Add files using upload-large-folder tool

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.CharP.Basic.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Semiconj.Defs.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.sym.json

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inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_5, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.16 c)) (CategoryTheory.Limits.Cone.pt.{u_4, max u_3 u_5, u_2, max (max u_1 u_3) u_5} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.8 (HomologicalComplex.{u_5, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_5, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.16 c) F cF)) j) q) (HomologicalComplex.X.{u_5, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.16 c (CategoryTheory.Functor.obj.{u_4, max u_3 u_5, u_2, max (max u_1 u_3) u_5} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.8 (HomologicalComplex.{u_5, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_5, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.5 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inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.16 c)) (CategoryTheory.Functor.const.{u_4, max u_3 u_5, u_2, max (max u_1 u_3) u_5} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.8 (HomologicalComplex.{u_5, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_5, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.3452901806._hygCtx._hyg.16 c)) (CategoryTheory.Limits.Cone.pt.{u_4, max u_3 u_5, u_2, max (max u_1 u_3) u_5} J 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{C : Type.{u_1}} {J : Type.{u_2}} {ι : Type.{u_3}} [inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 : CategoryTheory.Category.{u_4, u_1} C] [inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 : CategoryTheory.Category.{u_5, u_2} J] {c : ComplexShape.{u_3} ι} [inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.13 : CategoryTheory.IsCofiltered.{u_5, u_2} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8] [inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 : CategoryTheory.Limits.HasZeroMorphisms.{u_4, u_1} C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5] (F : CategoryTheory.Functor.{u_5, max u_3 u_4, u_2, max (max u_3 u_1) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c)) [inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.26 : forall (j : ι), CategoryTheory.Limits.HasLimit.{u_5, u_2, u_4, u_1} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 (CategoryTheory.Functor.comp.{u_5, max u_3 u_4, u_4, u_2, max (max u_1 u_3) u_4, u_1} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 F (HomologicalComplex.eval.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c j))] {cF : CategoryTheory.Limits.Cone.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) F}, (CategoryTheory.Limits.IsLimit.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) F cF) -> (forall [inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.45 : CategoryTheory.CategoryWithHomology.{u_4, u_1} C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16] (q₀ : ι) (q₁ : ι) (q₂ : ι), (Eq.{succ u_3} ι (ComplexShape.prev.{u_3} ι c q₁) q₀) -> (Eq.{succ u_3} ι (ComplexShape.next.{u_3} ι c q₁) q₂) -> (forall (j : J), (CategoryTheory.Functor.IsEventuallyConstantTo.{u_5, u_2, u_4, u_1} J C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 (CategoryTheory.Functor.comp.{u_5, max u_3 u_4, u_4, u_2, max (max u_1 u_3) u_4, u_1} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 F (HomologicalComplex.eval.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c q₀)) j) -> (CategoryTheory.Functor.IsEventuallyConstantTo.{u_5, u_2, u_4, u_1} J C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 (CategoryTheory.Functor.comp.{u_5, max u_3 u_4, u_4, u_2, max (max u_1 u_3) u_4, u_1} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 F (HomologicalComplex.eval.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c q₁)) j) -> (CategoryTheory.Functor.IsEventuallyConstantTo.{u_5, u_2, u_4, u_1} J C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 (CategoryTheory.Functor.comp.{u_5, max u_3 u_4, u_4, u_2, max (max u_1 u_3) u_4, u_1} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 F (HomologicalComplex.eval.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c q₂)) j) -> (QuasiIsoAt.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c (CategoryTheory.Functor.obj.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (CategoryTheory.Functor.obj.{max u_3 u_4, max u_2 u_3 u_4, max (max u_1 u_3) u_4, max (max (max u_2 u_5) (max u_1 u_3) u_4) u_3 u_4} (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (CategoryTheory.Functor.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c)) (CategoryTheory.Functor.category.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c)) (CategoryTheory.Functor.const.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c)) (CategoryTheory.Limits.Cone.pt.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) F cF)) j) (CategoryTheory.Functor.obj.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) F j) (CategoryTheory.NatTrans.app.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (CategoryTheory.Functor.obj.{max u_3 u_4, max u_2 u_3 u_4, max (max u_1 u_3) u_4, max (max (max u_2 u_5) (max u_1 u_3) u_4) u_3 u_4} (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (CategoryTheory.Functor.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c)) (CategoryTheory.Functor.category.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c)) (CategoryTheory.Functor.const.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c)) (CategoryTheory.Limits.Cone.pt.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) F cF)) F (CategoryTheory.Limits.Cone.π.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) F cF) j) q₁ (CategoryTheory.CategoryWithHomology.hasHomology.{u_4, u_1} C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.45 (HomologicalComplex.sc.{u_4, u_1, u_3} C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 ι c (CategoryTheory.Functor.obj.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (CategoryTheory.Functor.obj.{max u_3 u_4, max u_2 u_3 u_4, max (max u_1 u_3) u_4, max (max (max u_2 u_5) (max u_1 u_3) u_4) u_3 u_4} (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (CategoryTheory.Functor.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c)) (CategoryTheory.Functor.category.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c)) (CategoryTheory.Functor.const.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c) (HomologicalComplex.instCategory.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.16 c)) (CategoryTheory.Limits.Cone.pt.