDisjoint._proof_8 | Mathlib.Logic.Equiv.Embedding | [
"Eq.mpr",
"Disjoint.le_bot",
"congrArg",
"Equiv.sumEmbeddingEquivProdEmbeddingDisjoint.match_1",
"False.elim",
"Disjoint",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Sum.casesOn",
"Sum",
"id",
"BiheytingAlgebra.toHeytingAlgebra",
"Prod.mk",
"Sum.inl",
"BiheytingAlgebra.toCoheyti... | false |
_private.Mathlib.MeasureTheory.Function.ContinuousMapDense.0.MeasureTheory.Integrable.exists_hasCompactSupport_integral_sub_le._simp_1_2 | Mathlib.MeasureTheory.Function.ContinuousMapDense | [
"Real",
"ENNReal.ofReal",
"ENNReal.ofReal_one",
"Real.instOne",
"ENNReal",
"One.toOfNat1",
"ENNReal.instOne",
"OfNat.ofNat",
"Eq.symm",
"Eq"
] | false |
MeasurableEquiv.piCongrLeft_apply_apply | Mathlib.MeasureTheory.MeasurableSpace.Embedding | [
"MeasurableEquiv.instEquivLike",
"Eq.mpr",
"MeasurableEquiv.piCongrLeft._proof_2",
"Equiv.instEquivLike",
"congrArg",
"MeasurableEquiv.piCongrLeft",
"MeasurableEquiv.coe_mk",
"id",
"Equiv",
"Equiv.piCongrLeft",
"MeasurableEquiv.piCongrLeft._proof_3",
"MeasurableSpace",
"MeasurableSpace.pi",
... | true |
RestrictedProduct.range_coe | Mathlib.Topology.Algebra.RestrictedProduct.Basic | [
"Filter.Eventually",
"setOf",
"Membership.mem",
"RestrictedProduct.instDFunLike",
"RestrictedProduct",
"Subtype.range_val_subtype",
"Set.range",
"Eq",
"Set.instMembership",
"DFunLike.coe",
"Filter",
"Set"
] | true |
ConvexBody.instAddCommMonoid | Mathlib.Analysis.Convex.Body | [
"Real",
"ConvexBody.instAdd",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"ConvexBody.instSMulNat",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Set.addCommMonoid",
"Real.semiring",
"DistribSMul.toSMulZeroClass",
"Add... | true |
SSet.Truncated.hoFunctor.monoidal._proof_17 | Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal | [
"CategoryTheory.Cat.category",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"SSet.Truncated.instMonoidalTruncation",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"SSet.Truncated",
"Cat... | false |
MulEquiv.monoidHomCongrLeft_refl | Mathlib.Algebra.Group.Equiv.Basic | [
"MulEquiv.refl",
"MonoidHom",
"Monoid.toMulOneClass",
"MulOne.toMul",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"MulEquiv",
"MonoidHom.mul",
"MulOneClass",
"Eq",
"CommMonoid",
"rfl",
"MulEquiv.monoidHomCongrLeft"
] | true |
Topology.IsOpenEmbedding.adjunctionNhds | Mathlib.Topology.Category.TopCat.OpenNhds | [
"Topology.IsOpenEmbedding.isOpenMap",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"IsOpenMap.functorNhds",
"ContinuousMap",
"PartialOrder.toPreorder",
"Preorder.smallCategory",
"TopologicalSpace.OpenNhds.map",
"TopCat.str"... | true |
instAndOpUInt8 | Init.Data.UInt.Basic | [
"UInt8.land",
"AndOp",
"AndOp.mk",
"UInt8"
] | true |
_private.Mathlib.Algebra.Ring.GeomSum.0.Commute.geom_sum₂_succ_eq._simp_1_3 | Mathlib.Algebra.Ring.GeomSum | [
"Monoid",
"HMul.hMul",
"Monoid.toMulOneClass",
"MulOne.toMul",
"instOfNatNat",
"Monoid.toPow",
"instHAdd",
