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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Algebra.Spectrum.Pi.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.sym.json

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x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6))))))) AddCommGrpCat.carrier.{u_2} (fun (X : AddCommGrpCat.{u_2}) (Y : AddCommGrpCat.{u_2}) => AddMonoidHom.instFunLike.{u_2, u_2} (AddCommGrpCat.carrier.{u_2} X) (AddCommGrpCat.carrier.{u_2} Y) (AddZeroClass.toAddZero.{u_2} (AddCommGrpCat.carrier.{u_2} X) ((fun (X : AddCommGrpCat.{u_2}) => AddMonoid.toAddZeroClass.{u_2} (AddCommGrpCat.carrier.{u_2} X) (SubNegMonoid.toAddMonoid.{u_2} (AddCommGrpCat.carrier.{u_2} X) (AddGroup.toSubNegMonoid.{u_2} (AddCommGrpCat.carrier.{u_2} X) (AddCommGroup.toAddGroup.{u_2} (AddCommGrpCat.carrier.{u_2} X) (AddCommGrpCat.str.{u_2} X))))) X)) (AddZeroClass.toAddZero.{u_2} (AddCommGrpCat.carrier.{u_2} Y) (AddMonoid.toAddZeroClass.{u_2} (AddCommGrpCat.carrier.{u_2} Y) (SubNegMonoid.toAddMonoid.{u_2} (AddCommGrpCat.carrier.{u_2} Y) (AddGroup.toSubNegMonoid.{u_2} (AddCommGrpCat.carrier.{u_2} Y) (AddCommGroup.toAddGroup.{u_2} (AddCommGrpCat.carrier.{u_2} Y) (AddCommGrpCat.str.{u_2} Y))))))) 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inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)) (PresheafOfModules.instCategory.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_1, max (max (succ u_3) u_1) u_4} (CategoryTheory.Functor.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_1, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)) (SheafOfModules.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u_1 u_2, max (max (max u_3 u_1) (succ u_2)) u_4} (PresheafOfModules.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_1, max (max (succ u_3) u_1) u_4} (CategoryTheory.Functor.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_1, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)) (PresheafOfModules.instCategory.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_1, max (max (succ u_3) u_1) u_4} (CategoryTheory.Functor.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_1, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)) (CategoryTheory.Abelian.toPreadditive.{max u_1 u_2, max (max (max u_3 u_1) (succ u_2)) u_4} (PresheafOfModules.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_1, max (max (succ u_3) u_1) u_4} (CategoryTheory.Functor.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_1, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)) (PresheafOfModules.instCategory.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_1, max (max (succ u_3) u_1) u_4} (CategoryTheory.Functor.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_1, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)) (PresheafOfModules.instAbelian.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_1, max (max (succ u_3) u_1) u_4} (CategoryTheory.Functor.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_1, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)))) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u_1 u_2, max (max (max u_3 u_1) (succ u_2)) u_4} (SheafOfModules.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instPreadditive.{u_2, u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R)) (PresheafOfModules.sheafification.{u_2, u_4, u_3, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_1, max (max (succ u_3) u_1) u_4} (CategoryTheory.Functor.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_1, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R) R (CategoryTheory.CategoryStruct.id.{max u_3 u_1, max (max (succ u_3) u_1) u_4} (CategoryTheory.Functor.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Category.toCategoryStruct.{max u_3 u_1, max (max (succ u_3) u_1) u_4} (CategoryTheory.Functor.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3})) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_1, max (max (succ u_3) u_1) u_4} (CategoryTheory.Functor.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_1, succ u_3} (Opposite.{succ u_1} C) (CategoryTheory.Category.opposite.{u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_1, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)) (SheafOfModules.instAbelian._proof_1.{u_3, u_4, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instAbelian._proof_2.{u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.15 (CategoryTheory.instHasWeakSheafifyOfHasSheafify.{u_4, u_2, u_1, succ u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J AddCommGrpCat.{u_2} AddCommGrpCat.instCategory.{u_2} inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.11))","typeFull":"∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_4, u_1} C] {J : CategoryTheory.GrothendieckTopology C}\n  (R : CategoryTheory.Sheaf J RingCat) [inst_1 : CategoryTheory.HasSheafify J AddCommGrpCat]\n  [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat],\n  (PresheafOfModules.sheafification (CategoryTheory.CategoryStruct.id R.obj)).PreservesZeroMorphisms","typeReadable":"∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_4, u_1} C] {J : CategoryTheory.GrothendieckTopology C}\n  (R : CategoryTheory.Sheaf J RingCat) [inst_1 : CategoryTheory.HasSheafify J AddCommGrpCat]\n  [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat],\n  (PresheafOfModules.sheafification (CategoryTheory.CategoryStruct.id R.obj)).PreservesZeroMorphisms","typeReferences":[["SheafOfModules","instAbelian","_proof_2"],["AddCommGroup","toAddGroup"],["Opposite"],["CategoryTheory","Category"],["PresheafOfModules"],["PresheafOfModules","instAbelian"],["PresheafOfModules","instCategory"],["CategoryTheory","CategoryStruct","id"],["AddMonoidHom"],["CategoryTheory","Presheaf","IsSheaf"],["AddMonoidHom","instFunLike"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["AddGroup","toSubNegMonoid"],["AddCommGrpCat","carrier"],["AddCommGrpCat","instConcreteCategoryAddMonoidHomCarrier"],["SheafOfModules","instCategory"],["SheafOfModules"],["AddCommGrpCat","instCategory"],["CategoryTheory","Functor"],["CategoryTheory","Category","opposite"],["CategoryTheory","Functor","PreservesZeroMorphisms"],["CategoryTheory","GrothendieckTopology"],["CategoryTheory","GrothendieckTopology","WEqualsLocallyBijective"],["AddZeroClass","toAddZero"],["CategoryTheory","ObjectProperty","FullSubcategory","obj"],["CategoryTheory","Category","toCategoryStruct"],["PresheafOfModules","sheafification"],["CategoryTheory","Abelian","toPreadditive"],["CategoryTheory","instHasWeakSheafifyOfHasSheafify"],["AddCommGrpCat"],["RingCat"],["AddCommGrpCat","str"],["SubNegMonoid","toAddMonoid"],["SheafOfModules","instAbelian","_proof_1"],["CategoryTheory","HasSheafify"],["RingCat","instCategory"],["CategoryTheory","Functor","category"],["SheafOfModules","instPreadditive"],["CategoryTheory","Sheaf"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["RingHom"],["PresheafOfModules","instIsLeftAdjointSheafOfModulesSheafification"],["Opposite"],["RingHom","instFunLike"],["CategoryTheory","Presheaf","isLocallySurjective_of_iso"],["PresheafOfModules"],["PresheafOfModules","instAbelian"],["PresheafOfModules","instCategory"],["CategoryTheory","CategoryStruct","id"],["RingCat","carrier"],["CategoryTheory","IsIso","id"],["Semiring","toNonAssocSemiring"],["CategoryTheory","Presheaf","IsSheaf"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["SheafOfModules","instCategory"],["AddCommGrpCat","instCategory"],["SheafOfModules"],["CategoryTheory","Category","opposite"],["CategoryTheory","Functor"],["CategoryTheory","Functor","preservesZeroMorphisms_of_isLeftAdjoint"],["CategoryTheory","ObjectProperty","FullSubcategory","obj"],["PresheafOfModules","sheafification"],["CategoryTheory","Category","toCategoryStruct"],["CategoryTheory","Abelian","toPreadditive"],["Ring","toSemiring"],["AddCommGrpCat"],["CategoryTheory","instHasWeakSheafifyOfHasSheafify"],["RingCat"],["CategoryTheory","Presheaf","instIsLocallyInjectiveOfIsIsoFunctorOpposite"],["RingCat","instCategory"],["RingCat","instConcreteCategoryRingHomCarrier"],["RingCat","ring"],["CategoryTheory","Functor","category"],["SheafOfModules","instPreadditive"]]},{"isProp":true,"kind":"theorem","name":["SheafOfModules","instAbelian","_proof_6"],"typeFallback":"forall {C : Type.{u_2}} [inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 : CategoryTheory.Category.{u_4, u_2} C] {J : CategoryTheory.GrothendieckTopology.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3} (R : CategoryTheory.Sheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J RingCat.{u_1} RingCat.instCategory.{u_1}) [inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.11 : CategoryTheory.HasSheafify.{u_4, u_3, u_2, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J AddCommGrpCat.{u_3} AddCommGrpCat.instCategory.{u_3}] [inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.15 : CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective.{u_3, u_3, u_4, succ u_3, u_2, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J AddCommGrpCat.{u_3} AddCommGrpCat.instCategory.{u_3} (fun (x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_3}) (x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_3}) => AddMonoidHom.{u_3, u_3} (AddCommGrpCat.carrier.{u_3} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.carrier.{u_3} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddZeroClass.toAddZero.{u_3} (AddCommGrpCat.carrier.{u_3} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_3} (AddCommGrpCat.carrier.{u_3} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_3} (AddCommGrpCat.carrier.{u_3} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_3} (AddCommGrpCat.carrier.{u_3} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_3} (AddCommGrpCat.carrier.{u_3} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_3} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6)))))) (AddZeroClass.toAddZero.{u_3} (AddCommGrpCat.carrier.{u_3} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_3} (AddCommGrpCat.carrier.