name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Fin.instCommRing._proof_11 | Mathlib.Data.ZMod.Defs | [
"Nat.instMulZeroClass",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocRing.toMul",
"Fin.instNonUnitalCommRing",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"instHAdd",
"AddSemigroup.toAdd",
"AddGroup.toSubNegMonoid",
... | false |
_private.Mathlib.Topology.Order.LiminfLimsup.0.tendsto_iSup_of_tendsto_limsup._simp_1_2 | Mathlib.Topology.Order.LiminfLimsup | [
"Filter.Eventually",
"Preorder.toLE",
"Exists",
"GE.ge",
"Filter.atTop",
"IsDirectedOrder",
"propext",
"Nonempty",
"Filter.eventually_atTop",
"Eq",
"Preorder"
] | false |
CategoryTheory.Functor.LaxBraided.ofNatIso | Mathlib.CategoryTheory.Monoidal.Braided.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.LaxBraided.mk",
"CategoryTheory.Iso",
"CategoryTheory.Functor.LaxBraided.toLaxMonoidal",
"CategoryTheory.BraidedCategory",
"CategoryTheory.Functor.LaxBraided",
"CategoryTheory.Func... | true |
FormalMultilinearSeries.compContinuousLinearMap | Mathlib.Analysis.Calculus.FormalMultilinearSeries | [
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"ContinuousConstSMul",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"AddZero.toZero",
"Nat",
"Semiring.toMonoid",
"Semiring",
"Mo... | true |
RingCat.instCreatesLimitSemiRingCatForget₂RingHomCarrierCarrier | Mathlib.Algebra.Category.Ring.Limits | [
"RingCat.limitRing",
"CategoryTheory.Limits.IsLimit.ofFaithful",
"RingCat.ofHom",
"CategoryTheory.Limits.Cone.π",
"SemiRingCat.instConcreteCategoryRingHomCarrier",
"RingCat.of",
"MulOne.toOne",
"CategoryTheory.Functor",
"RingCat.instCreatesLimitSemiRingCatForget₂RingHomCarrierCarrier._proof_16",
"... | true |
_private.Mathlib.Analysis.SpecialFunctions.Gamma.Beta.0.Complex.betaIntegral_symm._simp_1_2 | Mathlib.Analysis.SpecialFunctions.Gamma.Beta | [
"NegZeroClass.toNeg",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"intervalIntegral",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"intervalIntegral.integral_symm",
"SubtractionCommMonoid.toSubtractionMonoid",
"Real.measurableSpace",
"NormedAddCommGroup.toAddCom... | false |
CStarAlgebra.mk | Mathlib.Analysis.CStarAlgebra.Classes | [
"Semigroup.toMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"NormedRing.toRing",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"SeminormedRing.toRing",
"Algebra.toSMul",
"NormedField.toField",
"Semiring.zero_mul",
"NormedRing.toNonUnitalNormedRing",
"S... | true |
Nat.instConditionallyCompleteLinearOrderBot | Mathlib.Data.Nat.Lattice | [
"LinearOrder.toOrd",
"Lattice",
"Lattice.toSemilatticeSup",
"ConditionallyCompleteLinearOrder.mk",
"LinearOrder.toDecidableEq",
"LinearOrder",
"ConditionallyCompleteLinearOrderBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Nat.instConditionallyCompleteLinearOrderBot._proof_5",
... | true |
Lean.TSyntax.instCoeNumLitPrec | Init.Meta.Defs | [
"Lean.TSyntax.mk",
"Coe.mk",
"Lean.TSyntax.raw",
"Lean.Syntax.NumLit",
"List.cons",
"Lean.numLitKind",
"Lean.SyntaxNodeKind",
"Lean.Name.mkStr1",
"Coe",
"Lean.Syntax.Prec",
"List.nil"
] | true |
Pi.measurableMul | Mathlib.MeasureTheory.Group.Arithmetic | [
"Iff.mpr",
"HMul.hMul",
"measurable_pi_iff",
"Measurable",
"Mul",
"measurable_pi_apply",
"MeasurableMul",
"MeasurableMul.mk",
"MeasurableSpace",
"MeasurableSpace.pi",
"Pi.instMul",
"Measurable.const_mul",
"Measurable.mul_const",
"instHMul"
] | true |
FP.Float.nan | Mathlib.Data.FP.Basic | [
"FP.Float.nan",
"FP.FloatCfg",
"FP.Float"
] | true |
_private.Mathlib.Tactic.LinearCombination.0.Mathlib.Tactic.LinearCombination.elabLinearCombination.match_3 | Mathlib.Tactic.LinearCombination | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.Syntax.Term",
"Option.none",
"Unit",
"Option"
] | false |
Array.any_eq_true' | Init.Data.Array.Lemmas | [
"List.any_eq_true._simp_1",
"congrArg",
"Array.instMembership",
"Membership.mem",
"Exists",
"Array.casesOn",