"MulOneClass.toMulOne",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"instAddNat",
"instHPow",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"pow_succ'",
"instHMul"
] | false |
GradedTensorProduct.mulHom._proof_6 | Mathlib.LinearAlgebra.TensorProduct.Graded.Internal | [
"Submodule",
"Submodule.addSubgroupClass",
"CommRing",
"AddCommGroup.toAddCommMonoid",
"Algebra",
"AddCommGroup.toAddGroup",
"Algebra.toModule",
"CommRing.toCommSemiring",
"AddGroup.toSubNegMonoid",
"Ring.toAddCommGroup",
"Submodule.setLike",
"CommRing.toRing",
"AddSubgroupClass",
"Ring.to... | false |
IsDedekindDomain.HeightOneSpectrum.equivMaximalSpectrum._proof_5 | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"MaximalSpectrum.asIdeal",
"IsDedekindDomain.toIsDomain",
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Ring.ne_bot_of_isMaximal_of_not_isField",
"MaximalSpectrum.isMaximal",
"Ne",
"Bot.bot",
"MaximalSpectrum",
"Ideal",
"IsField",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
... | false |
IsFreeGroupoid.quiverGenerators | Mathlib.GroupTheory.FreeGroup.NielsenSchreier | [
"IsFreeGroupoid",
"CategoryTheory.Groupoid",
"IsFreeGroupoid.Generators",
"Quiver"
] | true |
TopCat.subpresheafContinuousPrelocalIsoPresheafToTop._proof_1 | Mathlib.Topology.Sheaves.LocalPredicate | [
"TopCat.subpresheafToTypes",
"CategoryTheory.Functor.op",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"TopCat.instCategory",
"ContinuousMap.mk",
"TopCat.PrelocalPredicate.pred",
"ContinuousMap",
"PartialOrder.toPreorder",
"Topo... | false |
Bundle.ContMDiffRiemannianMetric.mk | Mathlib.Geometry.Manifold.VectorBundle.Riemannian | [
"IsModuleTopology.toContinuousSMul",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedSpace._proof_1",
"ContinuousLinearMap.toNormedAddCommGroup",
"ContinuousLinearMap.continuousSMul",
"RingHomSurjective.ids",
"Real",
"Algebra.to_smulCommClass",
... | true |
MonoidHom.codRestrict.congr_simp | Mathlib.Algebra.Group.Subgroup.Ker | [
"SetLike",
"MonoidHom.instFunLike",
"SubmonoidClass.toMulOneClass",
"MonoidHom",
"Membership.mem",
"Eq.rec",
"Subtype",
"MonoidHom.codRestrict",
"MulOneClass.toMulOne",
"Eq.ndrec",
"Eq.refl",
"SubmonoidClass",
"MulOneClass",
"Eq",
"DFunLike.coe",
"SetLike.instMembership"
] | true |
IsOpen.exists_is_const_of_deriv_eq_zero | Mathlib.Analysis.Calculus.MeanValue | [
"ContinuousLinearMap.ext_ring",
"ContinuousLinearMap.toSpanSingleton_zero",
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"RCLike.toNormedAlgebra",
... | true |
SSet.nonDegenerateEquivOfIso.match_1 | Mathlib.AlgebraicTopology.SimplicialSet.Degenerate | [
"Opposite",
"SSet.nonDegenerate",
"Subtype.casesOn",
"Membership.mem",
"Set.Elem",
"SSet",
"Subtype.mk",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"CategoryTheory.types",
"SimplexCategory",
"CategoryTheory.Category.opposite",
"SimplexCategory.smallCategory",
"Set.instMembership",
"Ca... | false |
LieAlgebra.InvariantForm.restrict_nondegenerate | Mathlib.Algebra.Lie.InvariantForm | [
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"Eq.mpr",