{u_3} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_3} (AddCommGrpCat.carrier.{u_3} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_3} (AddCommGrpCat.carrier.{u_3} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_3} (AddCommGrpCat.carrier.{u_3} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_3} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6))))))) AddCommGrpCat.carrier.{u_3} (fun (X : AddCommGrpCat.{u_3}) (Y : AddCommGrpCat.{u_3}) => AddMonoidHom.instFunLike.{u_3, u_3} (AddCommGrpCat.carrier.{u_3} X) (AddCommGrpCat.carrier.{u_3} Y) (AddZeroClass.toAddZero.{u_3} (AddCommGrpCat.carrier.{u_3} X) ((fun (X : AddCommGrpCat.{u_3}) => AddMonoid.toAddZeroClass.{u_3} (AddCommGrpCat.carrier.{u_3} X) (SubNegMonoid.toAddMonoid.{u_3} (AddCommGrpCat.carrier.{u_3} X) (AddGroup.toSubNegMonoid.{u_3} (AddCommGrpCat.carrier.{u_3} X) (AddCommGroup.toAddGroup.{u_3} (AddCommGrpCat.carrier.{u_3} X) (AddCommGrpCat.str.{u_3} X))))) X)) (AddZeroClass.toAddZero.{u_3} (AddCommGrpCat.carrier.{u_3} Y) (AddMonoid.toAddZeroClass.{u_3} (AddCommGrpCat.carrier.{u_3} Y) (SubNegMonoid.toAddMonoid.{u_3} (AddCommGrpCat.carrier.{u_3} Y) (AddGroup.toSubNegMonoid.{u_3} (AddCommGrpCat.carrier.{u_3} Y) (AddCommGroup.toAddGroup.{u_3} (AddCommGrpCat.carrier.{u_3} Y) (AddCommGrpCat.str.{u_3} Y))))))) AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier.{u_3}], CategoryTheory.IsIso.{max (max (max u_1 u_2) (succ u_3)) u_4, max (max (max u_1 u_2) (succ u_3)) u_4} (CategoryTheory.Functor.{max u_2 u_3, max u_2 u_3, max (max (max u_1 u_2) (succ u_3)) u_4, max (max (max u_1 u_2) (succ u_3)) u_4} (SheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R)) (CategoryTheory.Functor.category.{max u_2 u_3, max u_2 u_3, max (max (max u_1 u_2) (succ u_3)) u_4, max (max (max u_1 u_2) (succ u_3)) u_4} (SheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R)) (CategoryTheory.Functor.comp.{max u_2 u_3, max u_2 u_3, max u_2 u_3, max (max (max u_1 u_2) (succ u_3)) u_4, max (max (max u_1 u_2) (succ u_3)) u_4, max (max (max u_1 u_2) (succ u_3)) u_4} (SheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (PresheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (PresheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (SheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (CategoryTheory.Functor.comp.{max u_2 u_3, max u_2 u_3, max u_2 u_3, max (max (max u_1 u_2) (succ u_3)) u_4, max (max (max u_1 u_2) (succ u_3)) u_4, max (max (max u_1 u_2) (succ u_3)) u_4} (SheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (PresheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (PresheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (PresheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (PresheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (SheafOfModules.forget.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (PresheafOfModules.restrictScalars.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R) (CategoryTheory.CategoryStruct.id.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1})) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)))) (PresheafOfModules.sheafification.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R) R (CategoryTheory.CategoryStruct.id.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1})) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (SheafOfModules.instAbelian._proof_1.{u_1, u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instAbelian._proof_2.{u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.15 (CategoryTheory.instHasWeakSheafifyOfHasSheafify.{u_4, u_3, u_2, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J AddCommGrpCat.{u_3} AddCommGrpCat.instCategory.{u_3} inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.11))) (CategoryTheory.Functor.id.{max u_2 u_3, max (max (max u_1 u_2) (succ u_3)) u_4} (SheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R)) (CategoryTheory.Adjunction.counit.{max u_2 u_3, max u_2 u_3, max (max (max u_1 u_2) (succ u_3)) u_4, max (max (max u_1 u_2) (succ u_3)) u_4} (PresheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (PresheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (SheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (PresheafOfModules.sheafification.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R) R (CategoryTheory.CategoryStruct.id.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1})) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (SheafOfModules.instAbelian._proof_1.{u_1, u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instAbelian._proof_2.{u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.15 (CategoryTheory.instHasWeakSheafifyOfHasSheafify.{u_4, u_3, u_2, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J AddCommGrpCat.{u_3} AddCommGrpCat.instCategory.{u_3} inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.11)) (CategoryTheory.Functor.comp.{max u_2 u_3, max u_2 u_3, max u_2 u_3, max (max (max u_1 u_2) (succ u_3)) u_4, max (max (max u_1 u_2) (succ u_3)) u_4, max (max (max u_1 u_2) (succ u_3)) u_4} (SheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (PresheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (PresheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (PresheafOfModules.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (PresheafOfModules.instCategory.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (SheafOfModules.forget.{u_3, u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (PresheafOfModules.restrictScalars.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R) (CategoryTheory.CategoryStruct.id.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1})) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)))) (PresheafOfModules.sheafificationAdjunction.{u_3, u_4, u_1, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R) R (CategoryTheory.CategoryStruct.id.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1})) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_1 u_2, max (max (succ u_1) u_2) u_4} (CategoryTheory.Functor.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Functor.category.{u_4, u_1, u_2, succ u_1} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_1} RingCat.instCategory.{u_1}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_1} RingCat.instCategory.{u_1} J) R)) (SheafOfModules.instAbelian._proof_1.{u_1, u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instAbelian._proof_2.{u_4, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.15 (CategoryTheory.instHasWeakSheafifyOfHasSheafify.{u_4, u_3, u_2, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J AddCommGrpCat.{u_3} AddCommGrpCat.instCategory.{u_3} inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.11)))","typeFull":"∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_4, u_2} C] {J : CategoryTheory.GrothendieckTopology C}\n  (R : CategoryTheory.Sheaf J RingCat) [inst_1 : CategoryTheory.HasSheafify J AddCommGrpCat]\n  [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat],\n  CategoryTheory.IsIso (PresheafOfModules.sheafificationAdjunction (CategoryTheory.CategoryStruct.id R.obj)).counit","typeReadable":"∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_4, u_2} C] {J : CategoryTheory.GrothendieckTopology C}\n  (R : CategoryTheory.Sheaf J RingCat) [inst_1 : CategoryTheory.HasSheafify J AddCommGrpCat]\n  [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat],\n  CategoryTheory.IsIso (PresheafOfModules.sheafificationAdjunction (CategoryTheory.CategoryStruct.id R.obj)).counit","typeReferences":[["CategoryTheory","Adjunction","counit"],["CategoryTheory","Functor","id"],["SheafOfModules","instAbelian","_proof_2"],["Opposite"],["AddCommGroup","toAddGroup"],["CategoryTheory","Category"],["CategoryTheory","IsIso"],["CategoryTheory","Functor","comp"],["PresheafOfModules"],["PresheafOfModules","instCategory"],["CategoryTheory","CategoryStruct","id"],["PresheafOfModules","restrictScalars"],["AddMonoidHom"],["CategoryTheory","Presheaf","IsSheaf"],["AddMonoidHom","instFunLike"],["AddGroup","toSubNegMonoid"],["AddCommGrpCat","carrier"],["AddCommGrpCat","instConcreteCategoryAddMonoidHomCarrier"],["SheafOfModules","instCategory"],["CategoryTheory","Category","opposite"],["AddCommGrpCat","instCategory"],["CategoryTheory","Functor"],["SheafOfModules"],["CategoryTheory","GrothendieckTopology"],["CategoryTheory","GrothendieckTopology","WEqualsLocallyBijective"],["CategoryTheory","ObjectProperty","FullSubcategory","obj"],["AddZeroClass","toAddZero"],["PresheafOfModules","sheafification"],["CategoryTheory","Category","toCategoryStruct"],["CategoryTheory","instHasWeakSheafifyOfHasSheafify"],["AddCommGrpCat"],["RingCat"],["AddCommGrpCat","str"],["PresheafOfModules","sheafificationAdjunction"],["SheafOfModules","forget"],["SubNegMonoid","toAddMonoid"],["SheafOfModules","instAbelian","_proof_1"],["CategoryTheory","HasSheafify"],["RingCat","instCategory"],["CategoryTheory","Functor","category"],["CategoryTheory","Sheaf"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["AddCommGrpCat","instCategory"],["CategoryTheory","Functor"],["CategoryTheory","Category","opposite"],["RingHom"],["PresheafOfModules","instIsIsoFunctorSheafOfModulesCounitSheafificationAdjunction"],["Opposite"],["RingHom","instFunLike"],["CategoryTheory","Presheaf","isLocallySurjective_of_iso"],["CategoryTheory","ObjectProperty","FullSubcategory","obj"],["CategoryTheory","Category","toCategoryStruct"],["Ring","toSemiring"],["AddCommGrpCat"],["CategoryTheory","instHasWeakSheafifyOfHasSheafify"],["RingCat","carrier"],["CategoryTheory","CategoryStruct","id"],["RingCat"],["CategoryTheory","IsIso","id"],["Semiring","toNonAssocSemiring"],["CategoryTheory","Presheaf","instIsLocallyInjectiveOfIsIsoFunctorOpposite"],["CategoryTheory","Presheaf","IsSheaf"],["RingCat","instCategory"],["RingCat","instConcreteCategoryRingHomCarrier"],["RingCat","ring"],["CategoryTheory","Functor","category"]]},{"isProp":true,"kind":"theorem","name":["SheafOfModules","instAbelian","_proof_5"],"typeFallback":"forall {C : Type.