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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.Balance.sym.json

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

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{M : Type.{u_1}} {N : Type.{u_2}} [inst._@.Mathlib.Algebra.BigOperators.GroupWithZero.Action.342036750._hygCtx._hyg.5 : Monoid.{u_1} M] [inst._@.Mathlib.Algebra.BigOperators.GroupWithZero.Action.342036750._hygCtx._hyg.8 : CommMonoid.{u_2} N] [inst._@.Mathlib.Algebra.BigOperators.GroupWithZero.Action.342036750._hygCtx._hyg.11 : MulDistribMulAction.{u_1, u_2} M N inst._@.Mathlib.Algebra.BigOperators.GroupWithZero.Action.342036750._hygCtx._hyg.5 (CommMonoid.toMonoid.{u_2} N inst._@.Mathlib.Algebra.BigOperators.GroupWithZero.Action.342036750._hygCtx._hyg.8)] {ι : Sort.{u_4}} [inst._@.Mathlib.Algebra.BigOperators.GroupWithZero.Action.342036750._hygCtx._hyg.16 : Finite.{u_4} ι] {f : ι -> N} (r : M), Eq.{succ u_2} N (HSMul.hSMul.{u_1, u_2, u_2} M N N (instHSMul.{u_1, u_2} M N (SemigroupAction.toSMul.{u_1, u_2} M N (Monoid.toSemigroup.{u_1} M inst._@.Mathlib.Algebra.BigOperators.GroupWithZero.Action.342036750._hygCtx._hyg.5) (MulAction.toSemigroupAction.{u_1, u_2} M N 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.RingEquiv.sym.json

@@ -0,0 +1 @@
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(Distrib.toAdd.{u_3} S (NonUnitalNonAssocSemiring.toDistrib.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S (CommSemiring.toSemiring.{u_3} S inst._@.Mathlib.Algebra.BigOperators.RingEquiv.3632911669._hygCtx._hyg.8)))))) R (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : R) => S) (EquivLike.toFunLike.{max (succ u_2) (succ u_3), succ u_2, succ u_3} (RingEquiv.{u_2, u_3} R S (Distrib.toMul.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (CommSemiring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.BigOperators.RingEquiv.3632911669._hygCtx._hyg.5))))) (Distrib.toMul.{u_3} S (NonUnitalNonAssocSemiring.toDistrib.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S (CommSemiring.toSemiring.{u_3} S inst._@.Mathlib.Algebra.BigOperators.RingEquiv.3632911669._hygCtx._hyg.8))))) (Distrib.toAdd.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (CommSemiring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.BigOperators.RingEquiv.3632911669._hygCtx._hyg.5))))) (Distrib.toAdd.{u_3} S (NonUnitalNonAssocSemiring.toDistrib.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S (CommSemiring.toSemiring.{u_3} S inst._@.Mathlib.Algebra.BigOperators.RingEquiv.3632911669._hygCtx._hyg.8)))))) R S (RingEquiv.instEquivLike.{u_2, u_3} R S (Distrib.toMul.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (CommSemiring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.BigOperators.RingEquiv.3632911669._hygCtx._hyg.5))))) (Distrib.toMul.{u_3} S (NonUnitalNonAssocSemiring.toDistrib.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S (CommSemiring.toSemiring.{u_3} S inst._@.Mathlib.Algebra.BigOperators.RingEquiv.3632911669._hygCtx._hyg.8))))) (Distrib.toAdd.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (CommSemiring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.BigOperators.RingEquiv.3632911669._hygCtx._hyg.5))))) (Distrib.toAdd.{u_3} S (NonUnitalNonAssocSemiring.toDistrib.{u_3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S (CommSemiring.toSemiring.{u_3} S inst._@.Mathlib.Algebra.BigOperators.RingEquiv.3632911669._hygCtx._hyg.8))))))) f) s))","typeFull":"∀ {R : Type u_2} {S : Type u_3} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f : R ≃+* S) (s : Multiset R),\n  f s.prod = (Multiset.map (⇑f) s).prod","typeReadable":"∀ {R : Type u_2} {S : Type u_3} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f : R ≃+* S) (s : Multiset R),\n  f s.prod = (Multiset.map (⇑f) 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.Projective.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["IsProjective","iff_projective"],"typeFallback":"forall {R : Type.{u}} [inst._@.Mathlib.Algebra.Category.ModuleCat.Projective.591963975._hygCtx._hyg.3 : Ring.{u} R] [inst._@.Mathlib.Algebra.Category.ModuleCat.Projective.591963975._hygCtx._hyg.8 : Small.{v, u} R] (P : Type.{v}) [inst._@.Mathlib.Algebra.Category.ModuleCat.Projective.591963975._hygCtx._hyg.12 : AddCommGroup.{v} P] [inst._@.Mathlib.Algebra.Category.ModuleCat.Projective.591963975._hygCtx._hyg.15 : Module.{u, v} R P (Ring.toSemiring.{u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Projective.591963975._hygCtx._hyg.3) (AddCommGroup.toAddCommMonoid.{v} P inst._@.Mathlib.Algebra.Category.ModuleCat.Projective.591963975._hygCtx._hyg.12)], Iff (Module.Projective.{u, v} R (Ring.toSemiring.{u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Projective.591963975._hygCtx._hyg.3) P (AddCommGroup.toAddCommMonoid.{v} P inst._@.Mathlib.Algebra.Category.ModuleCat.Projective.591963975._hygCtx._hyg.12) 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.CharZero.Defs.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.ContinuedFractions.Computation.ApproximationCorollaries.sym.json

