name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
HasCompactMulSupport.list_prod | Mathlib.Topology.Algebra.Support | [
"Monoid",
"MulOne.toOne",
"HasCompactMulSupport.submonoid",
"list_prod_mem",
"Monoid.toMulOneClass",
"HasCompactMulSupport",
"Membership.mem",
"Submonoid.instSubmonoidClass",
"MulOne.toMul",
"Pi.mulOneClass",
"TopologicalSpace",
"List",
"MulOneClass.toMulOne",
"List.instMembership",
"Pi.... | true |
CommRingCat.instCategory._proof_1 | Mathlib.Algebra.Category.Ring.Basic | [
"CommRingCat.carrier",
"CommSemiring.toSemiring",
"CommRingCat",
"id",
"CommRingCat.Hom",
"RingHom.comp",
"CommRing.toCommSemiring",
"_private.Mathlib.Algebra.Category.Ring.Basic.0.CommRingCat.Hom.mk",
"Eq.refl",
"CommRingCat.commRing",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"C... | false |
mul_eq_zero_iff_right | Mathlib.Algebra.GroupWithZero.Defs | [
"False",
"HMul.hMul",
"eq_false",
"MulZeroClass.toMul",
"congrArg",
"MulZeroClass",
"Ne",
"iff_self",
"Iff",
"NoZeroDivisors",
"True",
"of_eq_true",
"Zero.toOfNat0",
"congrFun'",
"or_false",
"Or",
"mul_eq_zero._simp_1",
"OfNat.ofNat",
"Eq",
"Eq.trans",
"MulZeroClass.toZero",
... | true |
WithLp.instProdPseudoMetricSpace | Mathlib.Analysis.Normed.Lp.ProdLp | [
"WithLp",
"UniformSpace",
"instUniformSpaceProd",
"PseudoMetricSpace.toBornology",
"WithLp.prodPseudoMetricAux",
"WithLp.instProdBornology",
"WithLp.instProdPseudoMetricSpace._proof_1",
"Fact",
"inferInstance",
"LE.le",
"PseudoMetricSpace.replaceBornology",
"PseudoMetricSpace",
"PseudoEMetri... | true |
CategoryTheory.Limits.LimitPresentation.changeDiag | Mathlib.CategoryTheory.Limits.Presentation | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Limits.IsLimit.postcomposeHomEquiv",
"CategoryTheory.Limits.LimitPresentation",
"CategoryTheory.Functor.category",
"CategoryTheory.Iso",
"CategoryTheory.Limits.LimitPresentation.mk",
"CategoryTheory.Limits.IsLimit",
"CategoryThe... | true |
Stream'.Seq.cons_not_terminatedAt_zero._simp_1 | Mathlib.Data.Seq.Defs | [
"Stream'.Seq",
"False",
"eq_false",
"Stream'.Seq.TerminatedAt",
"instOfNatNat",
"Stream'.Seq.cons_not_terminatedAt_zero",
"Nat",
"Stream'.Seq.cons",
"OfNat.ofNat",
"Eq"
] | false |
Denumerable | Mathlib.Logic.Denumerable | [
"Denumerable.mk"
] | true |
BitVec.toInt_sshiftRight' | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"Int.instHShiftRightNat",
"congrArg",
"BitVec.toInt_sshiftRight",
"BitVec",
"id",
"Int",
"BitVec.toNat",
"BitVec.sshiftRight'",
"BitVec.sshiftRight",
"HShiftRight.hShiftRight",
"Nat",
"Eq.refl",
"BitVec.sshiftRight_eq'",
"BitVec.toInt",
"Eq"
] | true |
TopologicalSpace.Opens.map_id_obj | Mathlib.Topology.Category.TopCat.Opens | [
"_private.Mathlib.Topology.Category.TopCat.Opens.0.TopologicalSpace.Opens.map_id_obj.match_1_1",
"TopologicalSpace.Opens.instPartialOrder",
"TopCat.instCategory",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"CategoryTheory.CategoryStruct.id",
"Preorder.smallCategory",
"TopCat.str",
"TopCat.... | true |
_private.Mathlib.Tactic.NormNum.Ineq.0.Mathlib.Meta.NormNum.evalLT.core.nnratArm | Mathlib.Tactic.NormNum.Ineq | [
"Qq.QuotedDefEq",
"Pure.pure",
"Mathlib.Meta.monadLiftOptionMetaM",
"ReaderT",
"Lean.Meta.State",
"Lean.Expr.const",
"Rat",
"instMonadLiftT",
"Mathlib.Meta.NormNum.Result.isFalse",
"Lean.Meta.MetaM",
"IO.RealWorld",
"liftM",
"Lean.Expr.sort",
"Lean.Level",
"Applicative.toPure",
"Mathli... | true |
Std.Internal.IO.Async.Signal.sigttou.elim | Std.Internal.Async.Signal | [
"PULift.up",
"Std.Internal.IO.Async.Signal.sigttou",
"Std.Internal.IO.Async.Signal.ctorIdx",
"Nat",
"Std.Internal.IO.Async.Signal",
"Eq.symm",
"Std.Internal.IO.Async.Signal.ctorElim",
"Eq"
] | false |
normSeminorm | Mathlib.Analysis.Seminorm | [
"NormedCommRing.toSeminormedCommRing",
"SeminormedAddGroup.toAddGroup",
"SeminormedAddCommGroup",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"AddZeroClass.t... | true |