{u_5, max u_3 u_4, u_2, max (max u_1 u_3) u_4} J inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.8 (HomologicalComplex.{u_4, u_1, u_3} ι C inst._@.Mathlib.Algebra.Homology.HomologicalComplexLimitsEventuallyConstant.534067431._hygCtx._hyg.5 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Equiv.Opposite.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["MulOpposite","coe_opLinearEquiv_symm"],"typeFallback":"forall (R : Type.{u}) {M : Type.{v}} [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 : Semiring.{u} R] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7 : AddCommMonoid.{v} M] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.10 : Module.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7], Eq.{succ v} ((MulOpposite.{v} M) -> M) (DFunLike.coe.{succ v, succ v, succ v} (LinearEquiv.{u, u, v, v} R R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4) (MulOpposite.{v} M) M (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.10) (MulOpposite.{v} M) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : MulOpposite.{v} M) => M) (EquivLike.toFunLike.{succ v, succ v, succ v} (LinearEquiv.{u, u, v, v} R R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4) (MulOpposite.{v} M) M (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.10) (MulOpposite.{v} M) M (LinearEquiv.instEquivLike.{u, u, v, v} R R (MulOpposite.{v} M) M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.10 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R 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inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.10) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4) (MulOpposite.opLinearEquiv.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2150017709._hygCtx._hyg.10))) (MulOpposite.unop.{v} M)","typeFull":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  ⇑(MulOpposite.opLinearEquiv R).symm = MulOpposite.unop","typeReadable":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  ⇑(MulOpposite.opLinearEquiv R).symm = MulOpposite.unop","typeReferences":[["Module"],["LinearEquiv"],["LinearEquiv","symm"],["DFunLike","coe"],["MulOpposite","instAddCommMonoid"],["AddCommMonoid"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MulOpposite","unop"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["MulOpposite","instModule"],["LinearEquiv","instEquivLike"],["Eq"],["MulOpposite","opLinearEquiv"],["Semiring"]],"valueReferences":[["rfl"],["LinearEquiv"],["DFunLike","coe"],["LinearEquiv","symm"],["MulOpposite","instAddCommMonoid"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["MulOpposite","instModule"],["LinearEquiv","instEquivLike"],["MulOpposite","opLinearEquiv"]]},{"isProp":true,"kind":"theorem","name":["MulOpposite","coe_opLinearEquiv_symm_addEquiv"],"typeFallback":"forall (R : Type.{u}) {M : Type.{v}} [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4 : Semiring.{u} R] 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(RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4) (MulOpposite.{v} M) M (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.10) (MulOpposite.{v} M) M (LinearEquiv.instEquivLike.{u, u, v, v} R R (MulOpposite.{v} M) M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.10 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} 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inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.10) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4) (MulOpposite.opLinearEquiv.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.10))) (AddEquiv.symm.{v, v} M (MulOpposite.{v} M) (AddCommMagma.toAdd.{v} M (AddCommSemigroup.toAddCommMagma.{v} M (AddCommMonoid.toAddCommSemigroup.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7))) (MulOpposite.instAdd.{v} M (AddCommMagma.toAdd.{v} M (AddCommSemigroup.toAddCommMagma.{v} M (AddCommMonoid.toAddCommSemigroup.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7)))) (MulOpposite.opAddEquiv.{v} M (AddCommMagma.toAdd.{v} M (AddCommSemigroup.toAddCommMagma.{v} M (AddCommMonoid.toAddCommSemigroup.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3967496093._hygCtx._hyg.7)))))","typeFull":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  ↑(MulOpposite.opLinearEquiv R).symm = MulOpposite.opAddEquiv.symm","typeReadable":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  ↑(MulOpposite.opLinearEquiv R).symm = MulOpposite.opAddEquiv.symm","typeReferences":[["MulOpposite","opAddEquiv"],["AddEquiv","symm"],["Module"],["SemilinearEquivClass","toAddEquivClass"],["AddEquivClass","toAddEquiv"],["LinearEquiv"],["LinearEquiv","symm"],["AddEquiv"],["MulOpposite","instAddCommMonoid"],["LinearEquiv","instSemilinearEquivClass"],["AddCommMonoid"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["MulOpposite","instModule"],["RingHomInvPair","ids"],["MulOpposite","instAdd"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["LinearEquiv","instEquivLike"],["Eq"],["MulOpposite","opLinearEquiv"],["Semiring"]],"valueReferences":[["rfl"],["SemilinearEquivClass","toAddEquivClass"],["AddEquivClass","toAddEquiv"],["LinearEquiv"],["LinearEquiv","symm"],["AddEquiv"],["MulOpposite","instAddCommMonoid"],["LinearEquiv","instSemilinearEquivClass"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["MulOpposite","instModule"],["MulOpposite","instAdd"],["RingHomInvPair","ids"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["LinearEquiv","instEquivLike"],["MulOpposite","opLinearEquiv"]]},{"isProp":true,"kind":"theorem","name":["MulOpposite","coe_opLinearEquiv_toLinearMap"],"typeFallback":"forall (R : Type.{u}) {M : Type.{v}} [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 : Semiring.{u} R] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7 : AddCommMonoid.{v} M] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.10 : Module.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7], Eq.{succ v} (M -> (MulOpposite.{v} M)) (DFunLike.coe.{succ v, succ v, succ v} (LinearMap.{u, u, v, v} R R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4)) M (MulOpposite.{v} M) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.10 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.10)) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => MulOpposite.{v} M) (LinearMap.instFunLike.{u, u, v, v} R R M (MulOpposite.{v} M) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.10 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.10) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4))) (LinearEquiv.toLinearMap.{u, u, v, v} R R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4) M (MulOpposite.{v} M) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.10 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.10) (MulOpposite.opLinearEquiv.