"List.mem_toArray._simp_1",
"Array.any",
"instOfNatNat",
"List.toArray",
"Array",
"iff_self",
"List.any_toArray'",
"Bool.true",
"funext",
"List",
"And",
"Iff",
"List.size_... | true |
ContinuousLinearMap.isInvertible_comp_equiv._simp_1 | Mathlib.Topology.Algebra.Module.Equiv | [
"ContinuousLinearMap.comp",
"ContinuousLinearMap.isInvertible_comp_equiv",
"ContinuousLinearMap.IsInvertible",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"ContinuousLinearEquiv",
"RingHomInvPair.ids",
"propext",
"Semiring",
"Module",
"RingHom.id",
"RingHomCompTriple.ids",
... | false |
Aesop.Frontend.Feature.ctorElim | Aesop.Frontend.RuleExpr | [
"Aesop.Frontend.Feature.priority",
"Aesop.Frontend.Feature.ctorIdx",
"Aesop.Frontend.Feature.ruleSets",
"Lean.Syntax.Term",
"Aesop.Frontend.DBuilderName",
"Aesop.Frontend.Feature.casesOn",
"Aesop.Frontend.Feature.builderOption",
"Aesop.PhaseName",
"Aesop.Frontend.Feature.builder",
"Aesop.Frontend.... | false |
UInt32.reduceAdd._regBuiltin.UInt32.reduceAdd.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt.2998934274._hygCtx._hyg.35 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | [
"IO",
"Bool.true",
"Unit",
"Lean.Meta.Simp.addSEvalprocBuiltinAttr",
"Sum.inr",
"Lean.Meta.Simp.DSimproc",
"UInt32.reduceAdd",
"Lean.Name.mkStr2",
"Lean.Meta.Simp.Simproc"
] | false |
Set.prod_pow | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Set.instSProd",
"Monoid",
"MulOne.toOne",
"Monoid.toMulOneClass",
"SProd.sprod",
"Prod.instMul",
"Nat.brecOn",
"MulOne.toMul",
"Set.monoid",
"Monoid.toPow",
"Set.prod_pow._f",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat",
"Set.NPow",
"instHPow",
"Prod",
"Eq",
"Prod.instOne",
"Se... | true |
_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal.match_1 | Mathlib.Data.ENNReal.Real | [
"Lean.Level.ctorIdx",
"Mathlib.Meta.Positivity.Strictness",
"_private.Mathlib.Data.ENNReal.Real.0.Mathlib.Meta.Positivity.evalENNRealOfReal._sparseCasesOn_1",
"Lean.Expr.const",
"Lean.Meta.MetaM",
"Nat.hasNotBit",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Level.zero",
"Le... | false |
Set.Finite.encard_lt_card | Mathlib.Data.Set.Card | [
"Iff.mpr",
"Set.encard",
"Set.univ",
"HasSSubset.SSubset",
"Set.instHasSSubset",
"Set.Finite",
"Eq.rec",
"Set.Finite.encard_lt_encard",
"Set.encard_univ",
"Ne",
"ENat",
"LT.lt",
"instLTENat",
"Set.ssubset_univ_iff",
"ENat.card",
"Eq",
"Set"
] | true |
CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse_obj_mon_mul_app | Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory | [
"CategoryTheory.CommMon.instCategory",
"CategoryTheory.Monoidal.monFunctorCategoryEquivalence",
"CategoryTheory.Functor",
"CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Func... | true |
_private.Mathlib.AlgebraicTopology.DoldKan.Degeneracies.0.AlgebraicTopology.DoldKan.DegeneraciesVanish.comp._simp_1_1 | Mathlib.AlgebraicTopology.DoldKan.Degeneracies | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"instOfNatNat",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTheory.Preadditive",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"AlgebraicTopology.DoldKan.DegeneraciesVanish",
"propext",
"... | false |
AddSubmonoid.fromLeftNeg_leftNegEquiv_symm | Mathlib.GroupTheory.Submonoid.Inverses | [
"Equiv.right_inv",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"IsAddUnit.addSubmonoid",
"Preorder.toLE",
"Membership.mem",
"Subtype",
"AddSubmonoid.add",
"AddSubmonoid",
"LE.le",
"AddCommMonoid",
"AddSubmonoid.leftNegEquiv",
"AddEquiv",
"AddCommMonoid.toAddMonoid",
"AddEquiv.... | true |
AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks | Mathlib.AlgebraicGeometry.Sites.MorphismProperty | [
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"CategoryTheory.Precoverage.HasPullbacks",
"AlgebraicGeometry.Scheme.jointlySurjectivePrecoverage",
"Membership.mem",
"CategoryTheory.MorphismProperty.pre... | true |
Lean.Elab.Tactic.MkSimpContextResult.rec | Lean.Elab.Tactic.Simp | [