_private.Mathlib.Algebra.GroupWithZero.Basic.0.zero_pow.match_1_1 | Mathlib.Algebra.GroupWithZero.Basic | [
"False",
"False.elim",
"Ne",
"instOfNatNat",
"instHAdd",
"absurd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.zero",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"Nat.casesOn"
] | false |
CategoryTheory.ShortComplex.Splitting.map | Mathlib.Algebra.Homology.ShortComplex.Exact | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.Additive",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.Splitting.map._proof_1",
"CategoryTheory.Functor.map",
"CategoryTheory.Preadditive",
"CategoryTheory.ShortComplex.Splitting.r",
"CategoryTheory.S... | true |
Lean.PersistentHashMap.Node.brecOn_3 | Lean.Data.PersistentHashMap | [
"Lean.PersistentHashMap.Node.below_2",
"Lean.PersistentHashMap.Entry",
"Lean.PersistentHashMap.Node",
"Lean.PersistentHashMap.Node.brecOn_3.go",
"Lean.PersistentHashMap.Node.below_3",
"Lean.PersistentHashMap.Node.below_1",
"Array",
"List",
"Lean.PersistentHashMap.Node.below"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.Reproducing.0.RKHS.isSelfAdjoint_finsuppSum | Mathlib.Analysis.InnerProductSpace.Reproducing | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Pi.instStarForall",
"IsSelfAdjoint",
"Semigroup.toMul",
"CompleteSpace",
"NormedRing.toRing",
"ContinuousLinearMap.semiring",
"ContinuousLinearMap.instStarId",
"HMul.hMul",
"star_star",
"Ring.toNonAssocRing",
"Fin... | true |
_private.Init.Data.String.Lemmas.Order.0.String.Pos.le_ofSliceFrom_iff._simp_1_2 | Init.Data.String.Lemmas.Order | [
"String.Pos.sliceFrom",
"String.sliceFrom",
"String",
"Exists",
"LE.le",
"String.instLTPos",
"LT.lt",
"String.instLTPos_1",
"String.Pos.ofSliceFrom",
"String.Pos.ofSliceFrom_lt_iff",
"propext",
"String.Pos",
"String.instLEPos",
"String.Slice.Pos",
"Eq"
] | false |
MeasureTheory.L1.SimpleFunc.setToL1SCLM.congr_simp | Mathlib.MeasureTheory.Integral.SetToL1 | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Real",
"MeasureTheory.Measure",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"MeasureTheory.Lp.simpleFunc.module",
"Real.denselyNormedField",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUnifo... | true |
deriv_const_rpow_id | Mathlib.Analysis.SpecialFunctions.Pow.Deriv | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"Real.instPow",
"Real",
"Semiring.toModule",
"NormedRing.toRing",
"HMul.hMul",
"Real.denselyNormedField",
"Real.instZero",
"congrArg",
"deriv",
"AddGroupWithOne.toAddMonoidWithOne",
"deriv_id'... | true |
Subgroup.prod_eq_bot_iff._simp_2 | Mathlib.Algebra.Group.Subgroup.Basic | [
"Group",
"Subgroup.prod_eq_bot_iff",
"Subgroup",
"Prod.instGroup",
"Bot.bot",
"And",
"Subgroup.prod",
"propext",
"Subgroup.instBot",
"Prod",
"Eq"
] | false |
specializingMap_iff_isClosed_image_closure_singleton | Mathlib.Topology.Inseparable | [
"Iff.mpr",
"Eq.mpr",
"Continuous",
"StableUnderSpecialization",
"congrArg",
"SpecializingMap",
"Set.instSingletonSet",
"id",
"IsClosed",
"TopologicalSpace",
"Iff",
"closure",
"IsClosed.stableUnderSpecialization",
"Iff.intro",
"Iff.mp",
"Set.image",
"specializingMap_iff_closure_single... | true |
Module.Basis.traceDual_traceDual | Mathlib.RingTheory.Trace.Basic | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Finite",
"Algebra",
"Field.toDivisionRing",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"DivisionRing.toRing",
"Field.toSemifield",
"Field.toCommRing",
"Alg... | true |
Lean.Meta.Match.Pattern.val.sizeOf_spec | Lean.Meta.Match.Basic | [
"Lean.Meta.Match.Pattern._sizeOf_inst",
"Lean.Meta.Match.Pattern.val",
"Lean.Expr",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"Lean.Meta.Match.Pattern",
"OfNat.ofNat",
"Eq",
"Lean.Expr._sizeOf_inst"
] | true |
MeasureTheory.MemLp.of_fst_of_snd_prodLp | Mathlib.MeasureTheory.SpecificCodomains.WithLp | [
"Iff.mpr",
"WithLp",
"MeasureTheory.Measure",
"WithLp.instProdTopologicalSpace",
"PseudoMetricSpace.toUniformSpace",