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3466955346._hygCtx._hyg.10))) (MulOpposite.op.{v} M)","typeFull":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  ⇑↑(MulOpposite.opLinearEquiv R) = MulOpposite.op","typeReadable":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  ⇑↑(MulOpposite.opLinearEquiv R) = MulOpposite.op","typeReferences":[["LinearMap","instFunLike"],["Module"],["LinearEquiv","toLinearMap"],["LinearMap"],["DFunLike","coe"],["MulOpposite","instAddCommMonoid"],["AddCommMonoid"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MulOpposite","op"],["RingHomInvPair","ids"],["MulOpposite","instModule"],["Eq"],["MulOpposite","opLinearEquiv"],["Semiring"]],"valueReferences":[["rfl"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["LinearMap","instFunLike"],["RingHom","id"],["RingHomInvPair","ids"],["MulOpposite","instModule"],["LinearEquiv","toLinearMap"],["LinearMap"],["DFunLike","coe"],["MulOpposite","opLinearEquiv"],["MulOpposite","instAddCommMonoid"]]},{"isProp":true,"kind":"theorem","name":["MulOpposite","opLinearEquiv_symm_toAddEquiv"],"typeFallback":"forall (R : Type.{u}) {M : Type.{v}} [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.4 : Semiring.{u} R] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.7 : AddCommMonoid.{v} M] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.10 : Module.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.7], Eq.{succ v} (AddEquiv.{v, v} (MulOpposite.{v} M) M (AddCommMagma.toAdd.{v} (MulOpposite.{v} M) (AddCommSemigroup.toAddCommMagma.{v} (MulOpposite.{v} M) (AddCommMonoid.toAddCommSemigroup.{v} (MulOpposite.{v} M) (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.7)))) (AddCommMagma.toAdd.{v} M (AddCommSemigroup.toAddCommMagma.{v} M (AddCommMonoid.toAddCommSemigroup.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.7)))) (LinearEquiv.toAddEquiv.{u, u, v, v} R R 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inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.10 (LinearEquiv.symm.{u, u, v, v} R R M (MulOpposite.{v} M) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.7 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.10 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.10) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.4)) (RingHom.id.{u} R 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(MulOpposite.opAddEquiv.{v} M (AddCommMagma.toAdd.{v} M (AddCommSemigroup.toAddCommMagma.{v} M (AddCommMonoid.toAddCommSemigroup.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.788520501._hygCtx._hyg.7)))))","typeFull":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  (MulOpposite.opLinearEquiv R).symm.toAddEquiv = MulOpposite.opAddEquiv.symm","typeReadable":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  (MulOpposite.opLinearEquiv R).symm.toAddEquiv = 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1","typeReferences":[["RingHom"],["LinearMap","instFunLike"],["Module"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap"],["DFunLike","coe"],["OfNat","ofNat"],["AddCommMonoid"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["Iff"],["AddMonoidWithOne","toOne"],["Semiring","toOppositeModule"],["MulOpposite","instNonAssocSemiring"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["MulOpposite","instSemiring"],["Semiring"]],"valueReferences":[["HEq","refl"],["LinearMap","instFunLike"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap","ext_ring_op"],["LinearMap"],["Eq","casesOn"],["DFunLike","coe"],["OfNat","ofNat"],["Iff","intro"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["Eq","refl"],["AddMonoidWithOne","toOne"],["Semiring","toOppositeModule"],["Eq","symm"],["HEq"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq","ndrec"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["MulOpposite","instSemiring"]]},{"isProp":true,"kind":"theorem","name":["MulOpposite","opLinearEquiv","_proof_2"],"typeFallback":"forall (R : Type.{u_2}) {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.4 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7 : AddCommMonoid.{u_1} M] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.10 : Module.{u_2, u_1} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7] (a : R) (b : M), Eq.{succ u_1} (MulOpposite.{u_1} M) (MulOpposite.op.{u_1} M (HSMul.hSMul.{u_2, u_1, u_1} R M M (instHSMul.{u_2, u_1} R M (SMulZeroClass.toSMul.{u_2, u_1} R M (AddZero.toZero.{u_1} M (AddZeroClass.toAddZero.{u_1} M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7)))) (DistribSMul.toSMulZeroClass.{u_2, u_1} R M (AddMonoid.toAddZeroClass.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M 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MulOpposite.op (a • b) = a • MulOpposite.op b","typeReadable":"∀ (R : Type u_2) {M : Type u_1} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (a : R) (b : M),\n  MulOpposite.op (a • b) = a • MulOpposite.op 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MulOpposite.opAddEquiv","typeReferences":[["MulOpposite","opAddEquiv"],["Module"],["SemilinearEquivClass","toAddEquivClass"],["AddEquivClass","toAddEquiv"],["LinearEquiv"],["AddEquiv"],["MulOpposite","instAddCommMonoid"],["LinearEquiv","instSemilinearEquivClass"],["AddCommMonoid"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["MulOpposite","instModule"],["RingHomInvPair","ids"],["MulOpposite","instAdd"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["LinearEquiv","instEquivLike"],["Eq"],["MulOpposite","opLinearEquiv"],["Semiring"]],"valueReferences":[["rfl"],["SemilinearEquivClass","toAddEquivClass"],["AddEquivClass","toAddEquiv"],["LinearEquiv"],["AddEquiv"],["MulOpposite","instAddCommMonoid"],["LinearEquiv","instSemilinearEquivClass"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["RingHom","id"],["MulOpposite","instModule"],["MulOpposite","instAdd"],["RingHomInvPair","ids"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["LinearEquiv","instEquivLike"],["MulOpposite","opLinearEquiv"]]},{"isProp":true,"kind":"theorem","name":["LinearMap","ext_ring_op"],"typeFallback":"forall {R : Type.{u_1}} {S : Type.{u_2}} {M : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.5 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.8 : Semiring.{u_2} S] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.11 : AddCommMonoid.{u_3} M] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.14 : Module.{u_2, u_3} S M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.8 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.11] {σ : RingHom.{u_1, u_2} (MulOpposite.{u_1} R) S (MulOpposite.instNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.5)) (Semiring.toNonAssocSemiring.