"Lean.Elab.Tactic.MkSimpContextResult",
"Lean.Syntax",
"Array",
"Lean.Elab.Tactic.ElabSimpArgResult",
"Lean.Meta.Simp.SimprocsArray",
"Lean.Meta.Simp.Context",
"Lean.Elab.Tactic.Simp.DischargeWrapper",
"Lean.Elab.Tactic.MkSimpContextResult.mk",
"Prod"
] | false |
_private.Batteries.Data.List.Lemmas.0.List.getElem_idxsOf_lt._proof_1_8 | Batteries.Data.List.Lemmas | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"GetElem.getElem",
"List.getElem_filter_eq_getElem_getElem_findIdxs._proof_5",
"List.findIdxs",
"List",
"BEq.beq",
"Nat",
"List.filter",
"LT.lt",
"Eq.substr",
"instLTNat",
"_private.Batteries.Data.List.Lemmas.0.List.getElem_id... | false |
_private.Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset.0.Finset.inv_op_smul_finset_distrib₀._simp_1_3 | Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset | [
"GroupWithZero.toMonoidWithZero",
"instHSMul",
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Finset",
"GroupWithZero",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Finset.smulFinset",
"Ne",
"Inv.inv",
"MonoidWithZero.toMulZeroOneClass",
"Finset.instSetLike",
... | false |
CategoryTheory.Limits.Sigma.whiskerEquiv_hom | Mathlib.CategoryTheory.Limits.Shapes.Products | [
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Equiv",
"CategoryTheory.Iso",
"CategoryTheory.Limits.HasCoproduct",
"Eq.refl",
"CategoryTheory.Limits.Sigma.map'",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.sigmaObj",
"CategoryTheory.Iso.hom... | true |
Lean.Meta.Grind.Arith.Cutsat.EqCnstr._sizeOf_15 | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr._sizeOf_inst",
"Lean.Grind.CommRing.Poly._sizeOf_inst",
"Option._sizeOf_inst",
"Lean.Meta.Grind.Arith.Cutsat.CooperSplit",
"Lean.FVarId._sizeOf_inst",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstr",
"Lean.Expr",
"Lean.FVarId",
"instOfNatNat",
"Int... | false |
LinearMap.mulLeft._proof_2 | Mathlib.Algebra.Module.LinearMap.Defs | [
"instHSMul",
"instSMulOfMul",
"HMul.hMul",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",
"Distrib.toMul",
"Semiring.toMonoid",
"Semiring",
"NonUnitalNonAsso... | false |
Std.Iter.toList_zip_of_finite_left | Std.Data.Iterators.Lemmas.Combinators.Zip | [
"Pure.pure",
"Eq.mpr",
"_private.Std.Data.Iterators.Lemmas.Combinators.Zip.0.Std.Iter.toList_zip_of_finite_left._simp_1_1",
"_private.Std.Data.Iterators.Lemmas.Combinators.Zip.0.Std.Iter.toList_zip_of_finite_left._simp_1_3",
"Std.Iterators.Types.Take.instIterator",
"False",
"instAlternativeOption",
"S... | true |
IsTopologicalGroup.mulInvClosureNhd.casesOn | Mathlib.Topology.Algebra.OpenSubgroup | [
"IsTopologicalGroup.mulInvClosureNhd.rec",
"Filter.instMembership",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"nhds",
"MulOne.toMul",
"DivInvMonoid.toMono... | false |
SSet.Truncated.instMonoidalTruncation._aux_3 | Mathlib.AlgebraicTopology.SimplicialSet.Monoidal | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Functor.CoreMonoidal.μIso",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.Monoidal.whiskeringLeft._... | false |
Ordnode.insert'._unsafe_rec | Mathlib.Data.Ordmap.Ordnode | [
"Ordnode",
"Ordering",
"Ordnode.mem.match_1",
"cmpLE",
"Ordnode.node",
"LE",
"DecidableLE",
"Unit",
"Ordnode.singleton",
"Ordnode.balanceL",
"Nat",
"Ordnode.insert'._unsafe_rec",
"Ordnode.balanceR",
"Eq",
"Ordnode.adjustWith.match_1"
] | false |
CategoryTheory.Adjunction.right_triangle_components_assoc | Mathlib.CategoryTheory.Adjunction.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"Eq.mp",
"id",
"Mathlib.Tactic.Reasso... | true |
RingHom.FiniteType.of_surjective | Mathlib.RingTheory.FiniteType | [
"Eq.mpr",
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"RingHom.FiniteType",
"RingHom",
"id",
"RingHom.FiniteType.comp_surjective",
"RingHom.comp",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"RingHom.comp_id",
"Eq.symm",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