"Fact",
"SeminormedAddGroup.toContinuousENorm",
"WithLp.snd",
"MeasureTheory.MemLp",
"LE.le",
"MeasurableSpace",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"WithLp.fst",
... | true |
Equiv.completeAtomicBooleanAlgebra._proof_7 | Mathlib.Order.CompleteBooleanAlgebra | [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"CompleteAtomicBooleanAlgebra",
"Equiv",
"BooleanAlgebra.toTop",
"Equiv.symm",
"Top.top",
"CompleteBooleanAlgebra.toBooleanAlgebra",
"Eq",
"DFunLike.coe",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
"EquivLike.toFunLike"
] | false |
Delone.DeloneSet.mapIsometry_refl | Mathlib.Analysis.AperiodicOrder.Delone.Basic | [
"Set.ext",
"Delone.DeloneSet.mapIsometry._proof_1",
"Real",
"ENNReal.ofNNReal",
"Function.LeftInverse",
"Preorder.toLT",
"Equiv.instEquivLike",
"Delone.DeloneSet.mapBilipschitz",
"Delone.DeloneSet.mapIsometry._proof_8",
"Delone.DeloneSet.copy",
"IsometryEquiv.instEquivLike",
"Delone.DeloneSet.... | true |
_private.Lean.Server.FileWorker.WidgetRequests.0.Lean.Widget.TaggedTextHighlightState.mk.inj | Lean.Server.FileWorker.WidgetRequests | [
"String",
"_private.Lean.Server.FileWorker.WidgetRequests.0.Lean.Widget.TaggedTextHighlightState",
"_private.Lean.Server.FileWorker.WidgetRequests.0.Lean.Widget.TaggedTextHighlightState.mk",
"String.Pos.Raw",
"Array",
"_private.Lean.Server.FileWorker.WidgetRequests.0.Lean.Widget.TaggedTextHighlightState.m... | true |
Set.inv_mem_center | Mathlib.Algebra.Group.Center | [
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"InvolutiveInv.toInv",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"DivisionMonoid",
"id",
"MulOne.toMul",
"IsMulCentral.comm",
"DivInvMonoid.toM... | true |
QuotientGroup.mulEquivPiModRangePowMonoidHom._proof_1 | Mathlib.GroupTheory.QuotientGroup.Basic | [
"MulOne.toOne",
"MonoidHom.range",
"InvOneClass.toOne",
"CommMonoid.toCommSemigroup",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"QuotientGroup.mk",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"CommMagma.to_isCommutative",
"QuotientGroup.instHasQuotientSubgroup",
... | false |
MeasureTheory.Measure.pi.isOpenPosMeasure | Mathlib.MeasureTheory.Constructions.Pi | [
"ENNReal.instCanonicallyOrderedAdd",
"Eq.mpr",
"MeasureTheory.Measure",
"Preorder.toLT",
"Finset.univ",
"Pi.topologicalSpace",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"Set.univ",
"MeasureTheory.SigmaFinite",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"IsOpen.measure_... | true |
LocallyConstant.indicator_of_notMem | Mathlib.Topology.LocallyConstant.Basic | [
"LocallyConstant.indicator",
"Membership.mem",
"LocallyConstant",
"TopologicalSpace",
"Zero.toOfNat0",
"LocallyConstant.instFunLike",
"Set.indicator_of_notMem",
"IsClopen",
"OfNat.ofNat",
"Eq",
"Set.instMembership",
"DFunLike.coe",
"Not",
"Zero",
"Set"
] | true |
Lean.Grind.instCommRingUSize._proof_5 | Init.GrindInstances.Ring.UInt | [
"Int.cast",
"HMul.hMul",
"congrArg",
"USize.intCast",
"USize.intCast_ofNat",
"Int",
"Nat.cast",
"instMulUSize",
"Nat",
"instNatCastInt",
"Eq",
"USize.natCast",
"USize",
"instHMul"
] | false |
_private.Init.Data.BitVec.Bitblast.0.BitVec.msb_srem._proof_1_1 | Init.Data.BitVec.Bitblast | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"BitVec",
"id",
... | false |
Lean.Compiler.LCNF.specExtension | Lean.Compiler.LCNF.SpecInfo | [
"Inhabited.default",
"Lean.Compiler.LCNF.SpecState",
"Lean.Compiler.LCNF.instInhabitedSpecState",
"Lean.SimplePersistentEnvExtension",
"Lean.SimplePersistentEnvExtension.instInhabited",
"Lean.Compiler.LCNF.SpecEntry"
] | true |
Bipointed.swapEquiv_functor_map_toFun | Mathlib.CategoryTheory.Category.Bipointed | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Bipointed.toProd",
"CategoryTheory.Equivalence.functor",
"Bipointed.X",
"CategoryTheory.Functor.map",
"Bipointed",
"Bipointed.swapEquiv",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Prod.swap",