{u_2}} [inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 : CategoryTheory.Category.{u_4, u_2} C] {J : CategoryTheory.GrothendieckTopology.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3} (R : CategoryTheory.Sheaf.{u_4, u_3, u_2, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J RingCat.{u_3} RingCat.instCategory.{u_3}) [inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.11 : CategoryTheory.HasSheafify.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1}] [inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.15 : CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective.{u_1, u_1, u_4, succ u_1, u_2, u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (fun (x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) (x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) => AddMonoidHom.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6))))))) AddCommGrpCat.carrier.{u_1} (fun (X : AddCommGrpCat.{u_1}) (Y : AddCommGrpCat.{u_1}) => AddMonoidHom.instFunLike.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.carrier.{u_1} Y) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} X) ((fun (X : AddCommGrpCat.{u_1}) => AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} X) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.str.{u_1} X))))) X)) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGrpCat.str.{u_1} Y))))))) AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier.{u_1}], CategoryTheory.Limits.PreservesFiniteLimits.{max u_1 u_2, max u_1 u_2, max (max (max (succ u_1) u_2) u_3) u_4, max (max (max (succ u_1) u_2) u_3) u_4} (PresheafOfModules.{u_1, u_4, u_2, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_2, max (max (succ u_3) u_2) u_4} (CategoryTheory.Functor.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_2, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)) (PresheafOfModules.instCategory.{u_1, u_4, u_2, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_2, max (max (succ u_3) u_2) u_4} (CategoryTheory.Functor.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_2, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)) (SheafOfModules.{u_1, u_4, u_2, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instCategory.{u_1, u_4, u_2, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (PresheafOfModules.sheafification.{u_1, u_4, u_3, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_2, max (max (succ u_3) u_2) u_4} (CategoryTheory.Functor.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_2, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R) R (CategoryTheory.CategoryStruct.id.{max u_3 u_2, max (max (succ u_3) u_2) u_4} (CategoryTheory.Functor.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Category.toCategoryStruct.{max u_3 u_2, max (max (succ u_3) u_2) u_4} (CategoryTheory.Functor.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3})) (CategoryTheory.ObjectProperty.FullSubcategory.obj.{max u_3 u_2, max (max (succ u_3) u_2) u_4} (CategoryTheory.Functor.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Functor.category.{u_4, u_3, u_2, succ u_3} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3) RingCat.{u_3} RingCat.instCategory.{u_3}) (CategoryTheory.Presheaf.IsSheaf.{u_4, u_3, u_2, succ u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 RingCat.{u_3} RingCat.instCategory.{u_3} J) R)) (SheafOfModules.instAbelian._proof_1.{u_3, u_4, u_2} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) (SheafOfModules.instAbelian._proof_2.{u_4, u_2, u_3} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J R) inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.15 (CategoryTheory.instHasWeakSheafifyOfHasSheafify.{u_4, u_1, u_2, succ u_1} C inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.3 J AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} inst._@.Mathlib.Algebra.Category.ModuleCat.Sheaf.Abelian.2242072913._hygCtx._hyg.11))","typeFull":"∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_4, u_2} C] {J : CategoryTheory.GrothendieckTopology C}\n  (R : CategoryTheory.Sheaf J RingCat) [inst_1 : CategoryTheory.HasSheafify J AddCommGrpCat]\n  [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat],\n  CategoryTheory.Limits.PreservesFiniteLimits\n    (PresheafOfModules.sheafification (CategoryTheory.CategoryStruct.id R.obj))","typeReadable":"∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_4, u_2} C] {J : CategoryTheory.GrothendieckTopology C}\n  (R : CategoryTheory.Sheaf J RingCat) [inst_1 : CategoryTheory.HasSheafify J AddCommGrpCat]\n  [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat],\n  CategoryTheory.Limits.PreservesFiniteLimits\n    (PresheafOfModules.sheafification (CategoryTheory.CategoryStruct.id 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Central.Defs.sym.json

@@ -0,0 +1 @@
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Prop","typeFull":"(K : Type u) → [inst : CommSemiring K] → (D : Type v) → [inst_1 : Semiring D] → [Algebra K D] → Prop","typeReadable":"(K : Type u) → [inst : CommSemiring K] → (D : Type v) → [inst_1 : Semiring D] → [Algebra K D] → Prop","typeReferences":[["CommSemiring"],["Algebra"],["Semiring"]],"valueReferences":null},{"isProp":false,"kind":"definition","name":["Algebra","IsCentral","recOn"],"typeFallback":"forall {K : Type.{u}} [inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.3 : CommSemiring.{u} K] {D : Type.{v}} [inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.7 : Semiring.{v} D] [inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.10 : Algebra.{u, v} K D inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.7] {motive : (Algebra.IsCentral.{u, v} K inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.3 D inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.7 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t","typeReferences":[["Lattice","toSemilatticeSup"],["Subalgebra"],["PartialOrder","toPreorder"],["CompleteLattice","toLattice"],["CommSemiring"],["SemilatticeSup","toPartialOrder"],["Subalgebra","center"],["Bot","bot"],["Algebra","IsCentral"],["Algebra"],["Algebra","IsCentral","mk"],["Algebra","instCompleteLatticeSubalgebra"],["BoundedOrder","toOrderBot"],["LE","le"],["OrderBot","toBot"],["Preorder","toLE"],["CompleteLattice","toBoundedOrder"],["Subalgebra","instPartialOrder"],["Semiring"]],"valueReferences":[["Algebra","IsCentral","rec"]]},{"isProp":false,"kind":"recursor","name":["Algebra","IsCentral","rec"],"typeFallback":"forall {K : Type.{u}} [inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.3 : CommSemiring.{u} K] {D : Type.{v}} [inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.7 : Semiring.{v} D] [inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.10 : Algebra.{u, v} K D inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.7] {motive : (Algebra.IsCentral.{u, v} K inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.3 D inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.10) -> Sort.{u_1}}, (forall (out : LE.le.{v} (Subalgebra.{u, v} K D inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.10) (Preorder.toLE.{v} (Subalgebra.{u, v} K D inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.10) (PartialOrder.toPreorder.{v} (Subalgebra.{u, v} K D inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Central.Defs.2842438463._hygCtx._hyg.7 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.CharP.Invertible.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Nat.Defs.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Subgroup.ZPowers.Lemmas.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.TypeTags.Pointwise.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Action.Faithful.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Commute.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.HomologicalComplexAbelian.sym.json

@@ -0,0 +1 @@
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inst._@.Mathlib.Algebra.Homology.HomologicalComplexAbelian.3845103716._hygCtx._hyg.6 (CategoryTheory.Abelian.toPreadditive.{v_1, u_1} C inst._@.Mathlib.Algebra.Homology.HomologicalComplexAbelian.3845103716._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Homology.HomologicalComplexAbelian.3845103716._hygCtx._hyg.9)) c) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v_1, u_1} C inst._@.Mathlib.Algebra.Homology.HomologicalComplexAbelian.3845103716._hygCtx._hyg.6 (CategoryTheory.Abelian.toPreadditive.{v_1, u_1} C inst._@.Mathlib.Algebra.Homology.HomologicalComplexAbelian.3845103716._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Homology.HomologicalComplexAbelian.3845103716._hygCtx._hyg.9)) S (HomologicalComplex.eval.