{u_2} S inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.8)} {f : LinearMap.{u_1, u_2, u_1, u_3} (MulOpposite.{u_1} R) S (MulOpposite.instSemiring.{u_1} R 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u_1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.5)))))))) -> (Eq.{max (succ u_1) (succ u_3)} (LinearMap.{u_1, u_2, u_1, u_3} (MulOpposite.{u_1} R) S (MulOpposite.instSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.5) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.8 σ R M (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.5))) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.11 (Semiring.toOppositeModule.{u_1} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.5) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.4067268619._hygCtx._hyg.14) f g)","typeFull":"∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]\n  [inst_3 : Module S M] {σ : Rᵐᵒᵖ →+* S} {f g : R →ₛₗ[σ] M}, f 1 = g 1 → f = g","typeReadable":"∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]\n  [inst_3 : Module S M] {σ : Rᵐᵒᵖ →+* S} {f g : R →ₛₗ[σ] M}, f 1 = g 1 → f = g","typeReferences":[["RingHom"],["LinearMap","instFunLike"],["Module"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearMap"],["DFunLike","coe"],["OfNat","ofNat"],["AddCommMonoid"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["Semiring","toOppositeModule"],["MulOpposite","instNonAssocSemiring"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["MulOpposite","instSemiring"],["Semiring"]],"valueReferences":[["MulOneClass","toMulOne"],["RingHom"],["LinearMap","instFunLike"],["RingHom","instFunLike"],["HMul","hMul"],["SMulZeroClass","toSMul"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["congrArg"],["op_smul_eq_mul"],["MulOpposite"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["LinearMap","ext"],["MonoidWithZero","toMonoid"],["Eq","symm"],["instHSMul"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["MulOpposite","instSemiring"],["NonAssocSemiring","toMulZeroOneClass"],["DistribSMul","toSMulZeroClass"],["MulOne","toOne"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearMap"],["OfNat","ofNat"],["LinearMap","map_smulₛₗ"],["Module","toDistribMulAction"],["One","toOfNat1"],["Eq","refl"],["MulOpposite","op"],["AddMonoidWithOne","toOne"],["Mul","toSMulMulOpposite"],["HSMul","hSMul"],["Semiring","toOppositeModule"],["id"],["instHMul"],["Eq","mpr"],["AddZero","toZero"],["one_mul"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["MulOpposite","opLinearEquiv","_proof_4"],"typeFallback":"forall {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7 : AddCommMonoid.{u_1} M], Function.RightInverse.{succ u_1, succ u_1} M (MulOpposite.{u_1} M) (Equiv.invFun.{succ u_1, succ u_1} M (MulOpposite.{u_1} M) (AddEquiv.toEquiv.{u_1, u_1} M (MulOpposite.{u_1} M) (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7))) (MulOpposite.instAdd.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7)))) (MulOpposite.opAddEquiv.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7)))))) (Equiv.toFun.{succ u_1, succ u_1} M (MulOpposite.{u_1} M) (AddEquiv.toEquiv.{u_1, u_1} M (MulOpposite.{u_1} M) (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7))) (MulOpposite.instAdd.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7)))) (MulOpposite.opAddEquiv.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7))))))","typeFull":"∀ {M : Type u_1} [inst : AddCommMonoid M],\n  Function.RightInverse MulOpposite.opAddEquiv.invFun MulOpposite.opAddEquiv.toFun","typeReadable":"∀ {M : Type u_1} [inst : AddCommMonoid M],\n  Function.RightInverse MulOpposite.opAddEquiv.invFun 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inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7], Eq.{succ v} (M -> (MulOpposite.{v} M)) (DFunLike.coe.{succ v, succ v, succ v} (LinearEquiv.{u, u, v, v} R R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4) M (MulOpposite.{v} M) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.10 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.10)) M (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : M) => MulOpposite.{v} M) (EquivLike.toFunLike.{succ v, succ v, succ v} (LinearEquiv.{u, u, v, v} R R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4) M (MulOpposite.{v} M) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.10 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.10)) M (MulOpposite.{v} M) (LinearEquiv.instEquivLike.{u, u, v, v} R R M (MulOpposite.{v} M) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.10 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.10) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4))) (MulOpposite.opLinearEquiv.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2292874983._hygCtx._hyg.10)) (MulOpposite.op.{v} M)","typeFull":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  ⇑(MulOpposite.opLinearEquiv R) = MulOpposite.op","typeReadable":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  ⇑(MulOpposite.opLinearEquiv R) = MulOpposite.op","typeReferences":[["Module"],["LinearEquiv"],["DFunLike","coe"],["MulOpposite","instAddCommMonoid"],["AddCommMonoid"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MulOpposite","op"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["MulOpposite","instModule"],["LinearEquiv","instEquivLike"],["Eq"],["MulOpposite","opLinearEquiv"],["Semiring"]],"valueReferences":[["rfl"],["MulOpposite"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["MulOpposite","instModule"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["LinearEquiv"],["DFunLike","coe"],["MulOpposite","opLinearEquiv"],["MulOpposite","instAddCommMonoid"]]},{"isProp":true,"kind":"theorem","name":["MulOpposite","opLinearEquiv","_proof_1"],"typeFallback":"forall {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7 : AddCommMonoid.{u_1} M] (x : M) (y : M), Eq.{succ u_1} (MulOpposite.{u_1} M) (Equiv.toFun.{succ u_1, succ 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(MulOpposite.{u_1} M) (MulOpposite.{u_1} M) (instHAdd.{u_1} (MulOpposite.{u_1} M) (MulOpposite.instAdd.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7))))) (Equiv.toFun.{succ u_1, succ u_1} M (MulOpposite.{u_1} M) (AddEquiv.toEquiv.{u_1, u_1} M (MulOpposite.{u_1} M) (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7))) (MulOpposite.instAdd.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7)))) (MulOpposite.opAddEquiv.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7))))) x) (Equiv.toFun.{succ u_1, succ u_1} M (MulOpposite.{u_1} M) (AddEquiv.toEquiv.{u_1, u_1} M (MulOpposite.{u_1} M) (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7))) (MulOpposite.instAdd.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7)))) (MulOpposite.opAddEquiv.