name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Over.tensorHom_left_fst_assoc | Mathlib.CategoryTheory.Monoidal.Cartesian.Over | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Over",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Over.mk",
"CategoryTheory.Limits.WidePullbackShape.category",
"Eq.mp",
"id",
"Mathlib.Ta... | true |
IsCyclotomicExtension.Rat.mem_subgroupGalEquivSubgroupChar_symm_iff._simp_1 | Mathlib.NumberTheory.NumberField.Cyclotomic.Galois | [
"OrderDual.instLE",
"OrderDual.toDual",
"Units.val",
"Nat.instMulZeroClass",
"CommRing",
"MulEquiv.instEquivLike",
"Equiv.instEquivLike",
"ZMod.commRing",
"IsCyclotomicExtension.Rat.subgroupGalEquivSubgroupChar",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Rat",
"PartialOrder.toPreor... | false |
Lean.Elab.Tactic.SimpKind.ctorIdx | Lean.Elab.Tactic.Simp | [
"Lean.Elab.Tactic.SimpKind.casesOn",
"Nat",
"Lean.Elab.Tactic.SimpKind"
] | false |
_private.Init.Data.Array.Lemmas.0.List.filterMap_replicate.match_1.splitter | Init.Data.Array.Lemmas | [
"List.filterMap_replicate.match_1",
"Option.some",
"Option.none",
"Unit",
"Option"
] | true |
IsSimpleRing.one_mem_of_ne_bot | Mathlib.RingTheory.SimpleRing.Basic | [
"TwoSidedIdeal.instBot",
"TwoSidedIdeal",
"IsSimpleRing",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Preorder.toLE",
"Membership.mem",
"Eq.rec",
"CompleteLattice.toBoundedOrder",
"Or.resolve_left",
"Ne",
"NonAssocRing",
"Bot.bot",
"TwoSidedIdeal.i... | true |
Lean.version.major | Init.Meta.Defs | [
"Unit.unit",
"Nat",
"_private.Init.Meta.Defs.0.Lean.version.getMajor"
] | true |
CategoryTheory.Presheaf.IsLocallyInjective.mk._flat_ctor | Mathlib.CategoryTheory.Sites.LocallyInjective | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presheaf.equalizerSieve",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.category",
"Membership.mem",
"CategoryTheory.Sieve",
"CategoryTheory.ConcreteCategory",
"Category... | false |
Subgroup.mem_lowerCentralSeries_succ_iff | Mathlib.GroupTheory.Nilpotent | [
"Subgroup.closure",
"Iff.rfl",
"Bracket.bracket",
"setOf",
"Group",
"Membership.mem",
"Exists",
"Subgroup",
"instOfNatNat",
"commutatorElement",
"Subgroup.lowerCentralSeries",
"instHAdd",
"And",
"Iff",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Subgroup.instTop",
"Top.top",
"OfNat.ofNa... | true |
PointedCone.ofSubmodule_lineal | Mathlib.Geometry.Convex.Cone.Pointed | [
"IsOrderedRing.toPosMulMono",
"IsOrderedRing.toZeroLEOneClass",
"IsOrderedRing",
"Nonneg.semiring",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Submodule.pointwiseNeg",
"SemilatticeInf.toPartialOrder",
"PointedCone",
"AddCommGroup",
"DistribLat... | true |
_private.Mathlib.Data.W.Basic.0.WType.finv | Mathlib.Data.W.Basic | [
"WType",
"_private.Mathlib.Data.W.Basic.0.WType.finv._proof_1",
"instOfNatNat",
"LE.le",
"instLENat",
"Subtype.mk",
"WType.mk",
"instHAdd",
"Fintype",
"HAdd.hAdd",
"Nat",
"_private.Mathlib.Data.W.Basic.0.WType.finv.match_1",
"instAddNat",
"_private.Mathlib.Data.W.Basic.0.WType.WType'",
"... | true |
CategoryTheory.Dial.instMonoidalCategoryStruct | Mathlib.CategoryTheory.Dialectica.Monoidal | [
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.Dial.leftUnitorImpl",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Dial.associatorImpl",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Dial.tensorHomImpl",
"CategoryTheory.Limits.HasPullbacks",
"CategoryTheory.... | true |
Module.Basis.smulTower._proof_2 | Mathlib.RingTheory.AlgebraTower | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"Finsupp.module",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Module.Basis.isScalarTower_finsupp",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.IsScalarTower.compatibleSMul",
... | false |
_private.Init.Data.List.Lemmas.0.List.ne_nil_iff_exists_cons.match_1_1 | Init.Data.List.Lemmas | [
"Exists",
"List.cons",
"List",
"Exists.casesOn",
"Exists.intro",
"Eq"