"Submodule",
"instBracketSubtypeMemLieIdeal",
"LinearMap.BilinForm.restrict_nondegenerate_iff_isCompl_orthogonal",
"LieRing.toAddCommGroup",
"LinearMap.BilinForm",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
... | true |
_private.Mathlib.Data.List.Lattice.0.List.count_bagInter._proof_1_19 | Mathlib.Data.List.Lattice | [
"Int.Linear.not_eq_norm_expr",
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"Lean.Grind.nestedProof",
"eq_false",
"instLawfulBEq",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.Order.eq_of_le_of_le_0",
"congrArg",
"List.elem",... | false |
Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftLeftConst.go_denote_eq._unary | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.ShiftLeft | [
"Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftLeftConst.go_denote_eq._proof_2",
"dite_cond_eq_true",
"Std.Sat.AIG.RefVec.get",
"Eq.mpr",
"Std.Sat.AIG.Ref.cast",
"of_eq_false",
"Std.Sat.AIG.Decl",
"False",
"Decidable.casesOn",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Std.Sat.AIG.Ref.mk... | false |
Lean.Parser.Term.doLet.formatter | Lean.Parser.Do | [
"Lean.PrettyPrinter.Formatter",
"Lean.Parser.withCache.formatter",
"Lean.Parser.leadingNode.formatter",
"instOfNatNat",
"Lean.PrettyPrinter.Formatter.withAntiquot.formatter",
"Lean.Parser.symbol.formatter",
"Bool.true",
"Nat",
"Lean.Parser.optional.formatter",
"Lean.Parser.Term.letDecl.formatter",... | true |
Vector.append_assoc_symm._proof_2 | Init.Data.Vector.Lemmas | [
"_private.Init.Data.Vector.Lemmas.0.Vector.append_assoc_symm._proof_1",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Decidable.byContradiction",
"instAddNat",
"instDecidableEqNat",
"Eq",
"Not"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.TensorProduct.0.TensorProduct.adjoint_map._simp_1_1 | Mathlib.Analysis.InnerProductSpace.TensorProduct | [
"InnerProductSpace.toNormedSpace",
"Inner.inner",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"TensorProduct.ext_iff_inner_right",
"Field.toSemifield",
"TensorProduct.instInner",
"RCLike.toDenselyNormedField",
"RCLike",
"propext",
"TensorProduct",
"NormedAd... | false |
ContinuousLinearMap.smulRightₗ | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"ContinuousSMul",
"ContinuousLinearMap.smulRight",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"ContinuousLinearMap.addCommMonoid",
"AddZeroClass.toAddZero",
"ContinuousLinearMap.smulRightₗ._proof_1",
"DistribSMul.toSMul... | true |
_private.Mathlib.Algebra.Lie.Extension.0.LieAlgebra.Extension.ofTwoCocycle._simp_9 | Mathlib.Algebra.Lie.Extension | [
"LieHom",
"CommRing",
"LieSubalgebra.instSetLike",
"Membership.mem",
"Exists",
"LieHom.range",
"LieRing",
"propext",
"LieSubalgebra",
"LieAlgebra",
"LieHom.instFunLike",
"LieHom.mem_range",
"Eq",
"DFunLike.coe",
"SetLike.instMembership"
] | false |
LinearMap.BilinForm.tensorDistribEquiv._proof_7 | Mathlib.LinearAlgebra.BilinearForm.TensorProduct | [
"CommRing",
"CommSemiring.toSemiring",
"RingHomInvPair",