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7))))) y))","typeFull":"∀ {M : Type u_1} [inst : AddCommMonoid M] (x y : M),\n  MulOpposite.opAddEquiv.toFun (x + y) = MulOpposite.opAddEquiv.toFun x + MulOpposite.opAddEquiv.toFun y","typeReadable":"∀ {M : Type u_1} [inst : AddCommMonoid M] (x y : M),\n  MulOpposite.opAddEquiv.toFun (x + y) = MulOpposite.opAddEquiv.toFun x + MulOpposite.opAddEquiv.toFun y","typeReferences":[["HAdd","hAdd"],["MulOpposite","opAddEquiv"],["MulOpposite"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["instHAdd"],["MulOpposite","instAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Equiv","toFun"],["AddEquiv","toEquiv"],["Eq"]],"valueReferences":[["MulOpposite","opAddEquiv"],["MulOpposite"],["AddCommMonoid","toAddCommSemigroup"],["MulOpposite","instAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","map_add'"]]},{"isProp":true,"kind":"theorem","name":["MulOpposite","opLinearEquiv","_proof_3"],"typeFallback":"forall {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7 : AddCommMonoid.{u_1} M], Function.LeftInverse.{succ u_1, succ u_1} M (MulOpposite.{u_1} M) (Equiv.invFun.{succ u_1, succ 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inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7))) (MulOpposite.instAdd.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7)))) (MulOpposite.opAddEquiv.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7))))))","typeFull":"∀ {M : Type u_1} [inst : AddCommMonoid M],\n  Function.LeftInverse MulOpposite.opAddEquiv.invFun MulOpposite.opAddEquiv.toFun","typeReadable":"∀ {M : Type u_1} [inst : AddCommMonoid M],\n  Function.LeftInverse MulOpposite.opAddEquiv.invFun MulOpposite.opAddEquiv.toFun","typeReferences":[["MulOpposite","opAddEquiv"],["MulOpposite"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["MulOpposite","instAdd"],["Function","LeftInverse"],["Equiv","toFun"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"]],"valueReferences":[["MulOpposite","opAddEquiv"],["MulOpposite"],["Equiv","left_inv"],["AddCommMonoid","toAddCommSemigroup"],["MulOpposite","instAdd"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"]]},{"isProp":false,"kind":"definition","name":["MulOpposite","opLinearEquiv"],"typeFallback":"forall (R : Type.{u}) {M : Type.{v}} [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.4 : Semiring.{u} R] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.7 : AddCommMonoid.{v} M] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2332904755._hygCtx._hyg.10 : Module.{u, v} R M 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inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.7 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.10) (MulOpposite.{v} M) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : MulOpposite.{v} M) => M) (LinearMap.instFunLike.{u, u, v, v} R R (MulOpposite.{v} M) M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.7 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.10 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4))) (LinearEquiv.toLinearMap.{u, u, v, v} R R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4 (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4)) (RingHom.id.{u} R (Semiring.toNonAssocSemiring.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4)) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4) (RingHomInvPair.ids.{u} R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4) (MulOpposite.{v} M) M (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.7 (MulOpposite.instModule.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.10 (LinearEquiv.symm.{u, u, v, v} R R M (MulOpposite.{v} M) inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.7 (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.3295020441._hygCtx._hyg.7) 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[inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.7 : AddCommMonoid.{v} M] [inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.10 : Module.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.7], Eq.{succ v} (AddEquiv.{v, v} M (MulOpposite.{v} M) (AddCommMagma.toAdd.{v} M (AddCommSemigroup.toAddCommMagma.{v} M (AddCommMonoid.toAddCommSemigroup.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.7))) (AddCommMagma.toAdd.{v} (MulOpposite.{v} M) (AddCommSemigroup.toAddCommMagma.{v} (MulOpposite.{v} M) (AddCommMonoid.toAddCommSemigroup.{v} (MulOpposite.{v} M) (MulOpposite.instAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.7))))) (LinearEquiv.toAddEquiv.{u, u, v, v} R R inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.4 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inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.10) (MulOpposite.opLinearEquiv.{u, v} R M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.10)) (MulOpposite.opAddEquiv.{v} M (AddCommMagma.toAdd.{v} M (AddCommSemigroup.toAddCommMagma.{v} M (AddCommMonoid.toAddCommSemigroup.{v} M inst._@.Mathlib.Algebra.Module.Equiv.Opposite.2659627988._hygCtx._hyg.7))))","typeFull":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  (MulOpposite.opLinearEquiv R).toAddEquiv = MulOpposite.opAddEquiv","typeReadable":"∀ (R : Type u) {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],\n  (MulOpposite.opLinearEquiv R).toAddEquiv = 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.NeZero.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Archimedean.Hom.sym.json

@@ -0,0 +1 @@
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x","typeReferences":[["OrderRingHom"],["PartialOrder","toPreorder"],["Field","toCommRing"],["IsStrictOrderedRing"],["Lattice","toSemilatticeInf"],["Field"],["NonUnitalCommRing","toNonUnitalNonAssocCommRing"],["OrderRingHom","instFunLike"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["LinearOrder"],["CommRing","toNonUnitalCommRing"],["DivisionSemiring","toSemiring"],["DFunLike","coe"],["instDistribLatticeOfLinearOrder"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Semiring","toNonAssocSemiring"],["DistribLattice","toLattice"],["Archimedean"],["NonUnitalNonAssocCommRing","toNonUnitalNonAssocRing"],["Field","toSemifield"],["Semifield","toDivisionSemiring"],["Eq"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["OrderRingHom"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["OrderRingHom","id"],["OrderRingHom","instFunLike"],["DivisionSemiring","toSemiring"],["DFunLike","coe"],["congrArg"],["instDistribLatticeOfLinearOrder"],["Semiring","toNonAssocSemiring"],["DistribLattice","toLattice"],["Eq","refl"],["id"],["Field","toSemifield"],["Eq","mpr"],["Semifield","toDivisionSemiring"],["Eq"],["OrderRingHom","eq_id"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["OrderRingHom","eq_id"],"typeFallback":"forall 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Ring.Rat.