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[inst_1 : AddCommGroup α] [inst_2 : LinearOrder α]\n  [IsOrderedAddMonoid α] [OrderTopology α] {f : β → α} {x : Filter β} {a : α},\n  Filter.Tendsto f x (nhds a) = ∀ ε > 0, ∀ᶠ (b : β) in x, |f b - a| < ε","typeReadable":"∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : AddCommGroup α] [inst_2 : LinearOrder α]\n  [IsOrderedAddMonoid α] [OrderTopology α] {f : β → α} {x : Filter β} {a : α},\n  Filter.Tendsto f x (nhds a) = ∀ ε > 0, ∀ᶠ (b : β) in x, |f b - a| < 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.DirectSum.Idempotents.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Field.GeomSum.sym.json

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

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Fin.Basic.sym.json

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

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

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.DerivedCategory.Linear.sym.json

@@ -0,0 +1 @@
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C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.17) (DerivedCategory.instLinear.{t, w, v, u} R inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.3 C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.17) (DerivedCategory.instLinear.{t, w, v, u} R inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.3 C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.17) (CategoryTheory.shiftFunctor.{w, max u v, 0} (DerivedCategory.{w, v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.17) Int (instCategoryDerivedCategory.{w, u, v} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.17) Int.instAddMonoid (DerivedCategory.instHasShiftInt.{w, v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2115643472._hygCtx._hyg.17) n)","typeFull":"∀ (R : Type t) [inst : Ring R] (C : Type u) [inst_1 : CategoryTheory.Category.{v, u} C]\n  [inst_2 : CategoryTheory.Abelian C] [inst_3 : CategoryTheory.Linear R C] [inst_4 : HasDerivedCategory C] (n : ℤ),\n  CategoryTheory.Functor.Linear R (CategoryTheory.shiftFunctor (DerivedCategory C) n)","typeReadable":"∀ (R : Type t) [inst : Ring R] (C : Type u) [inst_1 : CategoryTheory.Category.{v, u} C]\n  [inst_2 : CategoryTheory.Abelian C] [inst_3 : CategoryTheory.Linear R C] [inst_4 : HasDerivedCategory C] (n : ℤ),\n  CategoryTheory.Functor.Linear R (CategoryTheory.shiftFunctor (DerivedCategory C) n)","typeReferences":[["CategoryTheory","Abelian"],["CategoryTheory","Linear"],["HasDerivedCategory"],["DerivedCategory","instLinear"],["CategoryTheory","Category"],["DerivedCategory","instPreadditive"],["DerivedCategory","instHasShiftInt"],["Ring","toSemiring"],["CategoryTheory","Abelian","toPreadditive"],["Int"],["instCategoryDerivedCategory"],["CategoryTheory","Functor","Linear"],["DerivedCategory"],["CategoryTheory","shiftFunctor"],["Int","instAddMonoid"],["Ring"]],"valueReferences":[["instIsRightCancelAddOfAddRightReflectLE"],["contravariant_swap_add_of_contravariant_add"],["PartialOrder","toPreorder"],["AddGroupWithOne","toAddMonoidWithOne"],["DerivedCategory","instPreadditive"],["DerivedCategory","instHasShiftInt"],["DerivedCategory","instIsLocalizationHomotopyCategoryIntUpQhTrWSubcategoryAcyclic"],["HomotopyCategory","instLinearIntUpShiftFunctor"],["Ring","toAddGroupWithOne"],["CategoryTheory","Abelian","hasZeroObject"],["SemilatticeInf","toPartialOrder"],["instLatticeInt"],["HomotopyCategory","hasShift"],["DerivedCategory","instLinear"],["CategoryTheory","Abelian","toPreadditive"],["Ring","toSemiring"],["DerivedCategory"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["instIsLeftCancelAddOfAddLeftReflectLE"],["AddMonoidWithOne","toOne"],["instCategoryHomotopyCategory"],["Int","instAddCommMonoid"],["DerivedCategory","instLinearHomotopyCategoryIntUpQh"],["HomotopyCategory"],["DerivedCategory","instCommShiftHomotopyCategoryIntUpQh"],["HomotopyCategory","instAdditiveIntUpShiftFunctor"],["HomotopyCategory","instPreadditive"],["Int","instAddCommSemigroup"],["ComplexShape","up"],["HomotopyCategory","instHasZeroObject"],["CategoryTheory","Shift","linear_of_localization"],["Int","instRing"],["instCategoryDerivedCategory"],["CategoryTheory","ObjectProperty","trW"],["contravariant_lt_of_covariant_le"],["Int","instIsStrictOrderedRing"],["Int","instAdd"],["CategoryTheory","Abelian","hasBinaryBiproducts"],["Int","instAddLeftMono"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["HomotopyCategory","instLinear"],["IsLeftCancelAdd","addLeftReflectLE_of_addLeftReflectLT"],["Preorder","toLE"],["DerivedCategory","Qh"],["IsStrictOrderedRing","toIsOrderedCancelAddMonoid"],["Int","instLinearOrder"],["HomotopyCategory","subcategoryAcyclic"],["Lattice","toSemilatticeInf"],["instHAdd"],["Int"],["HAdd","hAdd"],["Int","instSemiring"],["LE","le"],["HomotopyCategory","instPretriangulatedIntUp"],["Int","instAddMonoid"]]},{"isProp":true,"kind":"theorem","name":["DerivedCategory","instLinearHomotopyCategoryIntUpQh"],"typeFallback":"forall (R : Type.