"CommRing.toCommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
Real.rpow_lt_one | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Eq.mpr",
"Real.instPow",
"Real.instLE",
"Real",
"Real.instZero",
"congrArg",
"Real.instLT",
"id",
"Real.one_rpow",
"LE.le",
"Real.instOne",
"Real.rpow_lt_rpow",
"HPow.hPow",
"LT.lt",
"One.toOfNat1",
"Zero.toOfNat0",
"instHPow",
"OfNat.ofNat",
"Eq.symm",
"Eq"
] | true |
Substring.Raw.trimRight | Init.Data.String.Substring | [
"Char.isWhitespace",
"Substring.Raw",
"Substring.Raw.dropRightWhile"
] | true |
QuadraticAlgebra.basis_repr_apply | Mathlib.Algebra.QuadraticAlgebra.Defs | [
"Finsupp.instFunLike",
"QuadraticAlgebra.re",
"Semiring.toModule",
"Finsupp.module",
"QuadraticAlgebra",
"instOfNatNat",
"Module.Basis.repr",
"Finsupp.instAddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"RingHomInvPair.ids",
... | true |
Irrational.div_cases | Mathlib.NumberTheory.Real.Irrational | [
"Real",
"instHDiv",
"Real.instInv",
"Real.instDivInvMonoid",
"id",
"HDiv.hDiv",
"Inv.inv",
"Irrational",
"Irrational.of_inv",
"DivInvMonoid.toDiv",
"Irrational.mul_cases",
"Or",
"Or.imp"
] | true |
ContinuousLinearMap.toSeminormedRing._proof_15 | Mathlib.Analysis.Normed.Operator.Basic | [
"NormedCommRing.toNormedRing",
"Semiring.toNatCast",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"NormedSpace",
"Ring.toNeg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"IntCast.intCast",
"instOfNatNat",
"ContinuousLinearMap.ring",
"Nat.cas... | false |
CategoryTheory.Subgroupoid.map.congr_simp | Mathlib.CategoryTheory.Groupoid.Subgroupoid | [
"CategoryTheory.Functor",
"Eq.rec",
"CategoryTheory.Groupoid",
"CategoryTheory.Subgroupoid.map",
"CategoryTheory.Subgroupoid",
"Eq.ndrec",
"Eq.refl",
"Function.Injective",
"CategoryTheory.Groupoid.toCategory",
"Eq",
"CategoryTheory.Functor.obj"
] | true |
Std.Http.Internal.Char.quotedPairChar.eq_2 | Std.Internal.Http.Internal.Char | [
"Std.Http.Internal.Char.vchar",
"Bool.true",
"Bool",
"Bool.or",
"Eq.refl",
"Std.Http.Internal.Char.quotedPairChar",
"Eq",
"Char.ofNat"
] | true |
_private.Mathlib.Algebra.Group.Torsion.0.pow_eq_one_iff._simp_1_1 | Mathlib.Algebra.Group.Torsion | [
"Monoid",
"MulOne.toOne",
"IsMulTorsionFree",
"Monoid.toMulOneClass",
"Ne",
"instOfNatNat",
"Monoid.toPow",
"pow_eq_one_iff_left",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat",
"propext",
"One.toOfNat1",
"instHPow",
"OfNat.ofNat",
"Eq"
] | false |
_private.Mathlib.LinearAlgebra.Vandermonde.0.Matrix.det_vandermonde_eq_zero_iff._simp_1_2 | Mathlib.LinearAlgebra.Vandermonde | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
Lean.Elab.Command.elabOpenPrivate | Batteries.Tactic.OpenPrivate | [
"Pure.pure",
"Unit.unit",
"Lean.Elab.Command.CommandElab",
"Lean.Syntax.getArgs",
"Lean.Syntax.isOfKind",
"Option.some",
"Lean.Syntax",
"Lean.TSyntaxArray",
"Lean.Elab.Command.elabOpenPrivateLike",
"IO.RealWorld",
"EIO",
"instDecidableEqBool",
"instOfNatNat",
"instMonadEIO",
"Lean.TSynta... | true |
Lean.Meta.Cases.Context._sizeOf_1 | Lean.Meta.Tactic.Cases | [