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Ring.Action.Subobjects.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.LConvolution.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["MeasureTheory","measurable_mlconvolution"],"typeFallback":"forall {G : Type.{u_1}} {mG : MeasurableSpace.{u_1} G} [inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.5 : Mul.{u_1} G] [inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.8 : Inv.{u_1} G] [inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.11 : MeasurableMul₂.{u_1} G mG inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.5] [inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.14 : MeasurableInv.{u_1} G inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.8 mG] {f : G -> ENNReal} {g : G -> ENNReal} (μ : MeasureTheory.Measure.{u_1} G mG) [inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.29 : MeasureTheory.SFinite.{u_1} G mG μ], (Measurable.{u_1, 0} G ENNReal mG ENNReal.measurableSpace f) -> (Measurable.{u_1, 0} G ENNReal mG ENNReal.measurableSpace g) -> (Measurable.{u_1, 0} G ENNReal mG 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{G : Type.{u_1}} {mG : MeasurableSpace.{u_1} G} [inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.5 : Add.{u_1} G] [inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.8 : Neg.{u_1} G] [inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.11 : MeasurableAdd₂.{u_1} G mG inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.5] [inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.14 : MeasurableNeg.{u_1} G inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.8 mG] {f : G -> ENNReal} {g : G -> ENNReal} (μ : MeasureTheory.Measure.{u_1} G mG) [inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.29 : MeasureTheory.SFinite.{u_1} G mG μ], (Measurable.{u_1, 0} G ENNReal mG ENNReal.measurableSpace f) -> (Measurable.{u_1, 0} G ENNReal mG ENNReal.measurableSpace g) -> (Measurable.{u_1, 0} G ENNReal mG ENNReal.measurableSpace (MeasureTheory.lconvolution.{u_1} G mG inst._@.Mathlib.Analysis.LConvolution.4293277646._hygCtx._hyg.5 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{G : Type.{u_1}} {mG : MeasurableSpace.{u_1} G} [inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.5 : AddGroup.{u_1} G] [inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.8 : MeasurableAdd₂.{u_1} G mG (AddZero.toAdd.{u_1} G (AddZeroClass.toAddZero.{u_1} G (AddMonoid.toAddZeroClass.{u_1} G (SubNegMonoid.toAddMonoid.{u_1} G (AddGroup.toSubNegMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.5)))))] [inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.11 : MeasurableNeg.{u_1} G (NegZeroClass.toNeg.{u_1} G (SubNegZeroMonoid.toNegZeroClass.{u_1} G (SubtractionMonoid.toSubNegZeroMonoid.{u_1} G (AddGroup.toSubtractionMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.5)))) mG] {μ : MeasureTheory.Measure.{u_1} G mG} [inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.16 : MeasureTheory.Measure.IsAddLeftInvariant.{u_1} G mG (AddZero.toAdd.{u_1} G (AddZeroClass.toAddZero.{u_1} G 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μ","typeReadable":"∀ {G : Type u_1} {mG : MeasurableSpace G} [inst : AddGroup G] [MeasurableAdd₂ G] [MeasurableNeg G]\n  {μ : MeasureTheory.Measure G} [μ.IsAddLeftInvariant] [MeasureTheory.SFinite μ] {f g k : G → ENNReal},\n  Measurable f →\n    Measurable g →\n      Measurable k →\n        MeasureTheory.lconvolution f (MeasureTheory.lconvolution g k μ) μ =\n          MeasureTheory.lconvolution (MeasureTheory.lconvolution f g μ) k 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[inst._@.Mathlib.Analysis.LConvolution.3373480115._hygCtx._hyg.8 : Neg.{u_1} G] (f : G -> ENNReal) (μ : MeasureTheory.Measure.{u_1} G mG), Eq.{succ u_1} (G -> ENNReal) (MeasureTheory.lconvolution.{u_1} G mG inst._@.Mathlib.Analysis.LConvolution.3373480115._hygCtx._hyg.5 inst._@.Mathlib.Analysis.LConvolution.3373480115._hygCtx._hyg.8 (OfNat.ofNat.{u_1} (G -> ENNReal) 0 (Zero.toOfNat0.{u_1} (G -> ENNReal) (Pi.instZero.{u_1, 0} G (fun (a._@._internal._hyg.0 : G) => ENNReal) (fun (i : G) => instZeroENNReal)))) f μ) (OfNat.ofNat.{u_1} (G -> ENNReal) 0 (Zero.toOfNat0.{u_1} (G -> ENNReal) (Pi.instZero.{u_1, 0} G (fun (a._@._internal._hyg.0 : G) => ENNReal) (fun (i : G) => instZeroENNReal))))","typeFull":"∀ {G : Type u_1} {mG : MeasurableSpace G} [inst : Add G] [inst_1 : Neg G] (f : G → ENNReal)\n  (μ : MeasureTheory.Measure G), MeasureTheory.lconvolution 0 f μ = 0","typeReadable":"∀ {G : Type u_1} {mG : MeasurableSpace G} [inst : Add G] [inst_1 : Neg G] (f : G → ENNReal)\n  (μ : 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{G : Type.{u_1}} {mG : MeasurableSpace.{u_1} G} [inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.5 : Group.{u_1} G] [inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.8 : MeasurableMul₂.{u_1} G mG (MulOne.toMul.{u_1} G (MulOneClass.toMulOne.{u_1} G (Monoid.toMulOneClass.{u_1} G (DivInvMonoid.toMonoid.{u_1} G (Group.toDivInvMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.5)))))] [inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.11 : MeasurableInv.{u_1} G (InvOneClass.toInv.{u_1} G (DivInvOneMonoid.toInvOneClass.{u_1} G (DivisionMonoid.toDivInvOneMonoid.{u_1} G (Group.toDivisionMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.5)))) mG] {μ : MeasureTheory.Measure.{u_1} G mG} [inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.16 : MeasureTheory.Measure.IsMulLeftInvariant.{u_1} G mG (MulOne.toMul.{u_1} G (MulOneClass.toMulOne.{u_1} G (Monoid.toMulOneClass.{u_1} G 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(MeasureTheory.mlconvolution.{u_1} G mG (MulOne.toMul.{u_1} G (MulOneClass.toMulOne.{u_1} G (Monoid.toMulOneClass.{u_1} G (DivInvMonoid.toMonoid.{u_1} G (Group.toDivInvMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.5))))) (InvOneClass.toInv.{u_1} G (DivInvOneMonoid.toInvOneClass.{u_1} G (DivisionMonoid.toDivInvOneMonoid.{u_1} G (Group.toDivisionMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.5)))) g k μ) μ) (MeasureTheory.mlconvolution.{u_1} G mG (MulOne.toMul.{u_1} G (MulOneClass.toMulOne.{u_1} G (Monoid.toMulOneClass.{u_1} G (DivInvMonoid.toMonoid.{u_1} G (Group.toDivInvMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.5))))) (InvOneClass.toInv.{u_1} G (DivInvOneMonoid.toInvOneClass.{u_1} G (DivisionMonoid.toDivInvOneMonoid.{u_1} G (Group.toDivisionMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.2633532335._hygCtx._hyg.5)))) (MeasureTheory.mlconvolution.{u_1} G mG (MulOne.toMul.