] | false |
Lean.Meta.LazyDiscrTree.PreDiscrTree | Lean.Meta.LazyDiscrTree | [
"Lean.Meta.LazyDiscrTree.PreDiscrTree.mk"
] | true |
_private.Mathlib.Order.UpperLower.Prod.0.upperClosure_prod._simp_1_1 | Mathlib.Order.UpperLower.Prod | [
"Prod.instLE_mathlib",
"LE.le",
"Prod.fst",
"LE",
"And",
"propext",
"Prod",
"Eq",
"Prod.snd",
"Prod.le_def"
] | false |
instAlgebraUniversalEnvelopingAlgebra._aux_3 | Mathlib.Algebra.Lie.UniversalEnveloping | [
"LieAlgebra.toModule",
"UniversalEnvelopingAlgebra.Rel",
"MulOne.toOne",
"CommRing",
"RingHom.mk",
"Algebra.algebraMap",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"OneHom.mk",
"RingHom",
"RingQuot.instSemiring",
"instRingUniversalEnvelopingAlgebra",... | false |
Std.ExtTreeSet.min_insert_of_isEmpty | Std.Data.ExtTreeSet.Lemmas | [
"Unit.unit",
"Std.ExtTreeSet.isEmpty",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.ExtTreeMap.minKey_insertIfNew_of_isEmpty",
"Std.TransCmp",
"Std.ExtTreeSet.min",
"Bool.true",
"Unit",
"Std.ExtTreeSet",
"Bool",
"Std.ExtTreeSet.insert_ne_empty",
"Eq",
"Std.ExtTreeSet.insert"
] | true |
KaehlerDifferential.polynomialEquiv._proof_11 | Mathlib.RingTheory.Kaehler.Polynomial | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"IsScalarTower.to_smulCommClass'",
"CommRing",
"Algebra.to_smulCommClass",
"IsScalarTower.right",
"instAddCommGroupKaehlerDifferential",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass... | false |
Lean.DefinitionSafety.ctorElimType | Lean.Declaration | [
"cond",
"Nat.ble",
"Lean.DefinitionSafety.safe",
"Lean.DefinitionSafety.partial",
"PULift",
"Nat",
"Lean.DefinitionSafety.unsafe",
"Lean.DefinitionSafety"
] | false |
CompleteLattice.copy._proof_6 | Mathlib.Order.Copy | [
"Lattice",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Lattice.copy",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"CompleteLattice.toBoundedOrd... | false |
FiniteIndexNormalAddSubgroup.ctorIdx | Mathlib.GroupTheory.FiniteIndexNormalSubgroup | [
"FiniteIndexNormalAddSubgroup",
"AddGroup",
"Nat"
] | false |
Std.Internal.Parsec.Input.pos | Std.Internal.Parsec.Basic | [
"outParam",
"Std.Internal.Parsec.Input",
"DecidableEq"
] | true |
MeasureTheory.Measure.everywherePosSubset_subset | Mathlib.MeasureTheory.Measure.EverywherePos | [
"Filter.instMembership",
"MeasureTheory.Measure",
"Preorder.toLT",
"nhdsWithin",
"PartialOrder.toPreorder",
"Membership.mem",
"HasSubset.Subset",
"MeasurableSpace",
"TopologicalSpace",
"And.left",
"MeasureTheory.Measure.everywherePosSubset",
"LT.lt",
"ENNReal",
"ENNReal.instPartialOrder",
... | true |
UniformSpace.Completion.mapRingHom | Mathlib.Topology.Algebra.UniformRing | [
"UniformSpace",
"UniformSpace.Completion.extensionHom",
"Continuous",
"UniformSpace.Completion.coeRingHom",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"RingHom",
"UniformSpace.Completion.mapRingHom._proof_2",
"IsUniformAddGroup",
"NonAssocRing.toNonUnitalNonAssocRing",
"UniformSpace.Co... | true |
PowerBasis.liftEquiv'_apply_coe | Mathlib.RingTheory.PowerBasis | [
"PowerBasis",
"PowerBasis.liftEquiv'",
"IsDomain",
"CommRing",
"Equiv.instEquivLike",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"PowerBasis.gen",
"Algebra",
"Membership.mem",
"Multiset",
"Equiv",
"Subtype",
"minpoly",
"Multiset.instMembership",
"CommRing.toCommSemiring",... | true |
Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.ratUnits_performRupCheck | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult | [
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.performRupCheck",
"Prod.fst",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula",
"Array",
"Nat",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.ratUnits",
"eq_self",
"Std.Sat.CNF.Clause",
"Bool",
"of_eq_true",
"Prod",
"Std.Tactic.BVDecide.L... | true |
_private.Mathlib.Topology.LocallyFinite.0.locallyFinite_sum._simp_1_2 | Mathlib.Topology.LocallyFinite | [
"And",
"propext",
"Eq.symm",
"Eq",