"Lean.Meta.Cases.Context",
"Lean.Expr",
"instOfNatNat",
"Array._sizeOf_inst",
"Array",
"instHAdd",
"HAdd.hAdd",
"Lean.Meta.Cases.Context.rec",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"instSizeOfNat",
"Lean.InductiveVal._sizeOf_inst",
"Lean.LocalDecl",
"OfNat.ofNat",
"Lean.LocalDecl._size... | false |
Order.IsSuccLimit.le_iff_forall_le | Mathlib.Order.SuccPred.Limit | [
"Preorder.toLT",
"Order.IsSuccPrelimit.le_iff_forall_le",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Order.IsSuccLimit",
"LE.le",
"Iff",
"LT.lt",
"Order.IsSuccLimit.isSuccPrelimit",
"instDistribLatticeOfLinearOrder... | true |
IsLeftUniformGroup.recOn | Mathlib.Topology.Algebra.IsUniformGroup.Defs | [
"IsLeftUniformGroup.mk",
"UniformSpace",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"IsLeftUniformGroup.rec",
"Monoid.toMulOneClass",
"uniformity",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"nhds",
"MulOne.toMul",
"DivInvMonoid.toMonoid"... | false |
ContinuousLinearMap.semiring._proof_6 | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic | [
"Semigroup.toMul",
"HMul.hMul",
"AddCommMonoid",
"ContinuousLinearMap",
"MonoidWithZero.zero_mul",
"TopologicalSpace",
"MonoidWithZero.toZero",
"ContinuousLinearMap.monoidWithZero",
"Monoid.toSemigroup",
"Semiring",
"Zero.toOfNat0",
"Module",
"OfNat.ofNat",
"RingHom.id",
"Semiring.toNonA... | false |
_private.Mathlib.MeasureTheory.Integral.Lebesgue.Basic.0.MeasureTheory.lintegral_max._simp_1_1 | Mathlib.MeasureTheory.Integral.Lebesgue.Basic | [
"Compl.compl",
"setOf",
"Set.instCompl",
"Eq.symm",
"Eq",
"Not",
"Set.compl_setOf",
"Set"
] | false |
Std.TreeSet.Raw.contains_iff_mem._simp_1 | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.contains",
"Std.TreeSet.Raw.contains_iff_mem",
"Membership.mem",
"Ordering",
"Std.TreeSet.Raw.instMembership",
"Bool.true",
"Std.TreeSet.Raw",
"propext",
"Bool",
"Eq"
] | false |
Subrelation | Init.Core | [] | true |
_private.Mathlib.Topology.DiscreteSubset.0.discreteTopology_biUnion_finset._simp_1_1 | Mathlib.Topology.DiscreteSubset | [
"DiscreteTopology",
"Membership.mem",
"Set.Elem",
"TopologicalSpace",
"IsDiscrete",
"propext",
"isDiscrete_iff_discreteTopology",
"instTopologicalSpaceSubtype",
"Eq.symm",
"Eq",
"Set.instMembership",
"Set"
] | false |
Std.IterM.IsPlausibleNthOutputStep.rec | Init.Data.Iterators.Consumers.Monadic.Access | [
"Std.IterM.IsPlausibleNthOutputStep",
"Std.IterStep",
"Std.IterM.IsPlausibleNthOutputStep.zero_yield",
"Std.IterM.IsPlausibleStep",
"Std.IterStep.skip",
"Std.IterM.IsPlausibleNthOutputStep.skip",
"instOfNatNat",
"Std.Iterator",
"instHAdd",
"HAdd.hAdd",
"Std.IterStep.yield",
"Nat",
"Std.IterM... | false |
Polynomial.isFixedPt_newtonMap_of_aeval_eq_zero | Mathlib.Dynamics.Newton | [
"Polynomial.derivative",
"Eq.mpr",
"CommRing",
"Semiring.toModule",
"HMul.hMul",
"MulZeroClass.toMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"sub_zero",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"LinearMap.instFunLike",
"HSub.hSub",
"Alge... | true |