... | true |
_private.Lean.Meta.MkIffOfInductiveProp.0.Lean.Meta.Shape.casesOn | Lean.Meta.MkIffOfInductiveProp | [
"List",
"Nat",
"_private.Lean.Meta.MkIffOfInductiveProp.0.Lean.Meta.Shape.mk",
"Bool",
"_private.Lean.Meta.MkIffOfInductiveProp.0.Lean.Meta.Shape",
"Option",
"_private.Lean.Meta.MkIffOfInductiveProp.0.Lean.Meta.Shape.rec"
] | false |
Ring.DirectLimit.congr._proof_6 | Mathlib.Algebra.Colimit.Ring | [
"CommRing",
"CommSemiring.toSemiring",
"RingEquiv.instEquivLike",
"DFunLike.ext",
"RingEquiv.instRingEquivClass",
"Preorder.toLE",
"RingHom",
"Ring.DirectLimit.congr._proof_5",
"Distrib.toAdd",
"Ring.DirectLimit.congr._proof_1",
"LE.le",
"instDistribOfSemiring",
"RingHom.comp",
"CommRing.t... | false |
CategoryTheory.MorphismProperty.Under.mapPushoutAdj._proof_7 | Mathlib.CategoryTheory.MorphismProperty.OverAdjunction | [
"CategoryTheory.MorphismProperty.Under",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Comma.right",
"CategoryTheory.MorphismProperty.Over.map._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismP... | false |
RingQuot.ringQuotToIdealQuotient | Mathlib.Algebra.RingQuot | [
"CommRing",
"Equiv.instEquivLike",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"RingQuot.ringQuotToIdealQuotient._proof_2",
"RingHom",
"RingQuot.ringQuotToIdealQuotient._proof_1",
"RingQuot.instSemiring",
"Equiv",
"Subtype",
"RingQuot",
"Ideal.ofRel",
"Ideal",
"Subtype.mk",
"HasQuoti... | true |
Std.Format.noConfusion | Init.Data.Format.Basic | [
"String",
"Int",
"Std.Format.noConfusionType",
"Nat",
"Std.Format.casesOn",
"Std.Format",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Std.Format.FlattenBehavior",
"optParam",
"Eq",
"Std.Format.FlattenBehavior.allOrNone"
] | false |
Rat.cast_lt_natCast._simp_1 | Mathlib.Data.Rat.Cast.Order | [
"Preorder.toLT",
"DivisionRing.toRatCast",
"LinearOrder",
"Rat",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"IsStrictOrderedRing",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"Rat.cast_lt_natCast",
"DistribLattice.toLattice",
"Rat.cast",
"AddMonoidWithOne.t... | false |
List.maximum_of_length_pos_mem | Mathlib.Data.List.MinMax | [
"List.maximum",
"WithBot.some",
"WithBot",
"List.coe_maximum_of_length_pos",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"instOfNatNat",
"List",
"List.instMembership",
"LinearOrder.toDecidableLT",
"N... | true |
Lean.Json.below | Lean.Data.Json.Basic | [
"Lean.Json",
"Lean.Json.rec",
"String",
"Lean.JsonNumber",
"Ord.compare",
"Array",
"Std.TreeMap.Raw",
"List",
"PProd",
"PUnit",
"Nat",
"Bool",
"String.instOrd",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Raw"
] | false |
Num.commSemiring._proof_5 | Mathlib.Data.Num.Lemmas | [
"Eq.mpr",
"MulOne.toOne",
"Nat.instMulZeroClass",
"HMul.hMul",
"Nat.instOne",
"congrArg",
"Nat.instMulOneClass",
"id",
"MulOne.toMul",
"instMulNat",
"instOneNum",
"castNum",
"AddMonoidWithOne.toOne",
"Num",
"MulOneClass.toMulOne",
"Num.cast_one",
"Nat",
"propext",
"Num.instMul",
... | false |
CategoryTheory.AddMon.uniqueHomToTrivial | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"CategoryTheory.SemiCartesianMonoidalCategory",
"CategoryTheory.AddMon.uniqueHomToTrivial._proof_3",
"Unique.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Unique",
"CategoryTheory.AddMon.instCategory",
"CategoryTheory.AddMon.Hom.mk",
"CategoryTheory.SemiCartesianMonoidalCategory.toMo... | true |
NonUnitalSubalgebra.center.instNonUnitalCommRing._proof_13 | Mathlib.Algebra.Algebra.NonUnitalSubalgebra | [
"NonUnitalNonAssocRing",
"NonUnitalSubalgebra",
"instSMulOfMul",
"NonUnitalSubalgebra.center.instNonUnitalCommRing._aux_3",
"NonUnitalSubalgebra.toNonUnitalNonAssocSemiring",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"NonUnitalSubring.center.instNonUnitalCommRing._proof_9",
"CommSemiring.toSemiring",... | false |
_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.PadicSeq.norm_eq_of_equiv | Mathlib.NumberTheory.Padics.PadicNumbers | [