{u_1} G 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[μ.IsMulLeftInvariant] [MeasureTheory.SFinite μ] {f g k : G → ENNReal},\n  Measurable f →\n    Measurable g →\n      Measurable k →\n        MeasureTheory.mlconvolution f (MeasureTheory.mlconvolution g k μ) μ =\n          MeasureTheory.mlconvolution (MeasureTheory.mlconvolution f g μ) k 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{G : Type.{u_1}} {mG : MeasurableSpace.{u_1} G} [inst._@.Mathlib.Analysis.LConvolution.3522812524._hygCtx._hyg.5 : AddGroup.{u_1} G] [inst._@.Mathlib.Analysis.LConvolution.3522812524._hygCtx._hyg.8 : MeasurableAdd₂.{u_1} G mG (AddZero.toAdd.{u_1} G (AddZeroClass.toAddZero.{u_1} G (AddMonoid.toAddZeroClass.{u_1} G (SubNegMonoid.toAddMonoid.{u_1} G (AddGroup.toSubNegMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.3522812524._hygCtx._hyg.5)))))] [inst._@.Mathlib.Analysis.LConvolution.3522812524._hygCtx._hyg.11 : MeasurableNeg.{u_1} G (NegZeroClass.toNeg.{u_1} G (SubNegZeroMonoid.toNegZeroClass.{u_1} G (SubtractionMonoid.toSubNegZeroMonoid.{u_1} G (AddGroup.toSubtractionMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.3522812524._hygCtx._hyg.5)))) mG] {μ : MeasureTheory.Measure.{u_1} G mG} [inst._@.Mathlib.Analysis.LConvolution.3522812524._hygCtx._hyg.16 : MeasureTheory.Measure.IsAddLeftInvariant.{u_1} G mG (AddZero.toAdd.{u_1} G (AddZeroClass.toAddZero.{u_1} G (AddMonoid.toAddZeroClass.{u_1} G (SubNegMonoid.toAddMonoid.{u_1} G (AddGroup.toSubNegMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.3522812524._hygCtx._hyg.5))))) μ] [inst._@.Mathlib.Analysis.LConvolution.3522812524._hygCtx._hyg.19 : MeasureTheory.SFinite.{u_1} G mG μ] {f : G -> ENNReal} {g : G -> ENNReal}, (AEMeasurable.{u_1, 0} G ENNReal ENNReal.measurableSpace mG f μ) -> (AEMeasurable.{u_1, 0} G ENNReal ENNReal.measurableSpace mG g μ) -> (AEMeasurable.{u_1, 0} G ENNReal ENNReal.measurableSpace mG (MeasureTheory.lconvolution.{u_1} G mG (AddZero.toAdd.{u_1} G (AddZeroClass.toAddZero.{u_1} G (AddMonoid.toAddZeroClass.{u_1} G (SubNegMonoid.toAddMonoid.{u_1} G (AddGroup.toSubNegMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.3522812524._hygCtx._hyg.5))))) (NegZeroClass.toNeg.{u_1} G (SubNegZeroMonoid.toNegZeroClass.{u_1} G (SubtractionMonoid.toSubNegZeroMonoid.{u_1} G (AddGroup.toSubtractionMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.3522812524._hygCtx._hyg.5)))) f g μ) μ)","typeFull":"∀ {G : Type u_1} {mG : MeasurableSpace G} [inst : AddGroup G] [MeasurableAdd₂ G] [MeasurableNeg G]\n  {μ : MeasureTheory.Measure G} [μ.IsAddLeftInvariant] [MeasureTheory.SFinite μ] {f g : G → ENNReal},\n  AEMeasurable f μ → AEMeasurable g μ → AEMeasurable (MeasureTheory.lconvolution f g μ) μ","typeReadable":"∀ {G : Type u_1} {mG : MeasurableSpace G} [inst : AddGroup G] [MeasurableAdd₂ G] [MeasurableNeg G]\n  {μ : MeasureTheory.Measure G} [μ.IsAddLeftInvariant] [MeasureTheory.SFinite μ] {f g : G → ENNReal},\n  AEMeasurable f μ → AEMeasurable g μ → AEMeasurable (MeasureTheory.lconvolution f g μ) 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{G : Type.{u_1}} {mG : MeasurableSpace.{u_1} G} [inst._@.Mathlib.Analysis.LConvolution.612936202._hygCtx._hyg.5 : AddCommGroup.{u_1} G] [inst._@.Mathlib.Analysis.LConvolution.612936202._hygCtx._hyg.8 : MeasurableAdd₂.{u_1} G mG (AddZero.toAdd.{u_1} G (AddZeroClass.toAddZero.{u_1} G (AddMonoid.toAddZeroClass.{u_1} G (SubNegMonoid.toAddMonoid.{u_1} G (AddGroup.toSubNegMonoid.{u_1} G (AddCommGroup.toAddGroup.{u_1} G inst._@.Mathlib.Analysis.LConvolution.612936202._hygCtx._hyg.5))))))] [inst._@.Mathlib.Analysis.LConvolution.612936202._hygCtx._hyg.11 : MeasurableNeg.{u_1} G (NegZeroClass.toNeg.{u_1} G (SubNegZeroMonoid.toNegZeroClass.{u_1} G (SubtractionMonoid.toSubNegZeroMonoid.{u_1} G (SubtractionCommMonoid.toSubtractionMonoid.{u_1} G (AddCommGroup.toDivisionAddCommMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.612936202._hygCtx._hyg.5))))) mG] {μ : MeasureTheory.Measure.{u_1} G mG} [inst._@.Mathlib.Analysis.LConvolution.612936202._hygCtx._hyg.16 : MeasureTheory.Measure.IsAddLeftInvariant.{u_1} G mG (AddZero.toAdd.{u_1} G (AddZeroClass.toAddZero.{u_1} G (AddMonoid.toAddZeroClass.{u_1} G (SubNegMonoid.toAddMonoid.{u_1} G (AddGroup.toSubNegMonoid.{u_1} G (AddCommGroup.toAddGroup.{u_1} G inst._@.Mathlib.Analysis.LConvolution.612936202._hygCtx._hyg.5)))))) μ] [inst._@.Mathlib.Analysis.LConvolution.612936202._hygCtx._hyg.19 : MeasureTheory.Measure.IsNegInvariant.{u_1} G mG (NegZeroClass.toNeg.{u_1} G (SubNegZeroMonoid.toNegZeroClass.{u_1} G (SubtractionMonoid.toSubNegZeroMonoid.{u_1} G (SubtractionCommMonoid.toSubtractionMonoid.{u_1} G (AddCommGroup.toDivisionAddCommMonoid.{u_1} G inst._@.Mathlib.Analysis.LConvolution.612936202._hygCtx._hyg.5))))) μ] {f : G -> ENNReal} {g : G -> ENNReal}, Eq.{succ u_1} (G -> ENNReal) (MeasureTheory.lconvolution.{u_1} G mG (AddZero.toAdd.{u_1} G (AddZeroClass.toAddZero.{u_1} G (AddMonoid.toAddZeroClass.{u_1} G (SubNegMonoid.toAddMonoid.{u_1} G (AddGroup.toSubNegMonoid.{u_1} G 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u_1} {mG : MeasurableSpace G} [inst : AddCommGroup G] [MeasurableAdd₂ G] [MeasurableNeg G]\n  {μ : MeasureTheory.Measure G} [μ.IsAddLeftInvariant] [μ.IsNegInvariant] {f g : G → ENNReal},\n  MeasureTheory.lconvolution f g μ = MeasureTheory.lconvolution g f μ","typeReadable":"∀ {G : Type u_1} {mG : MeasurableSpace G} [inst : AddCommGroup G] [MeasurableAdd₂ G] [MeasurableNeg G]\n  {μ : MeasureTheory.Measure G} [μ.IsAddLeftInvariant] [μ.IsNegInvariant] {f g : G → ENNReal},\n  MeasureTheory.lconvolution f g μ = MeasureTheory.lconvolution g f 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.NormedSpace.PiTensorProduct.InjectiveSeminorm.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Comma.StructuredArrow.Final.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Generator.Sheaf.sym.json