_private.Init.Data.SInt.Lemmas.0.Int64.toInt_eq_toNatClampNeg._simp_1_1 | Init.Data.SInt.Lemmas | [
"Int64.toInt",
"Int64.toNat_toInt",
"Int64",
"Nat",
"Int64.toNatClampNeg",
"Int.toNat",
"Eq.symm",
"Eq"
] | false |
Task.Priority | Init.Core | [
"Nat"
] | true |
ModuleCat.restrictCoextendScalarsAdj | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | [
"ModuleCat.RestrictionCoextensionAdj.unit'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat.coextendScalars",
"ModuleCat",
"CategoryTheory.Adjunction.CoreHomEquivUnitCounit.mk",
"ModuleCat.restrictCoextendScalarsAdj._proof_4",
"CategoryTheory.Adjunction.mk'",
"RingHom",
"Equiv.... | true |
Lean.AttributeKind.noConfusion | Lean.Attributes | [
"noConfusionEnum",
"Lean.AttributeKind.ctorIdx",
"Nat",
"instDecidableEqNat",
"Eq",
"Lean.AttributeKind.noConfusionType",
"Lean.AttributeKind"
] | false |
DFA.union | Mathlib.Computability.DFA | [
"setOf",
"Membership.mem",
"DFA.mk",
"DFA.step",
"DFA.start",
"Prod.mk",
"Prod.fst",
"DFA.accept",
"Or",
"Prod",
"DFA",
"Set.instMembership",
"Prod.snd",
"Set"
] | true |
DomAddAct.instAddCommGroupOfAddOpposite | Mathlib.GroupTheory.GroupAction.DomAct.Basic | [
"AddOpposite",
"AddCommGroup",
"DomAddAct"
] | true |
List.kunion._f | Mathlib.Data.List.Sigma | [
"Sigma.fst",
"List.kerase",
"List.cons",
"List",
"List.below",
"List.kunion.match_1",
"Sigma",
"List.nil",
"DecidableEq"
] | false |
MeasureTheory.unifTight_congr_ae | Mathlib.MeasureTheory.Function.UnifTight | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"Filter.EventuallyEq",
"MeasurableSpace",
"Iff",
"Iff.intro",
"ENNReal",
"MeasureTheory.UnifTight.aeeq",
"MeasureTheory.UnifTight",
"Filter.EventuallyEq.symm",
"NormedAddCommGroup",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instO... | true |
MvPolynomial.optionEquivLeft_symm_C_C | Mathlib.Algebra.MvPolynomial.Equiv | [
"Finsupp.instAddZeroClass",
"Polynomial.C",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Algebra.algebraMap",
"AlgEquiv.symm",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.algebra",
"Polynomial.algebraOfAlgebra",
... | true |
IO.Error.invalidArgument | Init.System.IOError | [
"String",
"UInt32",
"IO.Error.invalidArgument",
"IO.Error",
"Option"
] | true |
Nat.dfoldRev_add._proof_8 | Init.Data.Nat.Fold | [
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Decidable.byContradiction",
"instAddNat",
"_private.Init.Data.Nat.Fold.0.Nat.dfoldRev_add._proof_7",
"Not",
"Nat.decLe"
] | false |
TopCommRingCat.instFunLikeSubtypeRingHomαContinuousCoe | Mathlib.Topology.Category.TopCommRingCat | [
"Continuous",
"DFunLike.mk",
"CommSemiring.toSemiring",
"RingHom",
"Subtype",
"TopCommRingCat.isTopologicalSpace",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"TopCommRingCat.instFunLikeSubtypeRingHomαContinuousCoe._proof_1",
"TopCommRingCat.isCommRing",
"TopCommRingCat",
"Subtype.val",
... | true |
Mathlib.Tactic.Linarith.ExprMap | Mathlib.Tactic.Linarith.Parsing | [
"Lean.Expr",
"List",
"Nat",
"Prod"
] | true |