{t}) [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.3 : Ring.{t} R] (C : Type.{u}) [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 : CategoryTheory.Category.{v, u} C] [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.10 : CategoryTheory.Abelian.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7] [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.13 : CategoryTheory.Linear.{t, v, u} R (Ring.toSemiring.{t} R inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.3) C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.10)] [inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.17 : HasDerivedCategory.{w, v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.10], CategoryTheory.Functor.Linear.{t, v, max u v, w, max u v} R (Ring.toSemiring.{t} R inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.3) (HomotopyCategory.{v, u, 0} Int C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.10) (ComplexShape.up.{0} Int Int.instAdd (instIsRightCancelAddOfAddRightReflectLE.{0} Int Int.instAdd (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) 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(IsOrderedCancelAddMonoid.toAddLeftReflectLE.{0} Int Int.instAddCommMonoid (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt))) (IsStrictOrderedRing.toIsOrderedCancelAddMonoid.{0} Int Int.instSemiring (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) Int.instIsStrictOrderedRing))) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_lt_of_covariant_le.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) => HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26) Int.instLinearOrder Int.instAddLeftMono)))) (AddMonoidWithOne.toOne.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRing))))) (DerivedCategory.{w, v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.17) (instCategoryHomotopyCategory.{v, u, 0} Int C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.10) (ComplexShape.up.{0} Int Int.instAdd (instIsRightCancelAddOfAddRightReflectLE.{0} Int Int.instAdd (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) 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(IsOrderedCancelAddMonoid.toAddLeftReflectLE.{0} Int Int.instAddCommMonoid (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt))) (IsStrictOrderedRing.toIsOrderedCancelAddMonoid.{0} Int Int.instSemiring (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) Int.instIsStrictOrderedRing))) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_lt_of_covariant_le.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) => HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26) Int.instLinearOrder Int.instAddLeftMono)))) (AddMonoidWithOne.toOne.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRing))))) (instCategoryDerivedCategory.{w, u, v} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.17) (HomotopyCategory.instPreadditive.{v, u, 0} Int C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.10) (ComplexShape.up.{0} Int Int.instAdd (instIsRightCancelAddOfAddRightReflectLE.{0} Int Int.instAdd (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_swap_add_of_contravariant_add.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) => LE.le.{0} Int (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41) Int.instAddCommSemigroup (IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (instIsLeftCancelAddOfAddLeftReflectLE.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (IsOrderedCancelAddMonoid.toAddLeftReflectLE.{0} Int Int.instAddCommMonoid (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt))) (IsStrictOrderedRing.toIsOrderedCancelAddMonoid.{0} Int Int.instSemiring (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) Int.instIsStrictOrderedRing))) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_lt_of_covariant_le.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) => HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26) Int.instLinearOrder Int.instAddLeftMono)))) (AddMonoidWithOne.toOne.{0} Int (AddGroupWithOne.toAddMonoidWithOne.{0} Int (Ring.toAddGroupWithOne.{0} Int Int.instRing))))) (DerivedCategory.instPreadditive.{w, v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.17) (HomotopyCategory.instLinear.{v, u, t, 0} R (Ring.toSemiring.{t} R inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.3) Int C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 (CategoryTheory.Abelian.toPreadditive.