"forall_and"
] | false |
Complex.taylorSeries_eq_on_emetric_ball | Mathlib.Analysis.Complex.TaylorSeries | [
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"CompleteSpace",
"Semiring.toModule",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"Complex.instNormedField",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpa... | true |
IsLocallyConstant.iff_isOpen_fiber_apply | Mathlib.Topology.LocallyConstant.Basic | [
"Filter.Eventually",
"IsLocallyConstant",
"setOf",
"List.instGetElem?NatLtLength",
"Membership.mem",
"Exists",
"nhds",
"Set.instSingletonSet",
"instOfNatNat",
"List.cons",
"TopologicalSpace",
"List",
"And",
"Iff",
"IsLocallyConstant.tfae",
"List.TFAE.out",
"Set.preimage",
"Nat",
... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.mem_insertUnit_fold_units._proof_1_1 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound | [
"False",
"eq_false",
"Lean.Grind.not_or",
"Classical.byContradiction",
"Membership.mem",
"Eq.mp",
"id",
"Array.toList",
"Array",
"And.casesOn",
"List",
"And",
"List.instMembership",
"Nat",
"True",
"eq_true",
"Std.Sat.CNF.Clause",
"Bool",
"Lean.Grind.intro_with_eq",
"Or",
"Pro... | false |
WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Basic | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"AddGroup.toSubtractionMonoid",
"Finsupp.instAddZeroClass",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Mathlib.T... | true |
InverseSystem.pEquivOnSucc._proof_1 | Mathlib.Order.DirectedInverseSystem | [
"Order.succ",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"Order.le_succ",
"SuccOrder",
"instDistribLatticeOfLinearOrder",
"Lattice.toSemilatticeInf"
] | false |
Asymptotics.isLittleO_const_left._simp_1 | Mathlib.Analysis.Asymptotics.Lemmas | [
"Norm.norm",
"Asymptotics.isLittleO_const_left",
"Real",
"Function.comp",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Filter.atTop",
"Filter.Tendsto",
"NormedAddCommGroup.toNorm",
"propext",
"Zero.toOfNat0",
"Normed... | false |
BoxIntegral.BoxAdditiveMap.volume.eq_1 | Mathlib.Analysis.BoxIntegral.Partition.Measure | [
"Real",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousLinearMap.addCommMonoid",
"BoxIntegral.BoxAdditiveMap.toSMul",
"AddCommGroup.toAddGroup",
"Real.measureSpace",
"BoxIntegral.BoxAdditiveMap.volume._proof_1",
"Real.semirin... | true |
NumberField.HeightOneSpectrum.adicAbv | Mathlib.NumberTheory.NumberField.Completion.FinitePlace | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroOneClass",
"Real.partialOrder",
"Real",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Ideal.absNorm",
"NumberField.HeightOneSpectrum.adicAbv._proof_1",
"CommSemiring.toSemiring",
"IsFractio... | true |
DoubleCentralizer.one_snd | Mathlib.Analysis.CStarAlgebra.Multiplier | [
"instSMulOfMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"DoubleCentralizer.instOne",
"NonUnitalNonAssocRing.toAddCommGroup",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"Non... | true |
CategoryTheory.Abelian.SpectralObject.liftCycles_i | Mathlib.Algebra.Homology.SpectralObject.Cycles | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.SpectralObject.cycles._proof_2",
"CategoryTheory.Abelian.SpectralObject.cycles",
"CategoryTheory.Abelian.SpectralObject.cycles._proof_3",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.liftCyc... | true |
Nat.ascFactorialBinary.eq_def | Mathlib.Data.Nat.Factorial.Basic | [
"Nat.ascFactorialBinary.match_1",
"instHDiv",
"HMul.hMul",
"id",
"HDiv.hDiv",
"instMulNat",
"instOfNatNat",
"instHAdd",
"Unit",
"Nat.ascFactorialBinary",
"HAdd.hAdd",
"Nat",
"Nat.instDiv",
"PSigma.mk",
"instAddNat",
"Nat.ascFactorialBinary._unary.eq_def",
"OfNat.ofNat",
"Eq",
"in... | true |
Ordering.isGE_iff_eq_gt_or_eq_eq | Init.Data.Ord.Basic | [
"Ordering.gt",
"instDecidableEqOrdering",
"of_decide_eq_true",
"Ordering",
"Ordering.eq",
"id",
"instDecidableEqBool",
"Bool.true",
"Iff",
"Bool",
"Eq.refl",
"Ordering.isGE",
"Or",