{v_1, u_1, u_2} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexAbelian.3845103716._hygCtx._hyg.6 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{v_1, u_1} C inst._@.Mathlib.Algebra.Homology.HomologicalComplexAbelian.3845103716._hygCtx._hyg.6 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c)","typeReferences":[["HomologicalComplex","instHasZeroMorphisms"],["CategoryTheory","Abelian"],["CategoryTheory","IsNormalMonoCategory"],["CategoryTheory","Category"],["ComplexShape"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["HomologicalComplex"],["HomologicalComplex","instCategory"],["CategoryTheory","Abelian","toPreadditive"]],"valueReferences":[["HomologicalComplex","eval"],["HomologicalComplex","instPreservesFiniteColimitsEvalOfHasFiniteColimits"],["CategoryTheory","Functor","map_mono"],["CategoryTheory","Functor","preservesHomologyOfExact"],["CategoryTheory","Limits","cokernel","π"],["HomologicalComplex","instPreservesZeroMorphismsEval"],["CategoryTheory","Limits","hasCokernels_of_hasCoequalizers"],["HomologicalComplex","instHasColimitsOfShape"],["CategoryTheory","Abelian","hasZeroObject"],["CategoryTheory","Abelian","hasCoequalizers"],["CategoryTheory","Limits","HasZeroMorphisms","zero"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["HomologicalComplex"],["CategoryTheory","Limits","PreservesColimitsOfShape","preservesColimit"],["HomologicalComplex","instHasColimit"],["HomologicalComplex","instPreservesColimitEval"],["CategoryTheory","IsNormalMonoCategory","mk"],["CategoryTheory","NormalMono","mk"],["CategoryTheory","Category","toCategoryStruct"],["CategoryTheory","Limits","walkingParallelPairHomCategory"],["HomologicalComplex","instCategory"],["CategoryTheory","Limits","HasCokernels","has_colimit"],["CategoryTheory","Abelian","toPreadditive"],["CategoryTheory","Abelian","hasFiniteLimits"],["CategoryTheory","Limits","instHasColimitCompOfPreservesColimit"],["CategoryTheory","Limits","hasColimitOfHasColimitsOfShape"],["CategoryTheory","Limits","parallelPair"],["HomologicalComplex","instHasZeroObject"],["CategoryTheory","Functor","instPreservesMonomorphisms"],["CategoryTheory","Limits","WalkingParallelPair"],["CategoryTheory","NormalMono"],["CategoryTheory","Functor","comp"],["HomologicalComplex","instPreadditive"],["HomologicalComplex","instPreservesColimitsOfShapeEvalOfHasColimitsOfShape"],["Nonempty","intro"],["Quiver","Hom"],["CategoryTheory","NonPreadditiveAbelian","toHasZeroMorphisms"],["Zero","toOfNat0"],["HomologicalComplex","isLimitOfEval"],["CategoryTheory","Limits","cokernel","condition"],["HomologicalComplex","instPreservesFiniteLimitsEvalOfHasFiniteLimits"],["CategoryTheory","Limits","cokernel"],["OfNat","ofNat"],["HomologicalComplex","instHasZeroMorphisms"],["CategoryTheory","Abelian","nonPreadditiveAbelian"],["CategoryTheory","CategoryStruct","toQuiver"],["CategoryTheory","Abelian","isLimitMapConeOfKernelForkOfι"],["CategoryTheory","Abelian","hasFiniteColimits"],["CategoryTheory","Limits","KernelFork","ofι"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Presentation.Free.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["Module","Relations","solutionFinsupp","isPresentationCore","_proof_4"],"typeFallback":"forall {A : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 : Ring.{u_1} A] (relations : Module.Relations.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) [inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.16 : IsEmpty.{succ u_4} (Module.Relations.R.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations)] {N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.72.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.41 : AddCommGroup.{u_3} N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40] [inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.75.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.42 : Module.{u_1, u_3} A N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (AddCommGroup.toAddCommMonoid.{u_3} N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.72.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.41)] {f._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.43 : LinearMap.{u_1, u_1, max u_1 u_2, u_3} A A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (RingHom.id.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3))) (Finsupp.{u_2, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A (MulZeroClass.toZero.{u_1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)))))) N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 (AddCommGroup.toAddCommMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A (MulZeroClass.toZero.{u_1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)))))) (Finsupp.instAddCommGroup.{u_2, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A (Ring.toAddCommGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3))) (AddCommGroup.toAddCommMonoid.{u_3} N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.72.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.41) (Finsupp.module.{u_2, u_1, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)))) (Semiring.toModule.{u_1} A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3))) inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.75.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.42} {f'._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.44 : LinearMap.{u_1, u_1, max u_1 u_2, u_3} A A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (RingHom.id.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3))) (Finsupp.{u_2, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A (MulZeroClass.toZero.{u_1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)))))) N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 (AddCommGroup.toAddCommMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A (MulZeroClass.toZero.{u_1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)))))) (Finsupp.instAddCommGroup.{u_2, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A (Ring.toAddCommGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3))) (AddCommGroup.toAddCommMonoid.{u_3} N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.72.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.41) (Finsupp.module.{u_2, u_1, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)))) (Semiring.toModule.{u_1} A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3))) inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.75.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.42}, (Eq.{max (succ u_3) (succ u_2)} (Module.Relations.Solution.{u_2, u_4, u_3, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.72.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.75.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.42) (Module.Relations.Solution.postcomp.{u_2, u_4, u_3, max u_1 u_2, u_1} A 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inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)))) (Semiring.toModule.{u_1} A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3))) (Module.Relations.solutionFinsupp.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.16) N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.72.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.41 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A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)) (Finsupp.module.{u_2, u_1, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)))) (Semiring.toModule.{u_1} A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3))) (Module.Relations.solutionFinsupp.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.16) N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.72.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.41 inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.75.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.42 f'._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.44)) -> (Eq.{max (succ (max u_1 u_2)) (succ u_3)} (LinearMap.{u_1, u_1, max u_1 u_2, u_3} A A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (RingHom.id.{u_1} A (Semiring.toNonAssocSemiring.{u_1} A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3))) (Finsupp.{u_2, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A (MulZeroClass.toZero.{u_1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)))))) N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 (AddCommGroup.toAddCommMonoid.{max u_1 u_2} (Finsupp.{u_2, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A (MulZeroClass.toZero.{u_1} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3)))))) (Finsupp.instAddCommGroup.{u_2, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A (Ring.toAddCommGroup.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3))) (AddCommGroup.toAddCommMonoid.{u_3} N._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.40 inst._@.Mathlib.Algebra.Module.Presentation.Basic.188742726._hygCtx.72.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.41) (Finsupp.module.{u_2, u_1, u_1} (Module.Relations.G.{u_2, u_4, u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3 relations) A A (Ring.toSemiring.{u_1} A inst._@.Mathlib.Algebra.Module.Presentation.Free.1746926596._hygCtx._hyg.3) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} A (NonAssocRing.toNonUnitalNonAssocRing.{u_1} A (Ring.toNonAssocRing.{u_1} A 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Submodule.Order.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Torsion.Pi.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Disjointed.sym.json

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inst._@.Mathlib.Algebra.Order.Disjointed.3712620708._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Order.Disjointed.3712620708._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Order.Disjointed.3712620708._hygCtx._hyg.22 : NoMaxOrder.{u_2} ι (Preorder.toLT.{u_2} ι (PartialOrder.toPreorder.{u_2} ι (SemilatticeInf.toPartialOrder.{u_2} ι (Lattice.toSemilatticeInf.{u_2} ι (DistribLattice.toLattice.{u_2} ι (instDistribLatticeOfLinearOrder.{u_2} ι inst._@.Mathlib.Algebra.Order.Disjointed.3712620708._hygCtx._hyg.7))))))] {f : ι -> α}, (Monotone.{u_2, u_1} ι α (PartialOrder.toPreorder.{u_2} ι (SemilatticeInf.toPartialOrder.{u_2} ι (Lattice.toSemilatticeInf.{u_2} ι (DistribLattice.toLattice.{u_2} ι (instDistribLatticeOfLinearOrder.{u_2} ι inst._@.Mathlib.Algebra.Order.Disjointed.3712620708._hygCtx._hyg.7))))) (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (GeneralizedCoheytingAlgebra.toLattice.{u_1} α 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Field.Pointwise.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["LinearOrderedField","smul_Iic"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Field.Pointwise.1703559998._hygCtx._hyg.3 : Field.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.1703559998._hygCtx._hyg.6 : LinearOrder.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.1703559998._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K (Field.toSemifield.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.1703559998._hygCtx._hyg.3))) (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.1703559998._hygCtx._hyg.6))))] {a : K} {r : K}, (LT.lt.{u_1} K (Preorder.toLT.