{v, u} C inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Homology.DerivedCategory.Linear.2146928131._hygCtx._hyg.10) (ComplexShape.up.{0} Int Int.instAdd (instIsRightCancelAddOfAddRightReflectLE.{0} Int Int.instAdd (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_swap_add_of_contravariant_add.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 : Int) => LE.le.{0} Int (Preorder.toLE.{0} Int (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)))) x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41 x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.2774610127._hygCtx._hyg.41) Int.instAddCommSemigroup (IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (instIsLeftCancelAddOfAddLeftReflectLE.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup)) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (IsOrderedCancelAddMonoid.toAddLeftReflectLE.{0} Int Int.instAddCommMonoid (PartialOrder.toPreorder.{0} Int (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt))) (IsStrictOrderedRing.toIsOrderedCancelAddMonoid.{0} Int Int.instSemiring (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) Int.instIsStrictOrderedRing))) (SemilatticeInf.toPartialOrder.{0} Int (Lattice.toSemilatticeInf.{0} Int instLatticeInt)) (contravariant_lt_of_covariant_le.{0} Int (fun (x1._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) (x2._@.Mathlib.Algebra.Order.Monoid.Unbundled.Defs.574338266._hygCtx._hyg.26 : Int) => HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int (AddCommMagma.toAdd.{0} Int (AddCommSemigroup.toAddCommMagma.{0} Int Int.instAddCommSemigroup))) 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Pi.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.MvPolynomial.Nilpotent.sym.json

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+[{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Algebra","MvPolynomial","Nilpotent",0,"MvPolynomial","isNilpotent_iff_of_fintype","_simp_1_1"],"typeFallback":"forall {α : Sort.{u_1}} [inst._@.Mathlib.Logic.Unique.1013877062._hygCtx._hyg.3 : Unique.{u_1} α] {p : α -> Prop}, Eq.{1} Prop (forall (a : α), p a) (p (Inhabited.default.{u_1} α (Unique.instInhabited.{u_1} α inst._@.Mathlib.Logic.Unique.1013877062._hygCtx._hyg.3)))","typeFull":"∀ {α : Sort u_1} [inst : Unique α] {p : α → Prop}, (∀ (a : α), p a) = p default","typeReadable":"∀ {α : Sort u_1} [inst : Unique α] {p : α → Prop}, (∀ (a : α), p a) = p default","typeReferences":[["Unique"],["Eq"],["Unique","instInhabited"],["Inhabited","default"]],"valueReferences":[["Unique","forall_iff"],["propext"],["Unique","instInhabited"],["Inhabited","default"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Algebra","MvPolynomial","Nilpotent",0,"MvPolynomial","instIsReduced","_simp_3"],"typeFallback":"forall {R : Type.{u}} {σ : Type.{u_1}} [inst._@.Mathlib.Algebra.MvPolynomial.Basic.722126854._hygCtx._hyg.23 : CommSemiring.{u} R] {p : MvPolynomial.{u_1, u} σ R inst._@.Mathlib.Algebra.MvPolynomial.Basic.722126854._hygCtx._hyg.23} {q : MvPolynomial.{u_1, u} σ R inst._@.Mathlib.Algebra.MvPolynomial.Basic.722126854._hygCtx._hyg.23}, Eq.{1} Prop (Eq.{max (succ u) (succ u_1)} (MvPolynomial.{u_1, u} σ R inst._@.Mathlib.Algebra.MvPolynomial.Basic.722126854._hygCtx._hyg.23) p q) (forall (m : Finsupp.{u_1, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)), Eq.{succ u} R (MvPolynomial.coeff.{u, u_1} R σ inst._@.Mathlib.Algebra.MvPolynomial.Basic.722126854._hygCtx._hyg.23 m p) (MvPolynomial.coeff.{u, u_1} R σ inst._@.Mathlib.Algebra.MvPolynomial.Basic.722126854._hygCtx._hyg.23 m q))","typeFull":"∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {p q : MvPolynomial σ R},\n  (p = q) = ∀ (m : σ →₀ ℕ), MvPolynomial.coeff m p = MvPolynomial.coeff m q","typeReadable":"∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {p q : MvPolynomial σ R},\n  (p = q) = ∀ (m : σ →₀ ℕ), MvPolynomial.coeff m p = MvPolynomial.coeff m q","typeReferences":[["Nat"],["MulZeroClass","toZero"],["MvPolynomial"],["CommSemiring"],["MvPolynomial","coeff"],["Nat","instMulZeroClass"],["Eq"],["Finsupp"]],"valueReferences":[["Nat"],["MvPolynomial","ext_iff"],["MulZeroClass","toZero"],["MvPolynomial"],["MvPolynomial","coeff"],["Nat","instMulZeroClass"],["Eq"],["Finsupp"],["propext"]]},{"isProp":true,"kind":"definition","name":["_private","Mathlib","Algebra","MvPolynomial","Nilpotent",0,"MvPolynomial","isUnit_iff","match_1_1"],"typeFallback":"forall {σ : Type.{u_2}} {R : Type.{u_1}} [inst._@.Mathlib.Algebra.MvPolynomial.Nilpotent.2423739694._hygCtx._hyg.4 : CommRing.{u_1} R] {P : MvPolynomial.{u_2, u_1} σ R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.Algebra.MvPolynomial.Nilpotent.2423739694._hygCtx._hyg.4)} (motive : (And (IsUnit.