"Ordering.instDecidableForallOfDecidablePred",
"Decidable.decide",
"Eq",
"instDecidableOr",
"instDeci... | true |
MulAction.isBlock_subtypeVal | Mathlib.GroupTheory.GroupAction.Blocks | [
"SubMulAction.instSetLike",
"Eq.mpr",
"instMulActionSemiHomClassMulActionHom",
"instHSMul",
"instSMulOfMul",
"ChainCompletePartialOrder.instOfCompleteLattice",
"SubMulAction.inclusion",
"MulAction.IsBlock",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Monoid.toMulOneClass",
"congrArg",
... | true |
Semiring.toOppositeModule | Mathlib.Algebra.Module.Opposite | [
"Semiring.toOppositeModule._proof_3",
"MulOpposite",
"Module.mk",
"DistribMulAction.mk",
"Semiring.toOppositeModule._proof_4",
"MulOpposite.instMonoidWithZero",
"MulActionWithZero",
"Semiring.toOppositeModule._proof_2",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"MonoidWithZero.toMulZeroOneClass... | true |
Field.finSepDegree_eq_of_equiv | Mathlib.FieldTheory.SeparableDegree | [
"Field.embEquivOfEquiv",
"Algebra",
"Field.finSepDegree",
"Field.toSemifield",
"Nat.card_congr",
"Semifield.toDivisionSemiring",
"AlgEquiv",
"Nat",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemiring",
"Eq",
"Field",
"Field.Emb"
] | true |
CategoryTheory.ComonObj.comul_assoc_flip | Mathlib.CategoryTheory.Monoidal.Comon_ | [
"CategoryTheory.ComonObj.comul",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.ComonObj",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso.hom_inv_id",
"CategoryTheo... | true |
Matrix.kroneckerMap_smul_right | Mathlib.LinearAlgebra.Matrix.Kronecker | [
"Matrix.smul",
"instHSMul",
"Matrix",
"SMul",
"Prod.fst",
"Matrix.kroneckerMap",
"HSMul.hSMul",
"Prod",
"Eq",
"Prod.snd",
"Matrix.ext"
] | true |
ValuationSubring.decompositionSubgroupMulSemiringAction._proof_1 | Mathlib.RingTheory.Valuation.RamificationGroup | [
"SubsemiringClass",
"CommRing.toNonAssocCommRing",
"Field.toCommRing",
"ValuationSubring.instSubringClass",
"ValuationSubring.instSetLike",
"Field",
"NonAssocRing.toNonAssocSemiring",
"SubringClass.toSubsemiringClass",
"ValuationSubring",
"NonAssocCommRing.toNonAssocRing"
] | false |
UpperHalfPlane.im_div_exp_dist_le | Mathlib.Analysis.Complex.UpperHalfPlane.Metric | [
"Iff.mpr",
"GroupWithZero.toMonoidWithZero",
"div_le_iff₀",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"MulZeroClass.toMul",
"IsStrictOrderedRing.toMulPosStrictMono",
"Real.instDivInvMonoid",
"UpperHalfPlane.im_le_im_mul_exp_dist",
... | true |
PrimeSpectrum.zeroLocus_span | Mathlib.RingTheory.Spectrum.Prime.Basic | [
"Set.ext",
"Submodule",
"Semiring.toModule",
"Submodule.gi",
"PrimeSpectrum.zeroLocus",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"CompleteLattice.toConditionallyCompleteLattice",
"Submodule.instPartialOrder",
"Ideal",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
... | true |
Set.inter_insert_of_notMem | Mathlib.Data.Set.Insert | [
"_private.Mathlib.Data.Set.Insert.0.Set.inter_insert_of_notMem._proof_1_1",
"Membership.mem",
"Insert.insert",
"Set.instInter",
"Inter.inter",
"Set.instInsert",
"Eq",
"Set.instMembership",
"Not",
"Set"
] | true |
SheafOfModules.Presentation.isColimit._proof_6 | Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent | [
"CategoryTheory.Functor",
"Opposite",
"Equiv.instEquivLike",
"AddCommGrpCat.hasLimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"ModuleCat",
"CategoryTheory.Limits.WalkingParallelPair",
"AddCommGroup.toAddCommMonoid",
"SheafOfModules.Presentat... | false |
MonotoneOn.set_prod | Mathlib.Data.Set.Prod | [
"Set.instSProd",
"SProd.sprod",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"BiheytingAlgebra.toCoheytingAlgebra",
"LE.le",
"BooleanAlgebra.toBiheytingAlgebra",
"MonotoneOn",
"Set.instBooleanAlgebra",
"CoheytingAlgebra.toGeneralizedCoheytingAl... | true |
neg_lt_sub_iff_lt_add._simp_1 | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"neg_lt_sub_iff_lt_add",
"AddMonoid.toAddZeroClass",
"AddRightStrictMono",