"padicNorm.instIsAbsoluteValueRat",
"NormedCommRing.toNormedRing",
"False",
"Nat.Prime",
"Preorder.toLT",
"NormedRing.toRing",
"Rat",
"PartialOrder.toPreorder",
"Rat.linearOrder",
"Preorder.toLE",
"PadicSeq.stationaryPoint",
"Fact",
"Ne.symm",
"LE.le",
"Or.casesOn",
"Rat.instNormedFiel... | true |
CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform_map_whiskerRight | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.snd",
"CategoryTheory.Functor",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.transform",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.instCategory",
"CategoryTheory.Limits.CatCospanTransformMorphism.right",
"CategoryTheor... | true |
Mathlib.Tactic.BicategoryLike.NormalExpr.brecOn.eq | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | [
"Mathlib.Tactic.BicategoryLike.NormalExpr",
"Mathlib.Tactic.BicategoryLike.NormalExpr.casesOn",
"Mathlib.Tactic.BicategoryLike.Mor₂",
"Mathlib.Tactic.BicategoryLike.NormalExpr.cons",
"Mathlib.Tactic.BicategoryLike.NormalExpr.nil",
"Mathlib.Tactic.BicategoryLike.Structural",
"Mathlib.Tactic.BicategoryLik... | true |
Function.locallyFinsuppWithin.closedSupport | Mathlib.Topology.LocallyFinsupp | [
"Filter.instMembership",
"Iff.mpr",
"Set.ext",
"Eq.mpr",
"False",
"Function.locallyFinsuppWithin.instFunLike",
"eq_false",
"Function.mem_support._simp_1",
"congrArg",
"and_self",
"Function.locallyFinsuppWithin.supportLocallyFiniteWithinDomain",
"HEq.refl",
"setOf",
"isClosed_sdiff_of_codis... | true |
Lean.StructureResolutionState.ctorIdx | Lean.Structure | [
"Lean.StructureResolutionState",
"Nat"
] | false |
CategoryTheory.CostructuredArrow.mk_hom_eq_self | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CostructuredArrow.hom",
"CategoryTheory.CostructuredArrow.mk",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.CostructuredArrow.left",
"CategoryTheory.Functor.obj",
"rfl",
"Catego... | true |
SubNegMonoid.sub._default | Mathlib.Algebra.Group.Defs | [
"Add.mk",
"Neg.mk",
"AddMonoid.mk",
"SubNegMonoid.sub'",
"id",
"instOfNatNat",
"AddSemigroup.mk",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Zero.mk",
"instAddNat",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
sub_eq_add_zero_sub | Mathlib.Algebra.Group.Basic | [
"Eq.mpr",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"SubNegMonoid",
"AddZeroClass.toAddZero",
"id",
"SubNegMonoid.toSub",
"AddZero.toZero",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"SubNegMonoid.toNeg",
"AddZero.toAdd",
"Zero.toOfNat0",
"Eq.refl",
"SubNegMo... | true |
DiffeologicalSpace.mkOfClosure._proof_1 | Mathlib.Geometry.Diffeology.Basic | [
"Set.preimage_inter",
"Real",
"TopologicalSpace.IsOpen",
"Iff.rfl",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Set.sUnion",
"Membership.mem",
"Eq.rec",
"AddMonoidWithOne.toNatCast",
"EuclideanSpace",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Set.instInter",
"TopologicalSpace.mk",
"i... | false |
DiscreteQuotient.comp_finsetClopens.match_1 | Mathlib.Topology.DiscreteQuotient | [
"setOf",
"Setoid",
"DiscreteQuotient",
"TopologicalSpace",
"DiscreteQuotient.casesOn",
"DiscreteQuotient.mk",
"IsOpen",
"Setoid.r"
] | false |
iSupIndep.comp' | Mathlib.Order.SupIndep | [
"Eq.mpr",
"Function.Surjective.iSup_comp",
"iSupIndep",
"congrArg",
"iSup",
"biSup_mono",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Function.comp",
"Exists",
"mt",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"id",
"Ne",
"congr_ar... | true |
PrimeSpectrum.isIrreducible_iff_vanishingIdeal_isPrime | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"Eq.mpr",
"Semiring.toModule",
"PrimeSpectrum.zeroLocus",
"PrimeSpectrum.vanishingIdeal",
"congrArg",
"CommSemiring.toSemiring",
"IsIrreducible",
"Iff.rfl",
"PrimeSpectrum.isIrreducible_zeroLocus_iff_of_radical",
"id",
"PrimeSpectrum.isRadical_vanishingIdeal",
"Ideal",
"CommSemiring",
"Non... | true |
bddAbove_preimage_toDual | Mathlib.Order.Bounds.Basic | [