"Bipointed.mk",
"Eq",
"Bipo... | true |
Batteries.RBNode.foldr.match_1 | Batteries.Data.RBMap.Basic | [
"Batteries.RBNode",
"Batteries.RBNode.casesOn",
"Batteries.RBNode.nil",
"Batteries.RBColor",
"Batteries.RBNode.node"
] | false |
Nat.greatestFib.eq_1 | Mathlib.Data.Nat.Fib.Zeckendorf | [
"instOfNatNat",
"Nat.findGreatest",
"LE.le",
"instLENat",
"Nat.greatestFib",
"instHAdd",
"HAdd.hAdd",
"Nat.fib",
"Nat",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Nat.decLe"
] | true |
_private.Lean.Elab.Structure.0.Lean.Elab.Command.Structure.getFieldDefaultValue? | Lean.Elab.Structure | [
"Pure.pure",
"Lean.instMonadEnvOfMonadLift",
"StateT.instMonadFunctor",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"_private.Lean.Elab.Structure.0.Lean.Elab.Command.Structure.addFieldInheritedDefault.match_1",
"_... | true |
surjOn_Icc_of_monotone_surjective | Mathlib.Order.Interval.Set.SurjOn | [
"Iff.mpr",
"Set.right_mem_Icc",
"Set.Ioo_subset_Icc_self",
"LinearOrder",
"Set.image_mono",
"PartialOrder.toPreorder",
"Monotone",
"surjOn_Ioo_of_monotone_surjective",
"Set.SurjOn",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"PartialOrder",
"DistribLattice.toLattic... | true |
MeasureTheory.JordanDecomposition.zero_posPart | Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan | [
"MeasureTheory.JordanDecomposition.posPart",
"MeasureTheory.Measure",
"MeasureTheory.Measure.instZero",
"MeasurableSpace",
"MeasureTheory.JordanDecomposition.instZero",
"MeasureTheory.JordanDecomposition",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_14 | Mathlib.Data.List.Triplewise | [
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"of_decide_eq_true",
"Lean.Grind.CommRing.Expr.var",
"Std.IsLinearPreorder.toIsPreorder",
"Lean.Grind.Order.le_eq_true_of_le_k",
"Lean.Grind.instIsLinearOrderInt",
"HSub.hSub",
"Nat.ToInt.add_congr",
"IntCas... | false |
MapClusterPt.prodMap | Mathlib.Topology.Constructions | [
"Filter.map_mono",
"SProd.sprod",
"instTopologicalSpaceProd",
"Filter.curry_le_prod",
"Prod.mk",
"Prod.map",
"TopologicalSpace",
"MapClusterPt.mono",
"MapClusterPt.curry_prodMap",
"MapClusterPt",
"Prod",
"Filter.instSProd",
"Filter.curry",
"Filter"
] | true |
Std.Tactic.BVDecide.Normalize.BitVec.zero_ult' | Std.Tactic.BVDecide.Normalize.BitVec | [
"False",
"beq_eq_false_iff_ne._simp_1",
"BEq.rfl",
"Bool.not",
"eq_false",
"instLawfulBEq",
"congrArg",
"true_iff",
"Bool.false_eq_true",
"BitVec",
"Std.Tactic.BVDecide.Normalize.BitVec.zero_lt_iff_zero_neq",
"Eq.mp",
"id",
"Ne",
"instOfNatNat",
"Decidable.not_not._simp_1",
"BitVec.o... | true |
GroupExtension.Splitting.semidirectProductMulEquiv | Mathlib.GroupTheory.GroupExtension.Basic | [
"Monoid.toMulOneClass",
"SemidirectProduct",
"GroupExtension.Equiv.toMulEquiv",
"GroupExtension.Splitting",
"GroupExtension.Splitting.conjAct",
"SemidirectProduct.instMul",
"Group",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"SemidirectProduct.instGroup",
"GroupExtension.Splitting.semidirectProduc... | true |
CompTriple.IsId.rec | Mathlib.Logic.Function.CompTypeclasses | [
"id",
"CompTriple.IsId.mk",
"Eq",
"CompTriple.IsId"
] | false |
_private.Lean.Data.Array.0.Array.mask.match_1 | Lean.Data.Array | [
"Unit.unit",
"Subarray",
"Option.casesOn",
"Option.some",
"Prod.mk",
"Option.none",
"Unit",
"Prod",
"Prod.casesOn",
"Option"
] | false |
Std.Tactic.BVDecide.BVExpr.bitblast.blastShiftLeftConst.go._unary._proof_3 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.ShiftLeft | [
"Std.Sat.AIG.RefVec.get",
"Unit.unit",
"False",
"Mul.mk",
"List.zipWith",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"HMul.hMul",
"Int.natCast_add",
"Nat.ne_of_beq_eq_false",
"of_decide_eq_true",
"le_of_le_of_eq",
"Std.Sat.AIG.RefVec.push",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Co... | false |
neg_add_cancel_comm_assoc | Mathlib.Algebra.Group.Defs | [
"Eq.mpr",
"congrArg",
"add_neg_cancel_right",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"id",