"HSub.hSub",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"instHAdd",
"AddGroup",
"Ad... | false |
_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.card_mul_finset_lt_two._simp_1_16 | Mathlib.Combinatorics.Additive.VerySmallDoubling | [
"SetLike",
"Membership.mem",
"SetLike.coe",
"SetLike.mem_coe",
"propext",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
CliffordAlgebra.gradedAlgebra._proof_2 | Mathlib.LinearAlgebra.CliffordAlgebra.Grading | [
"Subtype.coe_mk",
"AlgHom.toLinearMap",
"Eq.mpr",
"Submodule",
"DirectSum.coeAlgHom",
"CliffordAlgebra.ι",
"Submodule.addSubmonoidClass",
"CommRing",
"CliffordAlgebra.lift_ι_apply",
"Semiring.toModule",
"Equiv.instEquivLike",
"HMul.hMul",
"ZMod.commRing",
"instAddCommMonoidDirectSum",
"A... | false |
Metric.Sigma.completeSpace | Mathlib.Topology.MetricSpace.Gluing | [
"UniformSpace",
"Eq.mpr",
"Real.partialOrder",
"Real",
"IsComplete",
"CompleteSpace",
"Real.instZero",
"Real.instZeroLEOneClass",
"congrArg",
"HEq.refl",
"Set.univ",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Real.instLT",
"Membership.mem",
"Metric.Sigma.metricSpace",
"Set.instSin... | true |
Lean.ParseImports.atomic | Lean.Elab.ParseImportsFast | [
"Lean.ParseImports.State.mk",
"Lean.ParseImports.State.isModule",
"String",
"instDecidableEqBool",
"String.Pos.Raw",
"Bool.true",
"Lean.ParseImports.State.isMeta",
"Lean.ParseImports.State.badModifier",
"Bool",
"Lean.ParseImports.Parser",
"Lean.ParseImports.State.imports",
"Lean.ParseImports.S... | true |
_private.Init.Data.Int.Cooper.0.Int.add_of_le._proof_1 | Init.Data.Int.Cooper | [
"Eq.mpr",
"congrArg",
"Int.toNat_of_nonneg",
"HSub.hSub",
"id",
"Int.sub_nonneg_of_le",
"Int.add_sub_cancel",
"Int",
"LE.le",
"Int.add_comm",
"Nat.cast",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Int.instAdd",
"Eq.refl",
"Int.instSub",
"Int.toNat",
"instNatCastInt",
"Eq.symm",
"E... | false |
ConvexCone.Salient.anti | Mathlib.Geometry.Convex.Cone.Basic | [
"ConvexCone.Salient",
"NegZeroClass.toNeg",
"ConvexCone.instPartialOrder",
"AddCommGroup.toAddCommMonoid",
"SMul",
"PartialOrder.toPreorder",
"ConvexCone.instSetLike",
"Preorder.toLE",
"Membership.mem",
"PartialOrder",
"AddCommGroup",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
... | true |
TensorProduct.instStarModule | Mathlib.Algebra.Star.TensorProduct | [
"SemilinearMapClass.toMulActionSemiHomClass",
"CommSemiring.toSemiring",
"TensorProduct.instSMul",
"DistribMulAction.toDistribSMul",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"TensorProduct.instStar",
"AddZeroClass.toAddZero",
"SemilinearEquivClass.instSemilinearMapClass",
"MulAct... | true |
MeasurableEquiv.mulRight._proof_4 | Mathlib.MeasureTheory.Group.MeasurableEquiv | [
"Eq.mpr",
"Equiv.instEquivLike",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"Measurable",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"id",
"Equiv",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Equiv.mulRight_symm",
"Measur... | false |
_private.Init.Data.String.Basic.0.ByteArray.validateUTF8_eq_false_iff._simp_1_1 | Init.Data.String.Basic | [
"Bool.true",
"Bool.not_eq_true",
"Bool",
"Eq.symm",
"Bool.false",
"Eq",
"Not"
] | false |
_private.Mathlib.Algebra.Order.CauSeq.Basic.0.IsCauSeq.add.match_1_1 | Mathlib.Algebra.Order.CauSeq.Basic | [
"Preorder.toLT",
"AddGroupWithOne.toAddGroup",
"LinearOrder",
"PartialOrder.toPreorder",
"HSub.hSub",
"SemilatticeInf.toPartialOrder",
"GE.ge",
"DistribLattice.toLattice",
"instLENat",
"And.casesOn",
"SubNegMonoid.toSub",
"And",
"instHSub",
"AddGroup.toSubNegMonoid",
"Nat",
"And.intro"... | false |
Aesop.PersistentHashSet.toArray | Aesop.Util.Basic | [
"Array.push",
"List.toArray",
"Array",
"Lean.PersistentHashSet.fold",
"Hashable",
"Lean.PersistentHashSet",
"BEq",
"List.nil"
] | true |
String.Pos.ne_of_lt | Init.Data.String.Basic | [
"Eq.mpr",
"String.instLTRaw",
"congrArg",
"String",
"_private.Init.Data.String.Basic.0.String.Pos.ne_of_lt._simp_1_2",