"OrderDual.instLE",
"OrderDual.toDual",
"Equiv.instEquivLike",
"Iff.rfl",
"Preorder.toLE",
"Equiv",
"BddAbove",
"Iff",
"Set.preimage",
"BddBelow",
"OrderDual",
"DFunLike.coe",
"Preorder",
"EquivLike.toFunLike",
"Set"
] | true |
ENNReal.le_of_forall_nnreal_lt | Mathlib.Data.ENNReal.Inv | [
"le_of_forall_lt_imp_le_of_dense",
"ENNReal.canLift",
"ENNReal.ofNNReal",
"Preorder.toLT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"NNReal",
"Ne",
"ENNReal.instDenselyOrdered",
"LE.le",
"Exists.casesOn",
"LT.lt",
"ENNReal.instLE",
"ENNReal.instLinearOrder",
"ENNReal",
"... | true |
_private.Mathlib.RingTheory.FractionalIdeal.Operations.0.FractionalIdeal.ringEquivOfRingEquiv_spanSingleton._simp_1_3 | Mathlib.RingTheory.FractionalIdeal.Operations | [
"Submodule",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Submodule.mem_span_singleton",
"Exists",
"AddZeroClass.toAddZero",
"Set.instSingletonSet",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"AddZero.toZero",
"Submodule.setLike",
"Semi... | false |
CategoryTheory.FreeBicategory.Hom.ctorElimType | Mathlib.CategoryTheory.Bicategory.Free | [
"cond",
"CategoryTheory.FreeBicategory.Hom.comp",
"Quiver.Hom",
"Nat.ble",
"PULift",
"CategoryTheory.FreeBicategory.Hom.id",
"Nat",
"CategoryTheory.FreeBicategory.Hom",
"Quiver",
"CategoryTheory.FreeBicategory.Hom.of"
] | false |
LieIdeal.coe_toLieSubalgebra | Mathlib.Algebra.Lie.Ideal | [
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"CommRing",
"LieRing.toAddCommGroup",
"LieSubalgebra.instSetLike",
"LieRing",
"SetLike.coe",
"LieIdeal.toLieSubalgebra",
"LieIdeal",
"LieSubalgebra",
"LieAlgebra",
"Eq",
"lieRingSelfModule",
"rfl",
"Set"
] | true |
instAssociativeUInt64HXor | Init.Data.UInt.Bitwise | [
"UInt64",
"instXorOpUInt64",
"Std.Associative.mk",
"HXor.hXor",
"UInt64.xor_assoc",
"instHXorOfXorOp",
"Std.Associative"
] | true |
TopCat.instNegHomObjTopCommRingCatForget₂SubtypeRingHomαContinuousCoeContinuousMapCarrier | Mathlib.Topology.Sheaves.CommRingCat | [
"NegZeroClass.toNeg",
"Continuous",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"TopCommRingCat.instConcreteCategorySubtypeRingHomαContinuousCoe",
"TopCat.instCategory",
"ContinuousMap",
"Neg.mk",
"TopCommRingCat.instCategory",
"RingHom",
"ContinuousMap.i... | true |
_private.Mathlib.Combinatorics.Extremal.RuzsaSzemeredi.0.mem_triangleIndices._simp_1 | Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | [
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"Finset",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"Exists",
"Distrib.toAdd",
"Prod.mk",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"instDistribOfSemiring",
"instHAdd",
"And",
"CommRing... | false |
Lean.Meta.Grind.Context | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.Context.mk"
] | true |
Std.DHashMap.Internal.Raw.getKey?_eq | Std.Data.DHashMap.Internal.Raw | [
"dite_cond_eq_true",
"Std.DHashMap.Raw.WF",
"congrArg",
"Std.DHashMap.Internal.Raw₀.getKey?",
"Std.DHashMap.Raw",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"Subtype.mk",
"Option.none",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"True",
"eq_self",
"eq_true",
"of_eq_true",... | true |
_private.Mathlib.Algebra.Module.LocalizedModule.Submodule.0.IsLocalizedModule.toLocalizedQuotient'._simp_1 | Mathlib.Algebra.Module.LocalizedModule.Submodule | [
"Submodule",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"Submodule.Quotient.mk",
"SMul",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Submodule.hasQuotient",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass... | false |
_private.Init.Data.String.Basic.0.String.Pos.Raw.utf8GetAux.match_1.splitter | Init.Data.String.Basic | [
"String.Pos.Raw.utf8GetAux.match_1",
"String.Pos.Raw",
"List.cons",
"List",
"Char",
"List.nil"
] | true |
_private.Mathlib.MeasureTheory.Measure.AEDisjoint.0.MeasureTheory.exists_null_pairwise_disjoint_diff._simp_1_8 | Mathlib.MeasureTheory.Measure.AEDisjoint | [