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K 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a)","typeReferences":[["PartialOrder","toPreorder"],["Field"],["Preorder","toLT"],["HMul","hMul"],["SMulZeroClass","toSMul"],["MulZeroClass","toSMulWithZero"],["CommRing","toNonUnitalCommRing"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Set","smulSet"],["instHSMul"],["Zero","toOfNat0"],["Semifield","toDivisionSemiring"],["Eq"],["SemilatticeInf","toPartialOrder"],["Lattice","toSemilatticeInf"],["IsStrictOrderedRing"],["Field","toCommRing"],["NonUnitalNonAssocSemiring","toDistrib"],["Set"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["Distrib","toMul"],["LinearOrder"],["DivisionSemiring","toSemiring"],["Set","Iic"],["SMulWithZero","toSMulZeroClass"],["OfNat","ofNat"],["LT","lt"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["HSMul","hSMul"],["Field","toSemifield"],["instHMul"]],"valueReferences":[["IsStrictOrderedRing","toPosMulStrictMono"],["Field","toCommRing"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["MulZeroClass","toMul"],["DivisionSemiring","toSemiring"],["CommRing","toNonUnitalCommRing"],["DivisionSemiring","toGroupWithZero"],["OrderIso","image_Iic"],["PosMulReflectLE","toPosMulReflectLT"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["OrderIso","mulLeft₀"],["Field","toSemifield"],["Semifield","toDivisionSemiring"],["PosMulStrictMono","toPosMulReflectLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["LinearOrderedField","smul_Ico"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Field.Pointwise.2656330017._hygCtx._hyg.3 : Field.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.2656330017._hygCtx._hyg.6 : LinearOrder.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.2656330017._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K (Field.toSemifield.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.2656330017._hygCtx._hyg.3))) (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.2656330017._hygCtx._hyg.6))))] {a : K} {b : K} {r : K}, (LT.lt.{u_1} K (Preorder.toLT.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K 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(instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K (CommRing.toNonUnitalCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.2656330017._hygCtx._hyg.3)))))))) r a) (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K (CommRing.toNonUnitalCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.2656330017._hygCtx._hyg.3)))))))) r b)))","typeFull":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a b r : K},\n  0 < r → r • Set.Ico a b = Set.Ico (r * a) (r * b)","typeReadable":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a b r : K},\n  0 < r → r • Set.Ico a b = Set.Ico (r * a) (r * b)","typeReferences":[["PartialOrder","toPreorder"],["Field"],["Preorder","toLT"],["HMul","hMul"],["SMulZeroClass","toSMul"],["MulZeroClass","toSMulWithZero"],["CommRing","toNonUnitalCommRing"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Set","smulSet"],["instHSMul"],["Zero","toOfNat0"],["Semifield","toDivisionSemiring"],["Set","Ico"],["Eq"],["SemilatticeInf","toPartialOrder"],["Lattice","toSemilatticeInf"],["IsStrictOrderedRing"],["Field","toCommRing"],["NonUnitalNonAssocSemiring","toDistrib"],["Set"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["Distrib","toMul"],["LinearOrder"],["DivisionSemiring","toSemiring"],["SMulWithZero","toSMulZeroClass"],["OfNat","ofNat"],["LT","lt"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["HSMul","hSMul"],["Field","toSemifield"],["instHMul"]],"valueReferences":[["IsStrictOrderedRing","toPosMulStrictMono"],["Field","toCommRing"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["MulZeroClass","toMul"],["OrderIso","image_Ico"],["DivisionSemiring","toSemiring"],["CommRing","toNonUnitalCommRing"],["DivisionSemiring","toGroupWithZero"],["PosMulReflectLE","toPosMulReflectLT"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["OrderIso","mulLeft₀"],["Field","toSemifield"],["Semifield","toDivisionSemiring"],["PosMulStrictMono","toPosMulReflectLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["LinearOrderedField","smul_Ioo"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Field.Pointwise.522728589._hygCtx._hyg.3 : Field.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.522728589._hygCtx._hyg.6 : LinearOrder.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.522728589._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K (Field.toSemifield.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.522728589._hygCtx._hyg.3))) (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.522728589._hygCtx._hyg.6))))] {a : K} {b : K} {r : K}, (LT.lt.{u_1} K (Preorder.toLT.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K 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(MulZeroClass.toSMulWithZero.{u_1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K (CommRing.toNonUnitalCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.522728589._hygCtx._hyg.3))))))))))) r (Set.Ioo.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.522728589._hygCtx._hyg.6))))) a b)) (Set.Ioo.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.522728589._hygCtx._hyg.6))))) (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K (CommRing.toNonUnitalCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.522728589._hygCtx._hyg.3)))))))) r a) (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K (CommRing.toNonUnitalCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.522728589._hygCtx._hyg.3)))))))) r b)))","typeFull":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a b r : K},\n  0 < r → r • Set.Ioo a b = Set.Ioo (r * a) (r * b)","typeReadable":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a b r : K},\n  0 < r → r • Set.Ioo a b = Set.Ioo (r * a) (r * b)","typeReferences":[["PartialOrder","toPreorder"],["Field"],["Preorder","toLT"],["HMul","hMul"],["SMulZeroClass","toSMul"],["MulZeroClass","toSMulWithZero"],["CommRing","toNonUnitalCommRing"],["Set","Ioo"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Set","smulSet"],["instHSMul"],["Zero","toOfNat0"],["Semifield","toDivisionSemiring"],["Eq"],["SemilatticeInf","toPartialOrder"],["Lattice","toSemilatticeInf"],["IsStrictOrderedRing"],["Field","toCommRing"],["NonUnitalNonAssocSemiring","toDistrib"],["Set"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["Distrib","toMul"],["LinearOrder"],["DivisionSemiring","toSemiring"],["SMulWithZero","toSMulZeroClass"],["OfNat","ofNat"],["LT","lt"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["HSMul","hSMul"],["Field","toSemifield"],["instHMul"]],"valueReferences":[["IsStrictOrderedRing","toPosMulStrictMono"],["Field","toCommRing"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["MulZeroClass","toMul"],["DivisionSemiring","toSemiring"],["CommRing","toNonUnitalCommRing"],["DivisionSemiring","toGroupWithZero"],["PosMulReflectLE","toPosMulReflectLT"],["OrderIso","image_Ioo"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["OrderIso","mulLeft₀"],["Field","toSemifield"],["Semifield","toDivisionSemiring"],["PosMulStrictMono","toPosMulReflectLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["LinearOrderedField","smul_Iio"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Field.Pointwise.767270239._hygCtx._hyg.3 : Field.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.767270239._hygCtx._hyg.6 : LinearOrder.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.767270239._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K (Field.toSemifield.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.767270239._hygCtx._hyg.3))) (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.767270239._hygCtx._hyg.6))))] {a : K} {r : K}, (LT.lt.{u_1} K (Preorder.toLT.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K 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(instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K (CommRing.toNonUnitalCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.767270239._hygCtx._hyg.3)))))))) r a)))","typeFull":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a r : K},\n  0 < r → r • Set.Iio a = Set.Iio (r * a)","typeReadable":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a r : K},\n  0 < r → r • Set.Iio a = Set.Iio (r * a)","typeReferences":[["PartialOrder","toPreorder"],["Field"],["Preorder","toLT"],["HMul","hMul"],["SMulZeroClass","toSMul"],["Set","Iio"],["MulZeroClass","toSMulWithZero"],["CommRing","toNonUnitalCommRing"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Set","smulSet"],["instHSMul"],["Zero","toOfNat0"],["Semifield","toDivisionSemiring"],["Eq"],["SemilatticeInf","toPartialOrder"],["Lattice","toSemilatticeInf"],["IsStrictOrderedRing"],["Field","toCommRing"],["NonUnitalNonAssocSemiring","toDistrib"],["Set"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["Distrib","toMul"],["LinearOrder"],["DivisionSemiring","toSemiring"],["SMulWithZero","toSMulZeroClass"],["OfNat","ofNat"],["LT","lt"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["HSMul","hSMul"],["Field","toSemifield"],["instHMul"]],"valueReferences":[["IsStrictOrderedRing","toPosMulStrictMono"],["OrderIso","image_Iio"],["Field","toCommRing"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["MulZeroClass","toMul"],["DivisionSemiring","toSemiring"],["CommRing","toNonUnitalCommRing"],["DivisionSemiring","toGroupWithZero"],["PosMulReflectLE","toPosMulReflectLT"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["OrderIso","mulLeft₀"],["Field","toSemifield"],["Semifield","toDivisionSemiring"],["PosMulStrictMono","toPosMulReflectLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["LinearOrderedField","smul_Ioi"],"typeFallback":"forall 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(instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K (CommRing.toNonUnitalCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.2304703018._hygCtx._hyg.3)))))))) r a)))","typeFull":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a r : K},\n  0 < r → r • Set.Ioi a = Set.Ioi (r * a)","typeReadable":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a r : K},\n  0 < r → r • Set.Ioi a = Set.Ioi (r * a)","typeReferences":[["PartialOrder","toPreorder"],["Field"],["Preorder","toLT"],["HMul","hMul"],["SMulZeroClass","toSMul"],["MulZeroClass","toSMulWithZero"],["CommRing","toNonUnitalCommRing"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Set","smulSet"],["Set","Ioi"],["instHSMul"],["Zero","toOfNat0"],["Semifield","toDivisionSemiring"],["Eq"],["SemilatticeInf","toPartialOrder"],["Lattice","toSemilatticeInf"],["IsStrictOrderedRing"],["Field","toCommRing"],["NonUnitalNonAssocSemiring","toDistrib"],["Set"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["Distrib","toMul"],["LinearOrder"],["DivisionSemiring","toSemiring"],["SMulWithZero","toSMulZeroClass"],["OfNat","ofNat"],["LT","lt"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["HSMul","hSMul"],["Field","toSemifield"],["instHMul"]],"valueReferences":[["IsStrictOrderedRing","toPosMulStrictMono"],["Field","toCommRing"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["MulZeroClass","toMul"],["OrderIso","image_Ioi"],["DivisionSemiring","toSemiring"],["CommRing","toNonUnitalCommRing"],["DivisionSemiring","toGroupWithZero"],["PosMulReflectLE","toPosMulReflectLT"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["OrderIso","mulLeft₀"],["Field","toSemifield"],["Semifield","toDivisionSemiring"],["PosMulStrictMono","toPosMulReflectLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["LinearOrderedField","smul_Ioc"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Field.Pointwise.1666218686._hygCtx._hyg.3 : Field.