"String.Pos.Raw.ne_of_lt",
"id",
"Ne",
"String.Pos.Raw",
"implies_congr",
"String.instLTPos",
"LT.lt",
"String.Pos",
"Eq",
"_private.Init.Data.String.Basic.0.String.Pos.... | true |
MulAction.period_eq_one_iff | Mathlib.GroupTheory.GroupAction.Period | [
"Monoid",
"Eq.mpr",
"Nat.instMulZeroClass",
"instHSMul",
"Nat.instOne",
"congrArg",
"Nat.instZeroLEOneClass",
"Eq.rec",
"id",
"instOfNatNat",
"MulAction.pow_period_smul",
"MulAction.period_le_of_fixed",
"Monoid.toPow",
"le_antisymm",
"Iff",
"HPow.hPow",
"Nat.instNeZeroSucc",
"pow_o... | true |
AlgebraicGeometry.Scheme.AffineZariskiSite.instLocallyDirectedIsOpenImmersionDirectedCover._proof_8 | Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme.homOfLE",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.Scheme.AffineZariskiSite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Open... | false |
CategoryTheory.Abelian.coimIsoIm._proof_2 | Mathlib.CategoryTheory.Abelian.Basic | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.coim._proof_1",
"CategoryTheory.Abelian.coimageIsoImage._proof_1",
"CategoryTheory.Category.assoc",
"CategoryTheory.Abelian.coim",
"CategoryTheory.Abelian.coim._proof_2",
"CategoryTheory.Abelian.im",
"CategoryTheory.Limits.cokernel.desc",... | false |
BoxIntegral.TaggedPrepartition.isPartition_iff_iUnion_eq | Mathlib.Analysis.BoxIntegral.Partition.Tagged | [
"Real",
"BoxIntegral.Box.toSet",
"BoxIntegral.TaggedPrepartition.toPrepartition",
"BoxIntegral.TaggedPrepartition.iUnion",
"Iff",
"BoxIntegral.Prepartition.isPartition_iff_iUnion_eq",
"BoxIntegral.TaggedPrepartition.IsPartition",
"Eq",
"BoxIntegral.TaggedPrepartition",
"BoxIntegral.Box",
"Set"
] | true |
CategoryTheory.Limits.MonoFactorisation.recOn | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.MonoFactorisation.mk",
"CategoryTheory.Limits.MonoFactorisation.rec",
"CategoryTheory.Limits.MonoFactorisation",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq... | false |
Aesop.InstMap.insertMatch | Aesop.Forward.State | [
"Aesop.BaseM",
"instInhabitedProd",
"Aesop.InstMap",
"instInhabitedOfMonad",
"instInhabitedBool",
"ReaderT",
"String",
"Lean.Meta.State",
"_private.Aesop.Forward.State.0.Aesop.InstMap.insertMatch.match_1",
"instMonadLiftT",
"Aesop.PremiseIndex",
"panicWithPosWithDecl",
"Lean.Expr",
"Lean.M... | true |
AnalyticAt.hasStrictDerivAt | Mathlib.Analysis.Calculus.FDeriv.Analytic | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"deriv",
"NormedSpace.toModule",
"AddMonoid.to... | true |
Aesop.EqualUpToIds.MVarValue.delayedAssignment.sizeOf_spec | Aesop.Util.EqualUpToIds | [
"instOfNatNat",
"Lean.DelayedMetavarAssignment",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Aesop.EqualUpToIds.MVarValue._sizeOf_inst",
"instAddNat",
"Eq.refl",
"Lean.DelayedMetavarAssignment._sizeOf_inst",
"OfNat.ofNat",
"Eq",
"Aesop.EqualUpToIds.MVarValue.delayedAssignment",
"Aeso... | true |
Std.TreeMap.getElem!_insertIfNew | Std.Data.TreeMap.Lemmas | [
"instDecidableNot",
"Std.TreeMap.insertIfNew",
"instDecidableEqOrdering",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Ordering.eq",
"Std.TreeMap.instDecidableMem",
"Std.TransCmp",
"And",
"Std.TreeMap.instMembership",
"Std.TreeMap.instGetElem?Mem",
"Inhabited",
"Std.DTreeMap.Const.g... | true |
UInt64.ofNat_mod_size | Init.Data.UInt.Lemmas | [
"instPowNat",
"NeZero.mk",
"Dvd.dvd",
"UInt64.ofNat",
"Fin.ofNat._proof_1",
"congrArg",
"UInt64",
"Nat.pos_iff_ne_zero",
"BitVec.ofFin",
"Zero.ofOfNat0",
"UInt64.ofBitVec",
"BitVec",
"Fin.mk",
"Nat.instMod",
"instHMod",
"Ne",
"instOfNatNat",
"BitVec.ofNat",
"instNatPowNat",
"HM... | true |
CategoryTheory.CartesianMonoidalCategory | Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | [
"CategoryTheory.CartesianMonoidalCategory.mk",
"CategoryTheory.Category"
] | true |
Computation.parallel_congr_left | Mathlib.Data.Seq.Parallel | [
"Iff.mpr",
"Eq.mpr",
"congrArg",
"Computation.exists_of_mem_parallel",