"Exists",
"not_exists",
"propext",
"Eq",
"Not"
] | false |
gcdMonoidOfGCD._proof_1 | Mathlib.Algebra.GCDMonoid.Basic | [
"Eq.mpr",
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"Dvd.intro",
"MulZeroClass.zero_mul",
"semigroupDvd",
"SemigroupWithZero.toSemigroup",
"id",
"CommMonoidWithZero.toMonoidWithZero",
"if_pos",
"dite",
"MulZeroClass.mul_zero",
"Classical.choose_spec",... | false |
Lean.Widget.RpcEncodablePacket.«_@».Lean.Server.FileWorker.WidgetRequests.2734021171._hygCtx._hyg.1.noConfusion | Lean.Server.FileWorker.WidgetRequests | [
"Lean.Json",
"Lean.Widget.RpcEncodablePacket._@.Lean.Server.FileWorker.WidgetRequests.2734021171._hygCtx._hyg.1",
"Lean.Widget.RpcEncodablePacket.«_@».Lean.Server.FileWorker.WidgetRequests.2734021171._hygCtx._hyg.1.noConfusionType",
"Lean.Widget.RpcEncodablePacket.«_@».Lean.Server.FileWorker.WidgetRequests.27... | false |
ConvexCone.pointed_positive | Mathlib.Geometry.Convex.Cone.Basic | [
"le_refl",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddZeroClass.toAddZero",
"PartialOrder",
"DistribSMul.toSMulZeroClass",
"PosSMulMono",
"AddCommMonoid",
"AddZero.toZero",
"Semiring.toMonoid",
"Semiring",
"Zero.toOfNat0",
"Module.toDistrib... | true |
_private.Lean.Meta.Tactic.Simp.Simproc.0.Lean.Meta.Simp.getSimprocFromDeclImpl.match_6 | Lean.Meta.Tactic.Simp.Simproc | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Lean.ConstantInfo",
"Option"
] | false |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.le_min_iff._simp_1_2 | Std.Data.Internal.List.Associative | [
"Ordering.gt",
"Ordering",
"Std.OrientedCmp",
"Ordering.lt",
"Std.OrientedCmp.gt_iff_lt",
"propext",
"Eq"
] | false |
ModuleCat.biprodIsoProd_inv_comp_snd_apply | Mathlib.Algebra.Category.ModuleCat.Biproducts | [
"ModuleCat",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"LinearMap.snd",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"Eq.mp",
"id",
"ModuleCat.biprodIsoProd_inv_comp_snd",
"ModuleCat.instConcreteCategoryLinearMapIdCarrier",
"CategoryTheory.Limits.biprod",
"LinearMap",
"C... | true |
Std.Http.URI.instInhabitedQuery | Std.Internal.Http.Data.URI.Basic | [
"Std.Http.URI.instInhabitedQuery._aux_1",
"Std.Http.URI.Query",
"Inhabited",
"Inhabited.mk"
] | true |
BitVec.reduceHShiftLeft | Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec | [
"HShiftLeft.hShiftLeft",
"BitVec",
"BitVec.instHShiftLeftNat",
"instOfNatNat",
"Nat",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"BitVec.reduceShift",
"OfNat.ofNat"
] | true |
LocallyLipschitz.const_min | Mathlib.Topology.MetricSpace.Lipschitz | [
"Real",
"congrArg",
"min_comm",
"Eq.mp",
"EMetricSpace.toPseudoEMetricSpace",
"LocallyLipschitz",
"PseudoEMetricSpace",
"LocallyLipschitz.min_const",
"Real.instMin",
"funext",
"Real.metricSpace",
"LinearOrder.toMin",
"MetricSpace.toEMetricSpace",
"Min.min",
"Real.linearOrder"
] | true |
Int.Linear.Poly | Init.Data.Int.Linear | [
"Int.Linear.Poly.num",
"Int.Linear.Poly.add"
] | true |
Lean.Elab.liftMacroM | Lean.Elab.Util | [
"liftExcept",
"Pure.pure",
"Lean.MessageData",
"Std.instToFormatString",
"_private.Lean.Elab.Util.0.Lean.Elab.liftMacroM.match_3",
"Lean.MonadError.toMonadRef",
"Lean.maxRecDepthErrorMessage",
"Lean.MonadRef.getRef",
"Lean.MonadResolveName.getOpenDecls",
"Lean.MonadTrace",
"instForInOfForIn'",
... | true |
CategoryTheory.Pseudofunctor.hasCoeToLax | Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | [
"CategoryTheory.Pseudofunctor.toLax",
"Coe.mk",
"CategoryTheory.Bicategory",
"CategoryTheory.Pseudofunctor",
"CategoryTheory.LaxFunctor",
"Coe"
] | true |
_private.Init.Internal.Order.Basic.0.Lean.Order.admissible_pprod_snd.match_1_1 | Init.Internal.Order.Basic | [
"PProd.mk",
"Exists.casesOn",
"PProd",
"Exists.intro",
"Lean.Order.CCPO",
"Lean.Order.PProd.chain.snd"
] | false |
_private.Init.Data.Vector.Basic.0.Vector.mapM._proof_2 | Init.Data.Vector.Basic | [