"add_comm",
"instHAdd",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"SubNegMonoid.toNeg",
"AddZero.toAdd",
"E... | true |
Set.countable_setOf_finite_subset | Mathlib.Data.Set.Countable | [
"Set.mem_range_self",
"Subtype.val_injective",
"Function.Injective.injOn",
"Finset",
"setOf",
"Set.Finite",
"Membership.mem",
"Exists",
"Set.Elem",
"Subtype",
"HasSubset.Subset",
"Set.countable_range",
"And.casesOn",
"And",
"Exists.casesOn",
"SetLike.coe",
"Finset.instSetLike",
"Su... | true |
CategoryTheory.Pi.μ_def | Mathlib.CategoryTheory.Pi.Monoidal | [
"CategoryTheory.Pi.instMonoidalForallEval",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pi.monoidalCategory",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Pi.eval",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.pi",
"CategoryTheory.Functor.Monoidal.toLaxMonoid... | true |
IntervalIntegrable.mono_set | Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic | [
"TopologicalSpace.PseudoMetrizableSpace",
"Real",
"MeasureTheory.Measure",
"le_rfl",
"Real.lattice",
"IntervalIntegrable",
"ENormedAddMonoid",
"PartialOrder.toPreorder",
"HasSubset.Subset",
"TopologicalSpace",
"IntervalIntegrable.mono",
"Real.measurableSpace",
"MeasureTheory.Measure.instPart... | true |
Set.restrict_ite_compl | Mathlib.Data.Set.Restrict | [
"Compl.compl",
"Decidable",
"Membership.mem",
"Set.Elem",
"Set.instCompl",
"Set.restrict_dite_compl",
"Set.restrict",
"Eq",
"Set.instMembership",
"Not",
"ite",
"Set"
] | true |
CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution_map | Mathlib.CategoryTheory.Localization.DerivabilityStructure.Constructor | [
"CategoryTheory.StructuredArrow.homMk",
"CategoryTheory.LocalizerMorphism.IsRightDerivabilityStructure.Constructor.fromRightResolution._proof_5",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.LocalizerMorphism.RightResolution",
"CategoryTheory.LocalizerMorphism.RightResoluti... | true |
descPochhammer_eval_eq_descFactorial | Mathlib.RingTheory.Polynomial.Pochhammer | [
"Iff.mpr",
"Nat.cast_comm",
"Eq.mpr",
"Polynomial.eval",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Polynomial.instOne",
"Nat.instMulZeroClass",
"Nat.recAux",
"HMul.hMul",
"Ring.toNonAssocRing",
"mul_sub",
"MulZeroClass.toMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Nat.cast_sub",
... | true |
ONote.NFBelow | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.NFBelow.zero",
"ONote",
"ONote.NFBelow.oadd'",
"Ordinal"
] | true |
Units.instDecidableEq | Mathlib.Algebra.Group.Units.Defs | [
"Monoid",
"Units.val",
"Units.ext_iff",
"Units",
"decidable_of_iff'",
"Eq",
"DecidableEq"
] | true |
_private.Mathlib.Analysis.Complex.Convex.0.Complex.instPathConnectedSpaceUnits._simp_3 | Mathlib.Analysis.Complex.Convex | [
"And",
"not_and_or",
"propext",
"Or",
"Eq",
"Not"
] | false |
OneHomClass | Mathlib.Algebra.Group.Hom.Defs | [
"One",
"outParam",
"OneHomClass.mk",
"FunLike"
] | true |
Std.Do.«term_∧ₚ_» | Std.Do.PostCond | [
"Lean.Name.mkStr3",
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
R0Space.closure_singleton | Mathlib.Topology.Separation.Basic | [
"Set.ext",
"Specializes",
"congrArg",
"setOf",
"Membership.mem",
"nhds",
"ker_nhds_eq_specializes",
"Set.instSingletonSet",
"_private.Mathlib.Topology.Separation.Basic.0.R0Space.closure_singleton._simp_1_2",
"iff_self",
"TopologicalSpace",
"funext",
"Iff",
"closure",
"_private.Mathlib.To... | true |
Fin.val_natCast | Mathlib.Data.Fin.Basic | [
"Zero.ofOfNat0",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"Fin.val",
"Nat.cast",
"HMod.hMod",
"Nat",
"Fin.NatCast.instNatCast",
"NeZero",
"Fin",
"Eq",
"rfl"
] | true |
OneHom.coe_id | Mathlib.Algebra.Group.Hom.Defs | [
"One",
"id",
"OneHom.funLike",
"OneHom",
"OneHom.id",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
Std.DHashMap.Const.getKey!_unitOfList_of_contains_eq_false | Std.Data.DHashMap.Lemmas | [
"Inhabited.default",