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.1666218686._hygCtx._hyg.6 : LinearOrder.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.1666218686._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K (Field.toSemifield.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.1666218686._hygCtx._hyg.3))) (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.1666218686._hygCtx._hyg.6))))] {a : K} {b : K} {r : K}, (LT.lt.{u_1} K (Preorder.toLT.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K 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* a) (r * b)","typeReadable":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a b r : K},\n  0 < r → r • Set.Ioc a b = Set.Ioc (r * a) (r * 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{K : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Field.Pointwise.256921369._hygCtx._hyg.3 : Field.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.256921369._hygCtx._hyg.6 : LinearOrder.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.256921369._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K (Field.toSemifield.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.256921369._hygCtx._hyg.3))) (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.256921369._hygCtx._hyg.6))))] {a : K} {r : K}, (LT.lt.{u_1} K (Preorder.toLT.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K 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(MulZeroClass.toSMulWithZero.{u_1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K (CommRing.toNonUnitalCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.256921369._hygCtx._hyg.3))))))))))) r (Set.Ici.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.256921369._hygCtx._hyg.6))))) a)) (Set.Ici.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.256921369._hygCtx._hyg.6))))) (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K (CommRing.toNonUnitalCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.256921369._hygCtx._hyg.3)))))))) r a)))","typeFull":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a r : K},\n  0 < r → r • Set.Ici a = Set.Ici (r * a)","typeReadable":"∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {a r : K},\n  0 < r → r • Set.Ici a = Set.Ici (r * a)","typeReferences":[["PartialOrder","toPreorder"],["Field"],["Preorder","toLT"],["HMul","hMul"],["SMulZeroClass","toSMul"],["MulZeroClass","toSMulWithZero"],["CommRing","toNonUnitalCommRing"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Set","smulSet"],["instHSMul"],["Zero","toOfNat0"],["Semifield","toDivisionSemiring"],["Eq"],["SemilatticeInf","toPartialOrder"],["Lattice","toSemilatticeInf"],["IsStrictOrderedRing"],["Field","toCommRing"],["NonUnitalNonAssocSemiring","toDistrib"],["Set"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["Distrib","toMul"],["LinearOrder"],["DivisionSemiring","toSemiring"],["SMulWithZero","toSMulZeroClass"],["OfNat","ofNat"],["LT","lt"],["Set","Ici"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["HSMul","hSMul"],["Field","toSemifield"],["instHMul"]],"valueReferences":[["IsStrictOrderedRing","toPosMulStrictMono"],["Field","toCommRing"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["MulZeroClass","toMul"],["DivisionSemiring","toSemiring"],["CommRing","toNonUnitalCommRing"],["DivisionSemiring","toGroupWithZero"],["PosMulReflectLE","toPosMulReflectLT"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["DistribLattice","toLattice"],["MulZeroClass","toZero"],["OrderIso","image_Ici"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["OrderIso","mulLeft₀"],["Field","toSemifield"],["Semifield","toDivisionSemiring"],["PosMulStrictMono","toPosMulReflectLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["LinearOrderedField","smul_Icc"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Field.Pointwise.1706085340._hygCtx._hyg.3 : Field.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.1706085340._hygCtx._hyg.6 : LinearOrder.{u_1} K] [inst._@.Mathlib.Algebra.Order.Field.Pointwise.1706085340._hygCtx._hyg.9 : IsStrictOrderedRing.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K (Field.toSemifield.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.1706085340._hygCtx._hyg.3))) (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.1706085340._hygCtx._hyg.6))))] {a : K} {b : K} {r : K}, (LT.lt.{u_1} K (Preorder.toLT.{u_1} K (PartialOrder.toPreorder.{u_1} K (SemilatticeInf.toPartialOrder.{u_1} K (Lattice.toSemilatticeInf.{u_1} K (DistribLattice.toLattice.{u_1} K (instDistribLatticeOfLinearOrder.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.1706085340._hygCtx._hyg.6)))))) (OfNat.ofNat.{u_1} K 0 (Zero.toOfNat0.{u_1} K (MulZeroClass.toZero.{u_1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K (CommRing.toNonUnitalCommRing.{u_1} K (Field.toCommRing.{u_1} K inst._@.Mathlib.Algebra.Order.Field.Pointwise.1706085340._hygCtx._hyg.3))))))))) r) -> (Eq.{succ u_1} (Set.{u_1} K) (HSMul.hSMul.{u_1, u_1, u_1} K (Set.{u_1} K) (Set.{u_1} K) (instHSMul.{u_1, u_1} K (Set.{u_1} K) (Set.smulSet.{u_1, u_1} K K (SMulZeroClass.toSMul.{u_1, u_1} K K (MulZeroClass.toZero.{u_1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} K (NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing.{u_1} K (NonUnitalCommRing.toNonUnitalNonAssocCommRing.{u_1} K 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Hom.Submonoid.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Interval.Multiset.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["Multiset","map_add_right_Ioo"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Interval.Multiset.4114068709._hygCtx._hyg.3 : AddCommMonoid.{u_1} α] [inst._@.Mathlib.Algebra.Order.Interval.Multiset.4114068709._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Interval.Multiset.4114068709._hygCtx._hyg.9 : IsOrderedCancelAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.4114068709._hygCtx._hyg.3 (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.4114068709._hygCtx._hyg.6)] [inst._@.Mathlib.Algebra.Order.Interval.Multiset.4114068709._hygCtx._hyg.12 : ExistsAddOfLE.{u_1} α (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.4114068709._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α 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α),\n  Multiset.map (fun x => c + x) (Multiset.Icc a b) = Multiset.Icc (c + a) (c + b)","typeReferences":[["Multiset","map"],["PartialOrder","toPreorder"],["instHAdd"],["Multiset","Icc"],["Multiset"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["PartialOrder"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["PartialOrder","toPreorder"],["Finset"],["Finset","image_add_left_Icc"],["add_right_injective"],["Multiset","Icc"],["Classical","propDecidable"],["Multiset","Icc","eq_1"],["congrArg"],["Multiset","Nodup","dedup"],["Eq","symm"],["Finset","image_val"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["Multiset","map"],["Multiset","Nodup","map"],["Finset","val"],["instHAdd"],["Finset","nodup"],["Finset","Icc"],["Multiset"],["HAdd","hAdd"],["AddCommMonoid","toAddCommSemigroup"],["Eq","refl"],["Finset","image"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["instIsLeftCancelAddOfAddLeftReflectLE"],["id"],["Eq","mpr"],["Multiset","dedup"]]},{"isProp":true,"kind":"theorem","name":["Multiset","map_add_left_Ico"],"typeFallback":"forall 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LocallyFiniteOrder.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.361039034._hygCtx._hyg.6)] (a : α) (b : α) (c : α), Eq.{succ u_1} (Multiset.{u_1} α) (Multiset.map.{u_1, u_1} α α (fun (x._@.Mathlib.Algebra.Order.Interval.Multiset.361039034._hygCtx._hyg.32 : α) => HAdd.hAdd.{u_1, u_1, u_1} α α α (instHAdd.{u_1} α (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.361039034._hygCtx._hyg.3)))) c x._@.Mathlib.Algebra.Order.Interval.Multiset.361039034._hygCtx._hyg.32) (Multiset.Ico.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.361039034._hygCtx._hyg.6) inst._@.Mathlib.Algebra.Order.Interval.Multiset.361039034._hygCtx._hyg.15 a b)) (Multiset.Ico.