{u_1} R (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} 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(MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R (CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.Algebra.MvPolynomial.Nilpotent.2423739694._hygCtx._hyg.4)))) (MvPolynomial.coeff.{u_1, u_2} R σ (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.Algebra.MvPolynomial.Nilpotent.2423739694._hygCtx._hyg.4) (OfNat.ofNat.{u_2} (Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)) 0 (Zero.toOfNat0.{u_2} (Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)) (Finsupp.instZero.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)))) P)) (forall (i : Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)), (Ne.{succ u_2} (Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)) i (OfNat.ofNat.{u_2} (Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)) 0 (Zero.toOfNat0.{u_2} (Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat 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(CommSemiring.toSemiring.{u_1} R (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.Algebra.MvPolynomial.Nilpotent.2423739694._hygCtx._hyg.4)))) (MvPolynomial.coeff.{u_1, u_2} R σ (CommRing.toCommSemiring.{u_1} R inst._@.Mathlib.Algebra.MvPolynomial.Nilpotent.2423739694._hygCtx._hyg.4) (OfNat.ofNat.{u_2} (Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)) 0 (Zero.toOfNat0.{u_2} (Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)) (Finsupp.instZero.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)))) P)) (h₂ : forall (i : Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)), (Ne.{succ u_2} (Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)) i (OfNat.ofNat.{u_2} (Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)) 0 (Zero.toOfNat0.{u_2} (Finsupp.{u_2, 0} σ Nat (MulZeroClass.toZero.{0} Nat Nat.instMulZeroClass)) (Finsupp.instZero.{u_2, 0} σ Nat 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Field.Subfield.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Group.PartialSups.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["partialSups_mul_const"],"typeFallback":"forall {α : Type.{u_1}} {ι : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Group.PartialSups.2223228940._hygCtx._hyg.4 : SemilatticeSup.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.PartialSups.2223228940._hygCtx._hyg.7 : Group.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.PartialSups.2223228940._hygCtx._hyg.10 : Preorder.{u_2} ι] [inst._@.Mathlib.Algebra.Order.Group.PartialSups.2223228940._hygCtx._hyg.13 : LocallyFiniteOrderBot.{u_2} ι inst._@.Mathlib.Algebra.Order.Group.PartialSups.2223228940._hygCtx._hyg.10] [inst._@.Mathlib.Algebra.Order.Group.PartialSups.2223228940._hygCtx._hyg.16 : MulRightMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.PartialSups.2223228940._hygCtx._hyg.7))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.GroupWithZero.Finset.sym.json

@@ -0,0 +1 @@
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{G₀ : Type.{u_3}} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.213556095._hygCtx._hyg.5 : LinearOrderedCommGroupWithZero.{u_3} G₀] {a : G₀}, (LE.le.{u_3} G₀ (Preorder.toLE.{u_3} G₀ (PartialOrder.toPreorder.{u_3} G₀ (SemilatticeInf.toPartialOrder.{u_3} G₀ (Lattice.toSemilatticeInf.{u_3} G₀ (DistribLattice.toLattice.{u_3} G₀ (instDistribLatticeOfLinearOrder.{u_3} G₀ (LinearOrderedCommMonoidWithZero.toLinearOrder.{u_3} G₀ (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u_3} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.213556095._hygCtx._hyg.5)))))))) (OfNat.ofNat.{u_3} G₀ 0 (Zero.toOfNat0.{u_3} G₀ (MulZeroClass.toZero.{u_3} G₀ (MulZeroOneClass.toMulZeroClass.{u_3} G₀ (MonoidWithZero.toMulZeroOneClass.{u_3} G₀ (GroupWithZero.toMonoidWithZero.{u_3} G₀ (CommGroupWithZero.toGroupWithZero.{u_3} G₀ (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_3} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.213556095._hygCtx._hyg.5)))))))) a) -> (forall (s : 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{ι : Type.{u_1}} {G₀ : Type.{u_3}} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2002998384._hygCtx._hyg.5 : GroupWithZero.{u_3} G₀] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2002998384._hygCtx._hyg.8 : SemilatticeSup.{u_3} G₀] {a : G₀} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2002998384._hygCtx._hyg.14 : MulPosReflectLT.{u_3} G₀ (MulZeroClass.toMul.{u_3} G₀ (MulZeroOneClass.toMulZeroClass.{u_3} G₀ (MonoidWithZero.toMulZeroOneClass.{u_3} G₀ (GroupWithZero.toMonoidWithZero.{u_3} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2002998384._hygCtx._hyg.5)))) (MulZeroClass.toZero.{u_3} G₀ (MulZeroOneClass.toMulZeroClass.{u_3} G₀ (MonoidWithZero.toMulZeroOneClass.{u_3} G₀ (GroupWithZero.toMonoidWithZero.