"Std.DHashMap.getKey!",
"Std.DHashMap.Const.unitOfList",
"List.contains",
"LawfulHashable",
"List",
"Unit",
"EquivBEq",
"Bool",
"Inhabited",
"Hashable",
"Std.DHashMap.Internal.Raw₀.Const.getKey!_insertManyIfNewUnit_emptyWithCapacity_list_of_contains_eq_false",
"Bool.fals... | true |
Finset.SupIndep.le_sup_iff | Mathlib.Order.SupIndep | [
"Lattice",
"Lattice.toSemilatticeSup",
"Finset",
"OrderBot.toBot",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"OrderBot",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"HasSubset.Subset",
"Ne",
"Bot.bot",
"LE.le",
"Iff",
"Finset.instSetL... | true |
_private.Mathlib.Dynamics.TopologicalEntropy.CoverEntropy.0.Dynamics.nonempty_inter_of_coverMincard._simp_1_1 | Mathlib.Dynamics.TopologicalEntropy.CoverEntropy | [
"Membership.mem",
"SDiff.sdiff",
"And",
"Set.mem_diff",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.instSDiff",
"Set"
] | false |
_private.Mathlib.MeasureTheory.Integral.Bochner.L1.0.MeasureTheory.SimpleFunc.integral_mono_measure._simp_1_1 | Mathlib.MeasureTheory.Integral.Bochner.L1 | [
"MeasureTheory.SimpleFunc.forall_mem_range",
"Finset",
"MeasureTheory.SimpleFunc",
"Membership.mem",
"MeasureTheory.SimpleFunc.instFunLike",
"MeasurableSpace",
"Finset.instSetLike",
"propext",
"MeasureTheory.SimpleFunc.range",
"Eq",
"DFunLike.coe",
"SetLike.instMembership"
] | false |
_private.Mathlib.RingTheory.PowerSeries.Derivative.0.PowerSeries.derivativeFun_coe_mul_coe | Mathlib.RingTheory.PowerSeries.Derivative | [
"Polynomial.derivative",
"Eq.mpr",
"Polynomial.derivative_mul",
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"MvPowerSeries.instMul",
"id",
"Distrib.toAdd",
"CommMagma.toMul",
"NonUnitalCommSemirin... | true |
TensorProduct.LieModule.map._proof_1 | Mathlib.Algebra.Lie.TensorProduct | [
"CommRing",
"TensorProduct.LieModule.lieRingModule",
"SemilinearMapClass.distribMulActionSemiHomClass",
"LieModuleHom",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"Bracket.bracket",
"LinearMap.instFunLike",
... | false |
_private.Init.Data.String.Lemmas.Pattern.String.ForwardSearcher.0.String.Slice.Pattern.Model.ForwardSliceSearcher.PartialMatch.isValidForSlice | Init.Data.String.Lemmas.Pattern.String.ForwardSearcher | [
"String.Slice.Pattern.Model.ForwardSliceSearcher.matchesAt_iff_isLongestMatchAt",
"Eq.mpr",
"String.Slice.pos",
"String.Pos.Raw.unoffsetBy",
"congrArg",
"String.Slice.utf8ByteSize_copy",
"String.Slice.Pos.offset",
"_private.Init.Data.String.Lemmas.Pattern.String.ForwardSearcher.0.String.Slice.Pattern.... | true |
FreeGroup.mulEquivIntOfUnique._proof_2 | Mathlib.GroupTheory.FreeGroup.Basic | [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
"Unique",
"Function.comp",
"Equiv",
"Int",
"FreeGroup.equivIntOfUnique",
"Multiplicative",
"True",
"eq_self",
"of_eq_true",
"Multiplicative.toAdd",
"congrFun'",
"Multiplicative.ofAdd",
"Equiv.symm",
"Eq",
"DFunLike.coe",
... | false |
ZeroHom.mk.noConfusion | Mathlib.Algebra.Group.Hom.Defs | [
"HEq.refl",
"id",
"ZeroHom.mk",
"ZeroHom",
"heq_of_eq",
"ZeroHom.noConfusion",
"Zero.toOfNat0",
"Eq.refl",
"HEq",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
_private.Init.Data.SInt.Lemmas.0.Int8.le_iff_lt_or_eq._simp_1_3 | Init.Data.SInt.Lemmas | [
"Int8",
"Int8.lt_iff_toInt_lt",
"Int8.toInt",
"Int",
"Int.instLTInt",
"LT.lt",
"propext",
"instLTInt8",
"Eq"
] | false |
_private.Batteries.Data.UnionFind.Basic.0.Batteries.UnionFind.findAux.match_1.splitter | Batteries.Data.UnionFind.Basic | [
"Batteries.UnionFind.FindAux.mk",
"Batteries.UFNode",
"Array",
"Nat",
"Batteries.UnionFind.findAux.match_1",
"Batteries.UnionFind",
"Fin",
"Batteries.UnionFind.FindAux",
"Eq",
"Array.size",
"Batteries.UnionFind.size"
] | true |
CategoryTheory.WithInitial.equivComma._proof_12 | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.WithInitial.equivComma._proof_2",
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.WithInitial.mkCommaMorphism",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"... | false |