_private.Mathlib.Data.EReal.Operations.0.EReal.mul_bot_of_pos.match_1_1 | Mathlib.Data.EReal.Operations | [
"Real",
"Preorder.toLT",
"PartialOrder.toPreorder",
"Option.casesOn",
"EReal",
"Option.some",
"instTopEReal",
"Bot.bot",
"instZeroEReal",
"Option.none",
"LT.lt",
"instPartialOrderEReal",
"Zero.toOfNat0",
"Top.top",
"OfNat.ofNat",
"instBotEReal",
"Real.toEReal",
"WithTop"
] | false |
ONote.sub.eq_2 | Mathlib.SetTheory.Ordinal.Notation | [
"PNat.val",
"Eq.mpr",
"False",
"ONote.sub",
"congrArg",
"ONote.oadd",
"ONote.sub.match_1",
"ONote.cmp",
"ONote.instZero",
"HSub.hSub",
"Ordering",
"id",
"ONote.zero",
"instSubNat",
"ONote.ofNat.match_1",
"Unit",
"instHSub",
"ONote.sub.eq_def",
"Nat.succPNat",
"Nat",
"Zero.toO... | true |
_private.Lean.Compiler.LCNF.Irrelevant.0.Lean.Compiler.LCNF.getRelevantCtorFields.match_1 | Lean.Compiler.LCNF.Irrelevant | [
"Lean.ConstructorVal",
"Nat.hasNotBit",
"Lean.ConstantInfo.ctorIdx",
"Lean.ConstantInfo.ctorInfo",
"Lean.ConstantInfo",
"_private.Lean.Compiler.LCNF.Irrelevant.0.Lean.Compiler.LCNF.getRelevantCtorFields._sparseCasesOn_1"
] | false |
CategoryTheory.Limits.MultispanIndex.multicoforkEquivSigmaCofork_inverse_obj_pt | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.Multicofork",
"CategoryTheory.Limits.WalkingMultispan",
"CategoryTheory.Limits.MultispanShape.L",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.MultispanShape",
"CategoryTheory.Limits.colimit.isColimit",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Li... | true |
QPF.SuppPreservation | Mathlib.Data.QPF.Univariate.Basic | [
"PFunctor.Obj",
"QPF",
"QPF.P",
"Functor.supp",
"PFunctor.instFunctorObj",
"QPF.abs",
"Eq",
"QPF.toFunctor",
"Set"
] | true |
inv_mul_le_of_le_mul | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"Iff.mpr",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulLeftMono",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"LE.le",
"LE",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"Inv... | true |
PadicAlgCl.isAlgebraic | Mathlib.NumberTheory.Padics.Complex | [
"Nat.Prime",
"instCommRingPadic",
"AlgebraicClosure.instAlgebra",
"Field.toDivisionRing",
"Fact",
"Algebra.id",
"DivisionRing.toRing",
"Algebra.IsAlgebraic",
"instFieldPadic",
"CommRing.toCommSemiring",
"Nat",
"AlgebraicClosure.instField",
"AlgebraicClosure.isAlgebraic",
"Padic",
"PadicA... | true |
HahnEmbedding.Seed.hahnCoeff._proof_1 | Mathlib.Algebra.Order.Module.HahnEmbedding | [
"DivisionRing.toDivisionSemiring",
"RingHomInvPair",
"RingHomInvPair.ids",
"DivisionSemiring.toSemiring",
"DivisionRing",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
NormalSpace.of_compactSpace_r1Space | Mathlib.Topology.Separation.Regular | [
"NormalSpace.mk",
"R1Space",
"CompactSpace",
"IsClosed",
"TopologicalSpace",
"NormalSpace",
"SeparatedNhds.of_isCompact_isCompact_isClosed",
"IsClosed.isCompact",
"Set"
] | true |
AddGroupFilterBasis.noConfusion | Mathlib.Topology.Algebra.FilterBasis | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"AddMonoid.toAddSemigroup",