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.361039034._hygCtx._hyg.6) 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α),\n  Multiset.map (fun x => c + x) (Multiset.Ico a b) = Multiset.Ico (c + a) (c + b)","typeReferences":[["Multiset","map"],["PartialOrder","toPreorder"],["instHAdd"],["Multiset"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["PartialOrder"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Multiset","Ico"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["PartialOrder","toPreorder"],["Finset"],["add_right_injective"],["Classical","propDecidable"],["congrArg"],["Multiset","Nodup","dedup"],["Eq","symm"],["Finset","image_val"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["Multiset","map"],["Multiset","Nodup","map"],["Finset","val"],["instHAdd"],["Finset","nodup"],["Multiset"],["HAdd","hAdd"],["AddCommMonoid","toAddCommSemigroup"],["Eq","refl"],["Finset","image"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["instIsLeftCancelAddOfAddLeftReflectLE"],["Finset","image_add_left_Ico"],["id"],["Multiset","Ico","eq_1"],["Finset","Ico"],["Eq","mpr"],["Multiset","dedup"],["Multiset","Ico"]]},{"isProp":true,"kind":"theorem","name":["Multiset","map_add_left_Ioo"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Interval.Multiset.447462470._hygCtx._hyg.3 : AddCommMonoid.{u_1} α] [inst._@.Mathlib.Algebra.Order.Interval.Multiset.447462470._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Interval.Multiset.447462470._hygCtx._hyg.9 : IsOrderedCancelAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.447462470._hygCtx._hyg.3 (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.447462470._hygCtx._hyg.6)] [inst._@.Mathlib.Algebra.Order.Interval.Multiset.447462470._hygCtx._hyg.12 : ExistsAddOfLE.{u_1} α (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.447462470._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Interval.Multiset.447462470._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Interval.Multiset.447462470._hygCtx._hyg.15 : 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α),\n  Multiset.map (fun x => c + x) (Multiset.Ioo a b) = Multiset.Ioo (c + a) (c + b)","typeReferences":[["Multiset","map"],["PartialOrder","toPreorder"],["instHAdd"],["Multiset"],["HAdd","hAdd"],["LocallyFiniteOrder"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["PartialOrder"],["Multiset","Ioo"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Preorder","toLE"],["Eq"],["ExistsAddOfLE"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["PartialOrder","toPreorder"],["Finset"],["Multiset","Ioo","eq_1"],["add_right_injective"],["Classical","propDecidable"],["congrArg"],["Finset","image_add_left_Ioo"],["Multiset","Nodup","dedup"],["Eq","symm"],["Finset","image_val"],["Multiset","Ioo"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["Multiset","map"],["Multiset","Nodup","map"],["Finset","val"],["instHAdd"],["Finset","nodup"],["Multiset"],["HAdd","hAdd"],["Finset","Ioo"],["AddCommMonoid","toAddCommSemigroup"],["Eq","refl"],["Finset","image"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["instIsLeftCancelAddOfAddLeftReflectLE"],["id"],["Eq","mpr"],["Multiset","dedup"]]},{"isProp":true,"kind":"theorem","name":["Multiset","map_add_left_Ioc"],"typeFallback":"forall 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Monoid.Basic.sym.json

@@ -0,0 +1 @@
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[IsOrderedAddMonoid α]\n  [inst_3 : AddCommMonoid β] [inst_4 : Preorder β] (f : β → α),\n  (∀ (x y : β), f (x + y) = f x + f y) → (∀ {x y : β}, f x ≤ f y ↔ x ≤ y) → IsOrderedAddMonoid 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x2._@.Mathlib.Order.Hom.Basic.1911761181._hygCtx._hyg.33)) (OrderEmbedding.addRight.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.17 m) n) (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.11) n m)","typeFull":"∀ {α : Type u_2} [inst : Add α] [inst_1 : LinearOrder α] [inst_2 : AddRightStrictMono α] (m n : α),\n  (OrderEmbedding.addRight m) n = n + m","typeReadable":"∀ {α : Type u_2} [inst : Add α] [inst_1 : LinearOrder α] [inst_2 : AddRightStrictMono α] (m n : α),\n  (OrderEmbedding.addRight m) n = n + m","typeReferences":[["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["AddRightStrictMono"],["instHAdd"],["Add"],["LinearOrder"],["Preorder","toLT"],["DFunLike","coe"],["RelEmbedding","instFunLike"],["HAdd","hAdd"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["OrderEmbedding","addRight"],["LE","le"],["Preorder","toLE"],["Eq"],["RelEmbedding"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["Eq","refl"],["OrderEmbedding","addRight"],["LE","le"],["Preorder","toLE"],["RelEmbedding"],["DFunLike","coe"],["RelEmbedding","instFunLike"],["SemilatticeInf","toPartialOrder"]]},{"isProp":false,"kind":"definition","name":["OrderEmbedding","mulRight"],"typeFallback":"forall {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.11 : Mul.{u_2} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.14 : LinearOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.17 : MulRightStrictMono.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.11 (Preorder.toLT.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.14))))))], α -> (OrderEmbedding.{u_2, u_2} α α (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.14)))))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.14)))))))","typeFull":"{α : Type u_2} → [inst : Mul α] → [inst_1 : LinearOrder α] → [MulRightStrictMono α] → α → α ↪o α","typeReadable":"{α : Type u_2} → [inst : Mul α] → [inst_1 : LinearOrder α] → [MulRightStrictMono α] → α → α ↪o α","typeReferences":[["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["MulRightStrictMono"],["Mul"],["Preorder","toLT"],["LinearOrder"],["Preorder","toLE"],["OrderEmbedding"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["OrderEmbedding","mulRight","_proof_1"],["OrderEmbedding","ofStrictMono"],["instHMul"],["HMul","hMul"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["StrictMono","isOrderedAddMonoid"],"typeFallback":"forall {α : Type.{u}} {β : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.4 : AddCommMonoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.7 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.10 : IsOrderedAddMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.7] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.13 : AddCommMonoid.{u_1} β] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.16 : LinearOrder.{u_1} β] (f : β -> α), (StrictMono.{u_1, u} β α (PartialOrder.toPreorder.{u_1} β (SemilatticeInf.toPartialOrder.{u_1} β (Lattice.toSemilatticeInf.{u_1} β (DistribLattice.toLattice.{u_1} β (instDistribLatticeOfLinearOrder.{u_1} β inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.16))))) inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.7 f) -> (forall (x : β) (y : β), Eq.{succ u} α (f (HAdd.hAdd.{u_1, u_1, u_1} β β β (instHAdd.{u_1} β (AddZero.toAdd.{u_1} β (AddZeroClass.toAddZero.{u_1} β (AddMonoid.toAddZeroClass.{u_1} β (AddCommMonoid.toAddMonoid.{u_1} β inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.13))))) x y)) 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inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.17 m))","typeFull":"∀ {α : Type u_2} [inst : Add α] [inst_1 : LinearOrder α] [inst_2 : AddLeftStrictMono α] (m : α),\n  OrderEmbedding.addLeft m = OrderEmbedding.ofStrictMono (fun n => m + n) ⋯","typeReadable":"∀ {α : Type u_2} [inst : Add α] [inst_1 : LinearOrder α] [inst_2 : AddLeftStrictMono α] (m : α),\n  OrderEmbedding.addLeft m = OrderEmbedding.ofStrictMono (fun n => m + n) 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inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.7] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.13 : CommMonoid.{u_1} β] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.16 : LinearOrder.{u_1} β] (f : β -> α), (StrictMono.{u_1, u} β α (PartialOrder.toPreorder.{u_1} β (SemilatticeInf.toPartialOrder.{u_1} β (Lattice.toSemilatticeInf.{u_1} β (DistribLattice.toLattice.{u_1} β (instDistribLatticeOfLinearOrder.{u_1} β inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.16))))) inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.7 f) -> (forall (x : β) (y : β), Eq.{succ u} α (f (HMul.hMul.{u_1, u_1, u_1} β β β (instHMul.{u_1} β (MulOne.toMul.{u_1} β (MulOneClass.toMulOne.{u_1} β (Monoid.toMulOneClass.{u_1} β (CommMonoid.toMonoid.{u_1} β inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453975._hygCtx._hyg.13))))) x y)) (HMul.hMul.{u, u, u} α α α (instHMul.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} 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[inst : Add α] → [inst_1 : LinearOrder α] → [AddRightStrictMono α] → α → α ↪o α","typeReferences":[["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["AddRightStrictMono"],["Add"],["Preorder","toLT"],["LinearOrder"],["Preorder","toLE"],["OrderEmbedding"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["HAdd","hAdd"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["instHAdd"],["OrderEmbedding","ofStrictMono"],["OrderEmbedding","addRight","_proof_1"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["StrictMono","isOrderedCancelMonoid"],"typeFallback":"forall {α : Type.{u}} {β : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.4 : CommMonoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.7 : Preorder.{u} α] 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{α : Type.{u}} {β : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638665._hygCtx._hyg.4 : CommMonoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638665._hygCtx._hyg.7 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638665._hygCtx._hyg.10 : IsOrderedCancelMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638665._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638665._hygCtx._hyg.7] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638665._hygCtx._hyg.13 : CommMonoid.{u_1} β] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638665._hygCtx._hyg.16 : Preorder.{u_1} β] (f : β -> α), (forall (x : β) (y : β), Eq.{succ u} α (f (HMul.hMul.{u_1, u_1, u_1} β β β (instHMul.{u_1} β (MulOne.toMul.{u_1} β (MulOneClass.toMulOne.{u_1} β (Monoid.toMulOneClass.{u_1} β (CommMonoid.toMonoid.{u_1} β inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638665._hygCtx._hyg.13))))) x y)) (HMul.hMul.{u, u, u} α α α (instHMul.{u} α (MulOne.toMul.