"Computation.Promises",
"Computation.parallel",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"Stream'.WSeq.LiftRel",
"Computation.mem_parallel",
"Computation",
"And",
"Computation.parallel_promises",
"Iff.intro",
"C... | true |
_private.Mathlib.RingTheory.Localization.Basic.0.Localization.r_iff_of_le_nonZeroDivisors.match_1_4 | Mathlib.RingTheory.Localization.Basic | [
"CommRing",
"HMul.hMul",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Membership.mem",
"Exists",
"MulOne.toMul",
"Subtype",
"MulZeroOneClass.toMulOneClass",
"And.casesOn",
"instMulZeroOneClassOfSemiring",
"MulOneClass.toMulOne",
"And",
"CommRing.toCommSemiring",
"Exists.casesOn",
... | false |
Hamming.instSMulWithZero | Mathlib.InformationTheory.Hamming | [
"SMulWithZero.toSMulZeroClass",
"Hamming.instSMulWithZero._proof_2",
"Hamming.instSMulWithZero._proof_1",
"SMulZeroClass.mk",
"Hamming",
"Hamming.instZero",
"SMulZeroClass.toSMul",
"SMulWithZero",
"SMulWithZero.mk",
"Zero",
"Hamming.instSMul"
] | true |
AlgebraicGeometry.ValuativeCommSq.mk | Mathlib.AlgebraicGeometry.ValuativeCriterion | [
"AlgebraicGeometry.ValuativeCommSq.mk",
"AlgebraicGeometry.ValuativeCommSq",
"IsDomain",
"AlgebraicGeometry.Spec",
"CommRing",
"AlgebraicGeometry.Scheme",
"Algebra.algebraMap",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CommSq",
"CommSemiring.toSemiring",
"IsFracti... | true |
IsLocalRing.instCommRingResidueField._proof_10 | Mathlib.RingTheory.LocalRing.ResidueField.Defs | [
"IsLocalRing.instCommRingResidueField._aux_4",
"CommRing",
"Semiring.toModule",
"Submodule.Quotient.addMonoid._proof_8",
"CommSemiring.toSemiring",
"AddMonoid.nsmul_zero._autoParam",
"IsLocalRing.maximalIdeal",
"instOfNatNat",
"IsLocalRing",
"autoParam",
"CommRing.toCommSemiring",
"IsLocalRing... | false |
_private.Mathlib.Topology.FiberBundle.Constructions.0.wrapped._proof_1._@.Mathlib.Topology.FiberBundle.Constructions.1875155857._hygCtx._hyg.8 | Mathlib.Topology.FiberBundle.Constructions | [
"definition._@.Mathlib.Topology.FiberBundle.Constructions.1875155857._hygCtx._hyg.8",
"Bundle.Pullback",
"TopologicalSpace",
"Bundle.TotalSpace",
"Eq",
"rfl"
] | false |
Cardinal.mk_compl_eq_mk_compl_finite_lift | Mathlib.SetTheory.Cardinal.Arithmetic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"Compl.compl",
"Finset",
"Subtype.finite",
"Finset.card_compl",
"Finite",
"Cardinal.commSemiring",
"HSub.hSub",
"Cardinal.lift",
"Classical.propDecidable",
"Set.Finite",
"Cardinal.mk",
"Member... | true |
_private.Mathlib.Probability.Martingale.OptionalStopping.0.MeasureTheory.smul_le_stoppedValue_hittingBtwn._simp_1_1 | Mathlib.Probability.Martingale.OptionalStopping | [
"Finset.le_sup'_iff",
"Lattice.toSemilatticeSup",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"And",
"Finset.instSetLike",
"propext",
"Finset.Nonempty",
"Finset.su... | false |
_private.Mathlib.RingTheory.Smooth.NoetherianDescent.0.Algebra.Smooth.DescentAux.exists_kerSquareLift_comp_eq_id._simp_1_7 | Mathlib.RingTheory.Smooth.NoetherianDescent | [
"SetLike",
"Membership.mem",
"SetLike.coe",
"SetLike.mem_coe",
"propext",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
IsNilpotent.pow_succ | Mathlib.Algebra.GroupWithZero.Basic | [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toMul",
"Monoid.toMulOneClass",
"congrArg",
"pow_add",
"id",
"MulOne.toMul",
"instMulNat",
"pow_mul",
"MulZeroClass.mul_zero",
"Monoid.toPow",
"instHAdd",
"MulOneClass.toMulOne",
"_private.Mathlib.Algebra.GroupWithZero.Basic.0.IsNilpotent.pow_succ.mat... | true |
CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone_π_app | Mathlib.CategoryTheory.Limits.Constructions.Filtered | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.HasProduct",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetObj",
"Quiver.Hom",
"Finset",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.categ... | true |
_private.Init.Data.Array.Lemmas.0.List.anyM.match_1.eq_2 | Init.Data.Array.Lemmas | [