{u_3} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2002998384._hygCtx._hyg.5)))) (PartialOrder.toPreorder.{u_3} G₀ (SemilatticeSup.toPartialOrder.{u_3} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2002998384._hygCtx._hyg.8))], (LE.le.{u_3} G₀ 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[inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3037893120._hygCtx._hyg.22 : MulPosMono.{u_2} M₀ (MulZeroClass.toMul.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3037893120._hygCtx._hyg.5))) (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3037893120._hygCtx._hyg.5))) (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeSup.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3037893120._hygCtx._hyg.16))], (forall (i : ι), (Membership.mem.{u_1, u_1} ι (Finset.{u_1} ι) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} ι) ι (Finset.instSetLike.{u_1} ι)) s i) -> (LE.le.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeSup.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3037893120._hygCtx._hyg.16))) (OfNat.ofNat.{u_2} M₀ 0 (Zero.toOfNat0.{u_2} M₀ (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3037893120._hygCtx._hyg.5))))) (a i))) -> (forall (i : ι), (Membership.mem.{u_1, u_1} ι (Finset.{u_1} ι) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} ι) ι (Finset.instSetLike.{u_1} ι)) s i) -> (LE.le.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeSup.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3037893120._hygCtx._hyg.16))) (OfNat.ofNat.{u_2} M₀ 0 (Zero.toOfNat0.{u_2} M₀ (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3037893120._hygCtx._hyg.5))))) (b i))) -> (forall (hs : Finset.Nonempty.{u_1} ι s), LE.le.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ 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(Finset.sup'.{u_2, u_1} M₀ ι inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3037893120._hygCtx._hyg.16 s hs b)))","typeFull":"∀ {ι : Type u_1} {M₀ : Type u_2} [inst : MonoidWithZero M₀] {s : Finset ι} {a b : ι → M₀} [inst_1 : SemilatticeSup M₀]\n  [PosMulMono M₀] [MulPosMono M₀],\n  (∀ i ∈ s, 0 ≤ a i) → (∀ i ∈ s, 0 ≤ b i) → ∀ (hs : s.Nonempty), s.sup' hs (a * b) ≤ s.sup' hs a * s.sup' hs b","typeReadable":"∀ {ι : Type u_1} {M₀ : Type u_2} [inst : MonoidWithZero M₀] {s : Finset ι} {a b : ι → M₀} [inst_1 : SemilatticeSup M₀]\n  [PosMulMono M₀] [MulPosMono M₀],\n  (∀ i ∈ s, 0 ≤ a i) → (∀ i ∈ s, 0 ≤ b i) → ∀ (hs : s.Nonempty), s.sup' hs (a * b) ≤ s.sup' hs a * s.sup' hs b","typeReferences":[["Finset","instSetLike"],["Finset"],["PartialOrder","toPreorder"],["SetLike","instMembership"],["Finset","sup'"],["Pi","instMul"],["MulZeroClass","toMul"],["Membership","mem"],["SemilatticeSup","toPartialOrder"],["HMul","hMul"],["MonoidWithZero","toMulZeroOneClass"],["MulPosMono"],["OfNat","ofNat"],["MonoidWithZero"],["PosMulMono"],["MulZeroOneClass","toMulZeroClass"],["MulZeroClass","toZero"],["LE","le"],["instHMul"],["SemilatticeSup"],["Zero","toOfNat0"],["Preorder","toLE"],["Finset","Nonempty"]],"valueReferences":[["PartialOrder","toPreorder"],["Finset","sup'"],["Pi","instMul"],["MulZeroClass","toMul"],["SemilatticeSup","toPartialOrder"],["HMul","hMul"],["MonoidWithZero","toMulZeroOneClass"],["OfNat","ofNat"],["LE","le","trans"],["mul_le_mul"],["Finset","sup'_le"],["MulZeroOneClass","toMulZeroClass"],["MulZeroClass","toZero"],["instHMul"],["Zero","toOfNat0"],["Finset","le_sup'"]]},{"isProp":true,"kind":"theorem","name":["Finset","sup_mul_le_mul_sup_of_nonneg"],"typeFallback":"forall {ι : Type.{u_1}} {M₀ : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.5 : MonoidWithZero.{u_2} M₀] {s : Finset.{u_1} ι} {a : ι -> M₀} {b : ι -> M₀} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.16 : SemilatticeSup.{u_2} M₀] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.19 : OrderBot.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeSup.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.16)))] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.22 : PosMulMono.{u_2} M₀ (MulZeroClass.toMul.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.5))) (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.5))) (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeSup.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.16))] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.25 : MulPosMono.{u_2} M₀ (MulZeroClass.toMul.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.5))) (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.5))) (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeSup.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.16))], (forall (i : ι), (Membership.mem.{u_1, u_1} ι (Finset.{u_1} ι) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} ι) ι (Finset.instSetLike.{u_1} ι)) s i) -> (LE.le.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeSup.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.16))) (OfNat.ofNat.{u_2} M₀ 0 (Zero.toOfNat0.{u_2} M₀ (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.5))))) (a i))) -> (forall (i : ι), (Membership.mem.{u_1, u_1} ι (Finset.{u_1} ι) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} ι) ι (Finset.instSetLike.{u_1} ι)) s i) -> (LE.le.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeSup.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.16))) (OfNat.ofNat.{u_2} M₀ 0 (Zero.toOfNat0.{u_2} M₀ (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.5))))) (b i))) -> (LE.le.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeSup.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.16))) (Finset.sup.{u_2, u_1} M₀ ι inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.19 s (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (ι -> M₀) (ι -> M₀) (ι -> M₀) (instHMul.{max u_1 u_2} (ι -> M₀) (Pi.instMul.{u_1, u_2} ι (fun (a._@._internal._hyg.0 : ι) => M₀) (fun (i : ι) => MulZeroClass.toMul.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.5))))) a b)) (HMul.hMul.{u_2, u_2, u_2} M₀ M₀ M₀ (instHMul.{u_2} M₀ (MulZeroClass.toMul.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.5)))) (Finset.sup.{u_2, u_1} M₀ ι inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.19 s a) (Finset.sup.{u_2, u_1} M₀ ι inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.1276959786._hygCtx._hyg.19 s b)))","typeFull":"∀ {ι : Type u_1} {M₀ : Type u_2} [inst : MonoidWithZero M₀] {s : Finset ι} {a b : ι → M₀} [inst_1 : SemilatticeSup M₀]\n  [inst_2 : OrderBot M₀] [PosMulMono M₀] [MulPosMono M₀],\n  (∀ i ∈ s, 0 ≤ a i) → (∀ i ∈ s, 0 ≤ b i) → s.sup (a * b) ≤ s.sup a * s.sup b","typeReadable":"∀ {ι : Type u_1} {M₀ : Type u_2} [inst : MonoidWithZero M₀] {s : Finset ι} {a b : ι → M₀} [inst_1 : SemilatticeSup M₀]\n  [inst_2 : OrderBot M₀] [PosMulMono M₀] [MulPosMono M₀],\n  (∀ i ∈ s, 0 ≤ a i) → (∀ i ∈ s, 0 ≤ b i) → s.sup (a * b) ≤ s.sup a * s.sup b","typeReferences":[["Finset","instSetLike"],["SetLike","instMembership"],["Finset"],["PartialOrder","toPreorder"],["Pi","instMul"],["Membership","mem"],["MulZeroClass","toMul"],["SemilatticeSup","toPartialOrder"],["HMul","hMul"],["MonoidWithZero","toMulZeroOneClass"],["MulPosMono"],["OfNat","ofNat"],["MonoidWithZero"],["PosMulMono"],["MulZeroOneClass","toMulZeroClass"],["MulZeroClass","toZero"],["LE","le"],["Finset","sup"],["instHMul"],["SemilatticeSup"],["Zero","toOfNat0"],["Preorder","toLE"],["OrderBot"]],"valueReferences":[["Finset","sup_le"],["PartialOrder","toPreorder"],["Finset","le_sup"],["Pi","instMul"],["MulZeroClass","toMul"],["SemilatticeSup","toPartialOrder"],["HMul","hMul"],["MonoidWithZero","toMulZeroOneClass"],["OfNat","ofNat"],["LE","le","trans"],["mul_le_mul"],["MulZeroOneClass","toMulZeroClass"],["MulZeroClass","toZero"],["Finset","sup"],["instHMul"],["Zero","toOfNat0"]]},{"isProp":true,"kind":"theorem","name":["Finset","mul_inf_le_inf_mul_of_nonneg"],"typeFallback":"forall {ι : Type.{u_1}} {M₀ : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.5 : MonoidWithZero.{u_2} M₀] {s : Finset.{u_1} ι} {a : ι -> M₀} {b : ι -> M₀} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.16 : SemilatticeInf.{u_2} M₀] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.19 : OrderTop.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeInf.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.16)))] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.22 : PosMulMono.{u_2} M₀ (MulZeroClass.toMul.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.5))) (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.5))) (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeInf.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.16))] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.25 : MulPosMono.{u_2} M₀ (MulZeroClass.toMul.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.5))) (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.5))) (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeInf.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.16))], (forall (i : ι), (Membership.mem.{u_1, u_1} ι (Finset.{u_1} ι) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} ι) ι (Finset.instSetLike.{u_1} ι)) s i) -> (LE.le.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeInf.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.16))) (OfNat.ofNat.{u_2} M₀ 0 (Zero.toOfNat0.{u_2} M₀ (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.5))))) (a i))) -> (forall (i : ι), (Membership.mem.{u_1, u_1} ι (Finset.{u_1} ι) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} ι) ι (Finset.instSetLike.{u_1} ι)) s i) -> (LE.le.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeInf.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.16))) (OfNat.ofNat.{u_2} M₀ 0 (Zero.toOfNat0.