"HEq.refl",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"AddGroupFilterBasis",
"FilterBasis.sets",
"instHAdd",
"AddSemigroup.toAdd"... | false |
AddGroupSeminorm.toSeminormedAddCommGroup.eq_1 | Mathlib.Analysis.Normed.Group.Defs | [
"SeminormedAddGroup.toNorm",
"SeminormedAddGroup.toAddGroup",
"SeminormedAddCommGroup",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"AddGroupSeminorm",
"SeminormedAddCommGroup.ofAddDist._proof_1",
"SeminormedAddGroup.toPseudoMetricSpace",
"AddCommGroup.mk",
"AddGroupSeminorm.toSeminormedAddCommGrou... | true |
Rat.sqrt | Mathlib.Data.Rat.Sqrt | [
"Rat.num",
"Rat",
"Rat.den",
"Nat.sqrt",
"mkRat",
"Int.sqrt"
] | true |
Lean.PersistentArray.findSomeRevM? | Lean.Data.PersistentArray | [
"Pure.pure",
"Lean.PersistentArray.root",
"Monad.toApplicative",
"Lean.PersistentArray.tail",
"_private.Lean.Data.PersistentArray.0.Lean.PersistentArray.findSomeM?.match_1",
"Option.some",
"Lean.PersistentArray",
"Applicative.toPure",
"Unit",
"Lean.PersistentArray.findSomeRevMAux",
"Monad.toBind... | true |
DenselyNormedField.rec | Mathlib.Analysis.Normed.Field.Basic | [
"Norm.norm",
"Real.instLE",
"Real",
"Real.instZero",
"Real.instLT",
"Exists",
"NormedField.toNorm",
"LE.le",
"NormedField",
"And",
"DenselyNormedField",
"LT.lt",
"Zero.toOfNat0",
"OfNat.ofNat",
"DenselyNormedField.mk"
] | false |
UpperSet.coe_Ioi | Mathlib.Order.UpperLower.Principal | [
"Set.Ioi",
"UpperSet",
"UpperSet.instSetLike",
"Preorder.toLE",
"UpperSet.Ioi",
"SetLike.coe",
"Eq",
"rfl",
"Preorder",
"Set"
] | true |
CategoryTheory.Arrow.AugmentedCechNerve.ExtraDegeneracy.s._proof_2 | Mathlib.AlgebraicTopology.ExtraDegeneracy | [
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.hom",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"SimplexCategory",
"CategoryTheory.Arrow.cechNerve._proof_2",
"instAddNat",
"CategoryTheory.Limits.HasWidePullback",
"CategoryTheory.Arrow",
"OfNat.... | false |
AffineBasis.coe_smul._simp_1 | Mathlib.LinearAlgebra.AffineSpace.Basis | [
"AffineBasis.instFunLike",
"instHSMul",
"AffineBasis.coe_smul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Group",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Function.hasSMul",
"addGroupIsAddTorsor",
"DistribSMul.... | false |
Lean.Meta.Match.Pattern.recOn | Lean.Meta.Match.Basic | [
"Lean.Meta.Match.Pattern.as",
"Lean.Meta.Match.Pattern.ctor",
"Lean.Meta.Match.Pattern.val",
"Lean.Expr",
"Lean.FVarId",
"Lean.Meta.Match.Pattern.var",
"Lean.Level",
"List.cons",
"Lean.Meta.Match.Pattern.rec",
"List",
"Lean.Meta.Match.Pattern.inaccessible",
"Lean.Name",
"Lean.Meta.Match.Patt... | false |
QuotientAddGroup.mk' | Mathlib.GroupTheory.QuotientGroup.Defs | [
"AddMonoid.toAddZeroClass",
"QuotientAddGroup.Quotient.addGroup",
"AddZeroClass.toAddZero",
"QuotientAddGroup.mk",
"QuotientAddGroup.mk'._proof_1",
"AddSubgroup",
"AddSubgroup.Normal",
"HasQuotient.Quotient",
"AddGroup",
"AddGroup.toSubNegMonoid",
"QuotientAddGroup.instHasQuotientAddSubgroup",
... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.