"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",
"Lean.Omega.combo_s... | false |
toIcoMod_intCast_mul_add' | Mathlib.Algebra.Order.ToIntervalMod | [
"Int.cast",
"Eq.mpr",
"Preorder.toLT",
"HMul.hMul",
"congrArg",
"LinearOrder",
"NonUnitalNonAssocRing.toAddCommGroup",
"PartialOrder.toPreorder",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"SemilatticeInf.toPartialOrder",
"toIcoMod_add_intCast_mul'",
"DistribLattice.toLattice",
"id",
"Dis... | true |
TensorProduct.AlgebraTensorModule.map._proof_1 | Mathlib.LinearAlgebra.TensorProduct.Tower | [
"TensorProduct.leftHasSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"IsScalarTower.to_sm... | false |
addConGen._proof_1 | Mathlib.GroupTheory.Congruence.Defs | [
"AddConGen.Rel.trans",
"Equivalence",
"AddConGen.Rel",
"AddConGen.Rel.symm",
"Equivalence.mk",
"AddConGen.Rel.refl",
"Add"
] | false |
_private.Mathlib.Algebra.Ring.Periodic.0.Function.Antiperiodic.int_mul_eq_of_eq_zero.match_1_1 | Mathlib.Algebra.Ring.Periodic | [
"Int.casesOn",
"Int.ofNat",
"Int",
"Nat",
"Int.negSucc"
] | false |
sub_add_sub_cancel | Mathlib.Algebra.Group.Basic | [
"add_sub_assoc",
"Eq.mpr",
"congrArg",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddZeroClass.toAddZero",
"id",
"SubNegMonoid.toSub",
"instHAdd",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"AddZero.toAdd",
"Eq.refl",
"SubNegMonoid.toAddMonoid",
"Eq.symm",
"Eq",... | true |
Lean.Compiler.LCNF.ExtractClosed.M | Lean.Compiler.LCNF.ExtractClosed | [
"ReaderT",
"IO.RealWorld",
"Lean.Compiler.LCNF.ExtractClosed.State",
"StateRefT'",
"Lean.Compiler.LCNF.CompilerM",
"Lean.Compiler.LCNF.ExtractClosed.Context"
] | true |
CategoryTheory.EnrichedFunctor.obj | Mathlib.CategoryTheory.Enriched.Basic | [
"CategoryTheory.MonoidalCategory",
"CategoryTheory.EnrichedFunctor",
"CategoryTheory.EnrichedCategory",
"CategoryTheory.Category"
] | true |
iteratedDeriv_div_const | Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | [
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"NormedDivisionRing.toNormedRing",
"NormedDivisionRing.toDivisionRing",
"NormedRing.toNonUnitalNormedRing",
"DivisionRing.toDivisionSemiring",
"DivisionRing.toDivInvMonoid",
"MulOne.toMul",
"HDiv.hDiv",
"DivIn... | true |
_private.Mathlib.Data.List.Dedup.0.List.dedup_cons_of_mem'._simp_1_2 | Mathlib.Data.List.Dedup | [
"Classical.not_not",
"propext",
"Eq",
"Not"
] | false |
MvQPF.Comp.map' | Mathlib.Data.QPF.Multivariate.Constructions.Comp | [
"Nat",
"MvFunctor",
"TypeVec.Arrow",
"MvFunctor.map",
"Fin2",
"TypeVec"
] | true |
Std.TreeMap.contains_insert_self | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.insert",
"Std.TreeMap.inner",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.TreeMap.contains",
"Std.DTreeMap.contains_insert_self",
"Bool",
"Eq",
"Std.TreeMap"
] | true |
_private.Mathlib.Data.List.Cycle.0.Cycle.chain_of_pairwise._proof_1_1 | Mathlib.Data.List.Cycle | [
"False",
"eq_false",
"Lean.Grind.iff_eq",
"HEq.refl",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_true",
"Membership.mem",
"Eq.mp",
"id",
"Lean.Grind.or_eq_of_eq_false_right",
"List.cons",
"Cycle.ofList",
"instHAppendOfAppend",
"List",
"List.mem_append",
"Iff",
"List.... | false |
EIO.catchExceptions | Init.System.IO | [
"ST.Out.mk",
"IO.RealWorld",
"EIO",
"Void",
"_private.Init.System.IO.0.EIO.toBaseIO.match_1",
"ST.Out",
"BaseIO",
"EST.Out"
] | true |
NNReal.toReal_ne._simp_1 | Mathlib.Data.NNReal.Basic | [
"Real",
"NNReal.toReal_ne",
"NNReal",
"Ne",
"propext",
"Eq",
"NNReal.toReal"
] | false |
ContinuousAffineMap.differentiableOn | Mathlib.Analysis.Calculus.FDeriv.Affine | [
"NormedCommRing.toNormedRing",
"NormedRing.toRing",
"ContinuousAffineMap.differentiable",
"NormedSpace",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousAffineMap",
"NormedAddTorsor.toAddTorsor",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"SeminormedAddCommGroup.toNormedA... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.