{u_2} M₀ (MulZeroClass.toZero.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.5))))) (b i))) -> (LE.le.{u_2} M₀ (Preorder.toLE.{u_2} M₀ (PartialOrder.toPreorder.{u_2} M₀ (SemilatticeInf.toPartialOrder.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.16))) (HMul.hMul.{u_2, u_2, u_2} M₀ M₀ M₀ (instHMul.{u_2} M₀ (MulZeroClass.toMul.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.5)))) (Finset.inf.{u_2, u_1} M₀ ι inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.19 s a) (Finset.inf.{u_2, u_1} M₀ ι inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.19 s b)) (Finset.inf.{u_2, u_1} M₀ ι inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.19 s (HMul.hMul.{max u_1 u_2, max u_1 u_2, max u_1 u_2} (ι -> M₀) (ι -> M₀) (ι -> M₀) (instHMul.{max u_1 u_2} (ι -> M₀) (Pi.instMul.{u_1, u_2} ι (fun (a._@._internal._hyg.0 : ι) => M₀) (fun (i : ι) => MulZeroClass.toMul.{u_2} M₀ (MulZeroOneClass.toMulZeroClass.{u_2} M₀ (MonoidWithZero.toMulZeroOneClass.{u_2} M₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.3443235484._hygCtx._hyg.5))))) a b)))","typeFull":"∀ {ι : Type u_1} {M₀ : Type u_2} [inst : MonoidWithZero M₀] {s : Finset ι} {a b : ι → M₀} [inst_1 : SemilatticeInf M₀]\n  [inst_2 : OrderTop M₀] [PosMulMono M₀] [MulPosMono M₀],\n  (∀ i ∈ s, 0 ≤ a i) → (∀ i ∈ s, 0 ≤ b i) → s.inf a * s.inf b ≤ s.inf (a * b)","typeReadable":"∀ {ι : Type u_1} {M₀ : Type u_2} [inst : MonoidWithZero M₀] {s : Finset ι} {a b : ι → M₀} [inst_1 : SemilatticeInf M₀]\n  [inst_2 : OrderTop M₀] [PosMulMono M₀] [MulPosMono M₀],\n  (∀ i ∈ s, 0 ≤ a i) → (∀ i ∈ s, 0 ≤ b i) → s.inf a * s.inf b ≤ s.inf (a * 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Type.{u_3}} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2544986991._hygCtx._hyg.5 : GroupWithZero.{u_3} G₀] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2544986991._hygCtx._hyg.8 : SemilatticeSup.{u_3} G₀] {a : G₀} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2544986991._hygCtx._hyg.14 : MulPosReflectLT.{u_3} G₀ (MulZeroClass.toMul.{u_3} G₀ (MulZeroOneClass.toMulZeroClass.{u_3} G₀ (MonoidWithZero.toMulZeroOneClass.{u_3} G₀ (GroupWithZero.toMonoidWithZero.{u_3} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2544986991._hygCtx._hyg.5)))) (MulZeroClass.toZero.{u_3} G₀ (MulZeroOneClass.toMulZeroClass.{u_3} G₀ (MonoidWithZero.toMulZeroOneClass.{u_3} G₀ (GroupWithZero.toMonoidWithZero.{u_3} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2544986991._hygCtx._hyg.5)))) (PartialOrder.toPreorder.{u_3} G₀ (SemilatticeSup.toPartialOrder.{u_3} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Finset.2544986991._hygCtx._hyg.8))], (LE.le.{u_3} G₀ (Preorder.toLE.{u_3} 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["OrderIso","mulLeft₀_apply"],"typeFallback":"forall {G₀ : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.2381840360._hygCtx._hyg.3 : GroupWithZero.{u_1} G₀] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.2381840360._hygCtx._hyg.6 : PartialOrder.{u_1} G₀] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.2381840360._hygCtx._hyg.9 : PosMulReflectLT.{u_1} G₀ (MulZeroClass.toMul.{u_1} G₀ (MulZeroOneClass.toMulZeroClass.{u_1} G₀ (MonoidWithZero.toMulZeroOneClass.{u_1} G₀ (GroupWithZero.toMonoidWithZero.{u_1} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.2381840360._hygCtx._hyg.3)))) (MulZeroClass.toZero.{u_1} G₀ (MulZeroOneClass.toMulZeroClass.{u_1} G₀ (MonoidWithZero.toMulZeroOneClass.{u_1} G₀ (GroupWithZero.toMonoidWithZero.{u_1} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.2381840360._hygCtx._hyg.3)))) (PartialOrder.toPreorder.{u_1} G₀ 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 0 ≤ c → ∀ (a b : G₀), c * (a ⊔ b) = c * a ⊔ c * 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{G₀ : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.1632744248._hygCtx._hyg.3 : GroupWithZero.{u_1} G₀] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.1632744248._hygCtx._hyg.6 : SemilatticeInf.{u_1} G₀] [inst._@.Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.1632744248._hygCtx._hyg.9 : MulPosReflectLT.{u_1} G₀ (MulZeroClass.toMul.{u_1} G₀ (MulZeroOneClass.toMulZeroClass.{u_1} G₀ (MonoidWithZero.toMulZeroOneClass.{u_1} G₀ (GroupWithZero.toMonoidWithZero.{u_1} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.1632744248._hygCtx._hyg.3)))) (MulZeroClass.toZero.{u_1} G₀ (MulZeroOneClass.toMulZeroClass.{u_1} G₀ (MonoidWithZero.toMulZeroOneClass.{u_1} G₀ (GroupWithZero.toMonoidWithZero.{u_1} G₀ inst._@.Mathlib.Algebra.Order.GroupWithZero.Unbundled.OrderIso.1632744248._hygCtx._hyg.3)))) (PartialOrder.toPreorder.{u_1} G₀ (SemilatticeInf.toPartialOrder.{u_1} G₀ 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 0 ≤ c → ∀ (a b : G₀), (a ⊔ b) * c = a * c ⊔ b * 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