{u} α 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inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.17 m) n) (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.11) m n)","typeFull":"∀ {α : Type u_2} [inst : Add α] [inst_1 : LinearOrder α] [inst_2 : AddLeftStrictMono α] (m n : α),\n  (OrderEmbedding.addLeft m) n = m + n","typeReadable":"∀ {α : Type u_2} [inst : Add α] [inst_1 : LinearOrder α] [inst_2 : AddLeftStrictMono α] (m n : α),\n  (OrderEmbedding.addLeft m) n = m + 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[inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.14 : LinearOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.17 : AddLeftStrictMono.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.11 (Preorder.toLT.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.14))))))], α -> (OrderEmbedding.{u_2, u_2} α α (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.14)))))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.3455109452._hygCtx._hyg.14)))))))","typeFull":"{α : Type u_2} → [inst : Add α] → [inst_1 : LinearOrder α] → [AddLeftStrictMono α] → α → α ↪o α","typeReadable":"{α : Type u_2} → [inst : Add α] → [inst_1 : LinearOrder α] → [AddLeftStrictMono α] → α → α ↪o α","typeReferences":[["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["Add"],["AddLeftStrictMono"],["Preorder","toLT"],["LinearOrder"],["Preorder","toLE"],["OrderEmbedding"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["HAdd","hAdd"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["OrderEmbedding","addLeft","_proof_1"],["instHAdd"],["OrderEmbedding","ofStrictMono"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["StrictMono","isOrderedAddCancelMonoid"],"typeFallback":"forall {α : Type.{u}} {β : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.4 : AddCommMonoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.7 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.10 : IsOrderedCancelAddMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.7] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.13 : AddCommMonoid.{u_1} β] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.16 : LinearOrder.{u_1} β] (f : β -> α), (StrictMono.{u_1, u} β α (PartialOrder.toPreorder.{u_1} β (SemilatticeInf.toPartialOrder.{u_1} β (Lattice.toSemilatticeInf.{u_1} β (DistribLattice.toLattice.{u_1} β (instDistribLatticeOfLinearOrder.{u_1} β inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.16))))) inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.7 f) -> (forall (x : β) (y : β), Eq.{succ u} α (f (HAdd.hAdd.{u_1, u_1, u_1} β β β (instHAdd.{u_1} β (AddZero.toAdd.{u_1} β (AddZeroClass.toAddZero.{u_1} β (AddMonoid.toAddZeroClass.{u_1} β (AddCommMonoid.toAddMonoid.{u_1} β inst._@.Mathlib.Algebra.Order.Monoid.Basic.2396638666._hygCtx._hyg.13))))) x y)) 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[IsOrderedCancelAddMonoid α]\n  [inst_3 : AddCommMonoid β] [inst_4 : LinearOrder β] (f : β → α),\n  StrictMono f → (∀ (x y : β), f (x + y) = f x + f y) → IsOrderedCancelAddMonoid 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{α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.11 : Mul.{u_2} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.14 : LinearOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.17 : MulRightStrictMono.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.11 (Preorder.toLT.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.14))))))] (m : α), Eq.{succ u_2} (OrderEmbedding.{u_2, u_2} α α (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.14)))))) 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inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.11) n m) (OrderEmbedding.mulRight._proof_1.{u_2} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.11 inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Order.Monoid.Basic.1264609845._hygCtx._hyg.17 m))","typeFull":"∀ {α : Type u_2} [inst : Mul α] [inst_1 : LinearOrder α] [inst_2 : MulRightStrictMono α] (m : α),\n  OrderEmbedding.mulRight m = OrderEmbedding.ofStrictMono (fun n => n * m) ⋯","typeReadable":"∀ {α : Type u_2} [inst : Mul α] [inst_1 : LinearOrder α] [inst_2 : MulRightStrictMono α] (m : α),\n  OrderEmbedding.mulRight m = OrderEmbedding.ofStrictMono (fun n => n * m) 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Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453974._hygCtx._hyg.10 : IsOrderedMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453974._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453974._hygCtx._hyg.7] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453974._hygCtx._hyg.13 : CommMonoid.{u_1} β] [inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453974._hygCtx._hyg.16 : Preorder.{u_1} β] (f : β -> α), (forall (x : β) (y : β), Eq.{succ u} α (f (HMul.hMul.{u_1, u_1, u_1} β β β (instHMul.{u_1} β (MulOne.toMul.{u_1} β (MulOneClass.toMulOne.{u_1} β (Monoid.toMulOneClass.{u_1} β (CommMonoid.toMonoid.{u_1} β inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453974._hygCtx._hyg.13))))) x y)) (HMul.hMul.{u, u, u} α α α (instHMul.{u} α (MulOne.toMul.{u} α (MulOneClass.toMulOne.{u} α (Monoid.toMulOneClass.{u} α (CommMonoid.toMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.Basic.4051453974._hygCtx._hyg.4))))) (f x) (f y))) -> (forall {x : β} {y : β}, Iff 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Monoid.TypeTags.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Sub.Prod.sym.json

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+[{"isProp":true,"kind":"theorem","name":["Prod","orderedSub"],"typeFallback":"forall {α : Type.{u_1}} {β : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.4 : Preorder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.7 : Add.{u_1} α] [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.10 : Sub.{u_1} α] [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.13 : OrderedSub.{u_1} α (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.4) inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.10] [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.16 : Sub.{u_2} β] [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.19 : Preorder.{u_2} β] [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.22 : Add.{u_2} β] [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.25 : OrderedSub.{u_2} β (Preorder.toLE.{u_2} β inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.19) inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.22 inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.16], OrderedSub.{max u_2 u_1} (Prod.{u_1, u_2} α β) (Prod.instLE_mathlib.{u_1, u_2} α β (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.4) (Preorder.toLE.{u_2} β inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.19)) (Prod.instAdd.{u_1, u_2} α β inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.22) (Prod.instSub.{u_1, u_2} α β inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992951._hygCtx._hyg.16)","typeFull":"∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Add α] [inst_2 : Sub α] [OrderedSub α] [inst_4 : Sub β]\n  [inst_5 : Preorder β] [inst_6 : Add β] [OrderedSub β], OrderedSub (α × β)","typeReadable":"∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Add α] [inst_2 : Sub α] [OrderedSub α] [inst_4 : Sub β]\n  [inst_5 : Preorder β] [inst_6 : Add β] [OrderedSub β], OrderedSub (α × β)","typeReferences":[["Prod"],["Preorder"],["Add"],["OrderedSub"],["Prod","instLE_mathlib"],["Sub"],["Preorder","toLE"],["Prod","instSub"],["Prod","instAdd"]],"valueReferences":[["instHAdd"],["And","right"],["Iff","mp"],["Prod","snd"],["Prod","instAdd"],["Prod","instSub"],["Prod","fst"],["Iff","intro"],["Prod"],["HAdd","hAdd"],["And","intro"],["Iff","mpr"],["tsub_le_iff_right"],["LE","le"],["HSub","hSub"],["Prod","instLE_mathlib"],["OrderedSub","mk"],["Preorder","toLE"],["instHSub"],["And","left"]]},{"isProp":true,"kind":"theorem","name":["Pi","orderedSub"],"typeFallback":"forall {ι : Type.{u_3}} {α : ι -> Type.{u_4}} [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992952._hygCtx._hyg.8 : forall (i : ι), Preorder.{u_4} (α i)] [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992952._hygCtx._hyg.17 : forall (i : ι), Add.{u_4} (α i)] [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992952._hygCtx._hyg.26 : forall (i : ι), Sub.{u_4} (α i)] [inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992952._hygCtx._hyg.35 : forall (i : ι), OrderedSub.{u_4} (α i) (Preorder.toLE.{u_4} (α i) (inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992952._hygCtx._hyg.8 i)) (inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992952._hygCtx._hyg.17 i) (inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992952._hygCtx._hyg.26 i)], OrderedSub.{max u_3 u_4} (forall (i : ι), α i) (Pi.hasLe.{u_3, u_4} ι α (fun (i : ι) => Preorder.toLE.{u_4} (α i) (inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992952._hygCtx._hyg.8 i))) (Pi.instAdd.{u_3, u_4} ι α inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992952._hygCtx._hyg.17) (Pi.instSub.{u_3, u_4} ι α inst._@.Mathlib.Algebra.Order.Sub.Prod.2522992952._hygCtx._hyg.26)","typeFull":"∀ {ι : Type u_3} {α : ι → Type u_4} [inst : (i : ι) → Preorder (α i)] [inst_1 : (i : ι) → Add (α i)]\n  [inst_2 : (i : ι) → Sub (α i)] [∀ (i : ι), OrderedSub (α i)], OrderedSub ((i : ι) → α i)","typeReadable":"∀ {ι : Type u_3} {α : ι → Type u_4} [inst : (i : ι) → Preorder (α i)] [inst_1 : (i : ι) → Add (α i)]\n  [inst_2 : (i : ι) → Sub (α i)] [∀ (i : ι), OrderedSub (α i)], OrderedSub ((i : ι) → α i)","typeReferences":[["Pi","instAdd"],["Preorder"],["Pi","instSub"],["Add"],["Pi","hasLe"],["OrderedSub"],["Sub"],["Preorder","toLE"]],"valueReferences":[["Pi","instSub"],["instHAdd"],["Pi","hasLe"],["Iff","mp"],["Iff","intro"],["HAdd","hAdd"],["Pi","instAdd"],["Iff","mpr"],["LE","le"],["tsub_le_iff_right"],["HSub","hSub"],["OrderedSub","mk"],["Preorder","toLE"],["instHSub"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Polynomial.Monomial.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Ring.Hom.InjSurj.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Ring.Idempotent.sym.json

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