RatFunc.wrapped._@.Mathlib.FieldTheory.RatFunc.Basic.870781102._hygCtx._hyg.2 | Mathlib.FieldTheory.RatFunc.Basic | [
"CommRing",
"RatFunc.definition._@.Mathlib.FieldTheory.RatFunc.Basic.870781102._hygCtx._hyg.2",
"Subtype",
"Subtype.mk",
"RatFunc",
"Eq",
"_private.Mathlib.FieldTheory.RatFunc.Basic.0.RatFunc.wrapped._proof_1._@.Mathlib.FieldTheory.RatFunc.Basic.870781102._hygCtx._hyg.2"
] | false |
Aesop.RuleBuilderOptions.indexingMode? | Aesop.Builder.Basic | [
"Aesop.IndexingMode",
"Aesop.RuleBuilderOptions",
"Option"
] | true |
Units.inv_mul_of_eq | Mathlib.Algebra.Group.Units.Defs | [
"Monoid",
"Units.val",
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Units.inv_mul",
"Units",
"id",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Inv.inv",
"One.toOfNat1",
"Eq.refl",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Units.instInv",
"instHMul"
] | true |
Nonneg.mk_smul | Mathlib.Algebra.Order.Nonneg.Module | [
"instHSMul",
"SMul",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Subtype",
"LE.le",
"Subtype.mk",
"Semiring",
"Zero.toOfNat0",
"HSMul.hSMul",
"OfNat.ofNat",
"Eq",
"rfl",
"MulZeroClass.toZero",
"Nonneg.instSMul",
"instMulZeroClassOfSemiring"
] | true |
Set.preimage_singleton_eq_empty | Mathlib.Data.Set.Image | [
"Set.preimage_singleton_nonempty",
"Set.not_nonempty_iff_eq_empty",
"Membership.mem",
"Set.instSingletonSet",
"Iff.not",
"Iff",
"Set.Nonempty",
"Set.preimage",
"Set.instEmptyCollection",
"Iff.trans",
"Set.range",
"EmptyCollection.emptyCollection",
"Singleton.singleton",
"Eq",
"Set.instMe... | true |
Set.isSimpleOrder_Iic_iff_isAtom | Mathlib.Order.Atoms | [
"Iff.mpr",
"le_refl",
"isSimpleOrder_iff_isAtom_top",
"Preorder.toLT",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"IsSimpleOrder",
"le_of_lt",
"Subtype.mk_lt_mk",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"PartialOrder",
"Set.Elem",
"Subtype",
"Ne",
"Bot.bot",
"Subtype.mk",
... | true |
CategoryTheory.MonoidalCategory.fullSubcategory._proof_11 | Mathlib.CategoryTheory.Monoidal.Category | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ObjectProperty.ι",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.ObjectProperty.F... | false |
_private.Mathlib.RingTheory.MvPowerSeries.Rename.0.MvPowerSeries.killCompl_X._simp_1_1 | Mathlib.RingTheory.MvPowerSeries.Rename | [
"Finsupp.embDomain_single",
"Function.Embedding",
"Finsupp.embDomain",
"Function.instFunLikeEmbedding",
"Eq.symm",
"Eq",
"DFunLike.coe",
"Finsupp",
"Finsupp.single",
"Zero"
] | false |
Lean.Elab.Tactic.Conv.PatternMatchState.rec | Lean.Elab.Tactic.Conv.Pattern | [
"Lean.MVarId",
"Array",
"List",
"Lean.Elab.Tactic.Conv.PatternMatchState.occs",
"Nat",
"Lean.Elab.Tactic.Conv.PatternMatchState",
"Lean.Elab.Tactic.Conv.PatternMatchState.all",
"Prod"
] | false |
OrderMonoidHom.inrₗ | Mathlib.Algebra.Order.Monoid.Lex | [
"Monoid",
"OrderMonoidHom.inr",
"MulOne.toOne",
"OrderMonoidHom",
"Monoid.toMulOneClass",
"Lex",
"OneHom.mk",
"OrderMonoidHom.mk",
"PartialOrder.toPreorder",
"OrderHom.toFun",
"Prod.instMulOneClass",
"PartialOrder",
"OrderHom.comp",
"OrderMonoidHom.inrₗ._proof_3",
"MonoidHom.mk",
"Orde... | true |
selfAdjoint.instField._proof_12 | Mathlib.Algebra.Star.SelfAdjoint | [
"Int.cast",
"selfAdjoint.instIntCastSubtypeMemAddSubgroup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"AddGroupWithOne.toAddGroup",
"Membership.mem",
"Field.toDivisionRing",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"DivisionRing.toRing"... | false |
WithBot.map_zero | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"WithBot.some",
"WithBot",
"WithBot.zero",
"Zero.toOfNat0",
"OfNat.ofNat",
"WithBot.map",
"Eq",
"rfl",
"Zero"
] | true |
ZeroHom.instModule._proof_1 | Mathlib.Algebra.Module.Hom | [
"instHSMul",
"AddMonoid.toAddZeroClass",
"Module.toMulActionWithZero",
"AddZeroClass.toAddZero",
"MulActionWithZero.smul_zero",