"Unit.unit",
"_private.Init.Data.List.Control.0.List.anyM.match_1",
"Bool.true",
"Unit",
"Bool",
"Eq.refl",
"Bool.false",
"Eq"
] | true |
Real.rpow_rpow_inv | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"MulOne.toOne",
"Real.instPow",
"Real.instLE",
"Real",
"DivInvMonoid.toInv",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"mul_inv_cancel₀",
"MulZeroClass.toMul",
"Real.instZero",
"congrArg",
"Real.instInv",
"DivisionSemiring.toGroupWithZero",
... | true |
FirstOrder.Language.orderRel.rec | Mathlib.ModelTheory.Order | [
"instOfNatNat",
"FirstOrder.Language.orderRel.le",
"Nat",
"FirstOrder.Language.orderRel",
"OfNat.ofNat"
] | false |
Lean.Parser.Command.withWeakNamespace._regBuiltin.Lean.Parser.Command.withWeakNamespace.formatter_7 | Lean.Parser.Command | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Unit",
"Lean.Parser.Command.withWeakNamespace.formatter",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
Monoid.PushoutI.NormalWord.empty_toList | Mathlib.GroupTheory.PushoutI | [
"MonoidHom",
"Monoid.toMulOneClass",
"Monoid.PushoutI.NormalWord.empty",
"Group",
"Monoid.CoprodI.Word.toList",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"List",
"MulOneClass.toMulOne",
"Monoid.PushoutI.NormalWord.toWord",
"Eq.refl",
"Eq",
"Monoid.PushoutI.NormalWord.Transversal",
"... | true |
_private.Mathlib.Order.Ideal.0.Order.Ideal.mem_sInf._simp_1_1 | Mathlib.Order.Ideal | [
"SetLike",
"Membership.mem",
"SetLike.coe",
"SetLike.mem_coe",
"propext",
"Eq.symm",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
Mathlib.Tactic.ITauto.Proof.orInL.injEq | Mathlib.Tactic.ITauto | [
"Mathlib.Tactic.ITauto.Proof.orInL",
"Eq.propIntro",
"Mathlib.Tactic.ITauto.Proof",
"Eq.ndrec",
"Eq.refl",
"Mathlib.Tactic.ITauto.Proof.orInL.inj",
"Eq"
] | true |
Plausible.instInhabitedGenError | Plausible.Gen | [
"Inhabited",
"Plausible.instInhabitedGenError.default",
"Inhabited.mk",
"Plausible.GenError"
] | true |
TopologicalSpace.Compacts.map.congr_simp | Mathlib.Topology.Sets.Compacts | [
"Continuous",
"Eq.rec",
"TopologicalSpace",
"TopologicalSpace.Compacts.map",
"Eq.ndrec",
"Eq.refl",
"Eq",
"TopologicalSpace.Compacts"
] | true |
HomotopicalAlgebra.CofibrantObject | Mathlib.AlgebraicTopology.ModelCategory.Bifibrant | [
"HomotopicalAlgebra.cofibrantObjects",
"HomotopicalAlgebra.CategoryWithCofibrations",
"CategoryTheory.ObjectProperty.FullSubcategory",
"CategoryTheory.Limits.HasInitial",
"CategoryTheory.Category"
] | true |
Finset.add_one_le_card_pow | Mathlib.Geometry.Group.Growth.LinearLowerBound | [
"InvOneClass.toOne",
"Subgroup.closure",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Finset",
"Finset.npow",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Nat.brecOn",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Subgroup",
"instOfNa... | true |
Lean.Lsp.SymbolKind.file.sizeOf_spec | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SymbolKind._sizeOf_inst",
"instOfNatNat",
"Lean.Lsp.SymbolKind.file",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Lean.Lsp.SymbolKind",
"Eq"
] | true |
Std.Http.URI.EncodedFragment.ofByteArray? | Std.Internal.Http.Data.URI.Encoding | [
"Std.Http.Internal.Char.isFragmentChar",
"Std.Http.URI.EncodedFragment",
"Std.Http.URI.EncodedString.ofByteArray?",
"ByteArray",
"Option"
] | true |
SimplexCategory.exists_eq_const_of_zero | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"SimplexCategory.eq_const_of_zero",
"instNeZeroNatHAdd_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"Exists",
"Fin.instOfNat",
"instOfNatNat",
"instHAdd",
"OrderHom.instFunLike",
"Fin.instPartialOrder",
"SimplexCategory.const",
"HAdd.hAdd",
"Nat.in... | true |
_private.Mathlib.Util.ElabWithoutMVars.0.elabTermWithoutNewMVars.match_1 | Mathlib.Util.ElabWithoutMVars | [
"Lean.MVarId",
"Lean.Expr",
"Prod.mk",
"List",
"Prod",
"Prod.casesOn"
] | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.