"ZeroHom",
"AddCommMonoid",
"AddZero.toZero",
"AddMonoid",
"Monoid.toSemigroup",
"Semiring",
"MulActionWithZero.toMulAction",
"Zero.toOfNat0",
"HSMul.hSMul",
"S... | false |
_private.Init.Data.Range.Polymorphic.IntLemmas.0.Int.map_add_toList_rcc._proof_1_1 | Init.Data.Range.Polymorphic.IntLemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Int.lt_or_gt_of_ne",
"id",
"instDecidableEqBool",
"I... | false |
ConvexOn.lt_left_of_right_lt' | Mathlib.Analysis.Convex.Function | [
"not_le",
"NonAssocSemiring.toAddCommMonoidWithOne",
"add_lt_add_of_le_of_lt",
"instHSMul",
"Trans.trans",
"Preorder.toLT",
"PosSMulStrictMono.toPosSMulMono",
"lt_irrefl",
"DistribMulAction.toDistribSMul",
"instIsLeftCancelAddOfAddLeftReflectLE",
"LinearOrder",
"covariant_swap_add_of_covariant... | true |
MonoidAlgebra.mapAlgHom_apply | Mathlib.Algebra.MonoidAlgebra.Basic | [
"MonoidAlgebra.semiring",
"Finsupp.instFunLike",
"Monoid",
"AlgHom",
"AlgHom.funLike",
"MonoidAlgebra.mapRingHom_apply",
"Algebra",
"MonoidAlgebra.mapAlgHom",
"CommSemiring",
"MonoidAlgebra.algebra",
"AlgHom.toRingHom",
"MonoidAlgebra",
"Semiring",
"Eq",
"DFunLike.coe",
"Finsupp",
"M... | true |
Except.ctorIdx | Init.Prelude | [
"Nat",
"Except.casesOn",
"Except"
] | false |
_private.Mathlib.Algebra.Divisibility.Prod.0.pi_dvd_iff._simp_1_2 | Mathlib.Algebra.Divisibility.Prod | [
"funext_iff",
"propext",
"Eq"
] | false |
AlgebraicGeometry.Scheme.basicOpen_le | Mathlib.AlgebraicGeometry.Scheme | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"TopologicalSpace.Opens.instPartialOrder",
"CommRingCat",
"PartialOrder.toPreorder",
"AlgebraicGeometry.LocallyRingedSpace.... | true |
CategoryTheory.Precoverage.mem_coverings_of_isIso | Mathlib.CategoryTheory.Sites.Precoverage | [
"CategoryTheory.IsIso",
"CategoryTheory.Precoverage",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"Membership.mem",
"CategoryTheory.Precoverage.HasIsos",
"CategoryTheory.Precoverage.HasIsos.mem_coverings_of_isIso",
"CategoryTheory.Presieve.singleton",
"Catego... | true |
Primrec.PrimrecBounded | Mathlib.Computability.Primrec.Basic | [
"Primcodable.ofDenumerable",
"Exists",
"LE.le",
"instLENat",
"Primrec",
"And",
"Nat",
"Primcodable.toEncodable",
"Primcodable",
"Denumerable.nat",
"Encodable.encode"
] | true |
Order.Ideal.toLowerSet_injective | Mathlib.Order.Ideal | [
"Order.Ideal.casesOn",
"DirectedOn",
"Eq.rec",
"LE.le",
"LE",
"LowerSet.carrier",
"Set.Nonempty",
"Eq.ndrec",
"Eq.refl",
"Order.Ideal.toLowerSet",
"Function.Injective",
"LowerSet",
"Eq.symm",
"Order.Ideal.mk",
"Order.Ideal",
"Eq"
] | true |
SimpleGraph.cliqueFinset_eq_empty_iff | Mathlib.Combinatorics.SimpleGraph.Clique | [
"Eq.mpr",
"SimpleGraph.IsNClique",
"congrArg",
"Finset",
"SimpleGraph.Adj",
"DecidableRel",
"Membership.mem",
"id",
"Finset.instEmptyCollection",
"SimpleGraph",
"iff_self",
"Iff",
"SimpleGraph.mem_cliqueFinset_iff._simp_1",
"Fintype",
"Finset.instSetLike",
"SimpleGraph.CliqueFree",
"... | true |
LieAlgebra.IsExtension.range_eq_top | Mathlib.Algebra.Lie.Extension | [
"LieHom",
"CommRing",
"LieHom.range",
"LieSubalgebra.instTop",
"LieRing",
"LieAlgebra.IsExtension",
"LieSubalgebra",
"LieAlgebra",
"Top.top",
"Eq"
] | true |
CategoryTheory.OverPresheafAux.restrictedYoneda._proof_3 | Mathlib.CategoryTheory.Comma.Presheaf.Basic | [
"CategoryTheory.Over",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.instCategoryOver",
"CategoryTheory.Over.left",
"CategoryTheory.Over.Hom.w",
"CategoryTheory.type... | false |
Finset.Colex.toColex_sdiff_lt_toColex_sdiff' | Mathlib.Combinatorics.Colex | [
"Preorder.toLT",
"Equiv.instEquivLike",
"Finset.inter_subset_right",
"Colex",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Finset.Colex.toColex_sdiff_lt_toColex_sdiff",
"Finset.instSDiff",
"PartialOrder",
"Eq.mp",
"Equiv",
"Finset.Colex.instPartialOrder",
"Inter.inter",
"SDiff.sdiff... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.