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{C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology.{v, u} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.3) {A : Type.{u'}} [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.9 : CategoryTheory.Category.{v', u'} A] [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.12 : CategoryTheory.Limits.HasCoproducts.{v, v', u'} A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.9] [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.15 : CategoryTheory.HasWeakSheafify.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.3 J A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.9] {ι : Type.{w}} {S : ι -> A}, (CategoryTheory.ObjectProperty.IsSeparating.{v', u'} A 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inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.3) A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.9) (CategoryTheory.Presheaf.IsSheaf.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.3 A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.9 J)) (CategoryTheory.ObjectProperty.ofObj.{max u v', max (max (max u u') v) v', max u w} (CategoryTheory.Sheaf.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.3 J A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.9) (CategoryTheory.Category.toCategoryStruct.{max u v', max (max (max u u') v) v'} (CategoryTheory.Sheaf.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.3 J A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.3151734587._hygCtx._hyg.9) (CategoryTheory.ObjectProperty.FullSubcategory.category.{max u v', max (max (max u u') v) v'} 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CategoryTheory.Limits.HasCoproducts A]\n  [inst_3 : CategoryTheory.HasWeakSheafify J A] {ι : Type w} {S : ι → A},\n  (CategoryTheory.ObjectProperty.ofObj S).IsSeparating →\n    (CategoryTheory.ObjectProperty.ofObj fun x =>\n        match x with\n        | (X, i) => CategoryTheory.Sheaf.freeYoneda J X (S i)).IsSeparating","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {A : Type u'}\n  [inst_1 : CategoryTheory.Category.{v', u'} A] [inst_2 : CategoryTheory.Limits.HasCoproducts A]\n  [inst_3 : CategoryTheory.HasWeakSheafify J A] {ι : Type w} {S : ι → A},\n  (CategoryTheory.ObjectProperty.ofObj S).IsSeparating →\n    (CategoryTheory.ObjectProperty.ofObj fun x =>\n        match x with\n        | (X, i) => CategoryTheory.Sheaf.freeYoneda J X (S 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{C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology.{v, u} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.3) {A : Type.{u'}} [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.9 : CategoryTheory.Category.{v', u'} A] [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.12 : CategoryTheory.Limits.HasCoproducts.{v, v', u'} A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.9] [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.15 : CategoryTheory.HasWeakSheafify.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.3 J A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.9] {ι : Type.{w}} {S : ι -> A}, (CategoryTheory.ObjectProperty.IsSeparating.{v', u'} A 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(CategoryTheory.Functor.category.{v, v', u, u'} (Opposite.{succ u} C) (CategoryTheory.Category.opposite.{v, u} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.3) A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.9) (CategoryTheory.Presheaf.IsSheaf.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.3 A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.9 J)) (fun (x._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.34 : Prod.{u, w} C ι) => CategoryTheory.Sheaf.isSeparating.match_1.{u, w, max (max (max (succ u) (succ u')) (succ v)) (succ v')} C ι (fun (x._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx.34.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.67 : Prod.{u, w} C ι) => CategoryTheory.Sheaf.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.3 J A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.9) x._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.34 (fun (X : C) (i : ι) => CategoryTheory.Sheaf.freeYoneda.{v', v, u', u} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.3 J A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.9 inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.12 inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.15 X (S i)))] [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.40 : CategoryTheory.Preadditive.{v', u'} A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.9], CategoryTheory.IsSeparator.{max u v', max (max (max u u') v) v'} (CategoryTheory.Sheaf.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.3 J A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.9) 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inst._@.Mathlib.CategoryTheory.Generator.Sheaf.712464633._hygCtx._hyg.28))","typeFull":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {A : Type u'}\n  [inst_1 : CategoryTheory.Category.{v', u'} A] [inst_2 : CategoryTheory.Limits.HasCoproducts A]\n  [inst_3 : CategoryTheory.HasWeakSheafify J A] {ι : Type w} {S : ι → A},\n  (CategoryTheory.ObjectProperty.ofObj S).IsSeparating →\n    ∀\n      [inst_4 :\n        CategoryTheory.Limits.HasCoproduct fun x =>\n          match x with\n          | (X, i) => CategoryTheory.Sheaf.freeYoneda J X (S i)]\n      [CategoryTheory.Preadditive A],\n      CategoryTheory.IsSeparator\n        (∐ fun x =>\n          match x with\n          | (X, i) => CategoryTheory.Sheaf.freeYoneda J X (S i))","typeReadable":"∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {A : Type u'}\n  [inst_1 : CategoryTheory.Category.{v', u'} A] [inst_2 : CategoryTheory.Limits.HasCoproducts A]\n  [inst_3 : CategoryTheory.HasWeakSheafify J A] {ι : Type w} {S : ι → A},\n  (CategoryTheory.ObjectProperty.ofObj S).IsSeparating →\n    ∀\n      [inst_4 :\n        CategoryTheory.Limits.HasCoproduct fun x =>\n          match x with\n          | (X, i) => CategoryTheory.Sheaf.freeYoneda J X (S i)]\n      [CategoryTheory.Preadditive A],\n      CategoryTheory.IsSeparator\n        (∐ fun x =>\n          match x with\n          | (X, i) => CategoryTheory.Sheaf.freeYoneda J X (S i))","typeReferences":[["CategoryTheory","Category","opposite"],["CategoryTheory","Functor"],["CategoryTheory","Limits","HasCoproduct"],["Opposite"],["CategoryTheory","Preadditive"],["CategoryTheory","Category"],["CategoryTheory","ObjectProperty","FullSubcategory","category"],["CategoryTheory","GrothendieckTopology"],["CategoryTheory","HasWeakSheafify"],["CategoryTheory","Category","toCategoryStruct"],["CategoryTheory","Sheaf","isSeparating","match_1"],["Prod"],["CategoryTheory","IsSeparator"],["CategoryTheory","Limits","HasCoproducts"],["CategoryTheory","Limits","sigmaObj"],["CategoryTheory","Presheaf","IsSheaf"],["CategoryTheory","ObjectProperty","IsSeparating"],["CategoryTheory","Functor","category"],["CategoryTheory","Sheaf"],["CategoryTheory","Sheaf","freeYoneda"],["CategoryTheory","ObjectProperty","ofObj"]],"valueReferences":[["CategoryTheory","Functor"],["CategoryTheory","Category","opposite"],["CategoryTheory","Sheaf","isSeparating"],["Opposite"],["CategoryTheory","ObjectProperty","FullSubcategory","category"],["CategoryTheory","Sheaf","isSeparating","match_1"],["Prod"],["CategoryTheory","ObjectProperty","instHasZeroMorphismsFullSubcategory"],["CategoryTheory","Limits","instHasZeroMorphismsFunctor"],["CategoryTheory","Presheaf","IsSheaf"],["CategoryTheory","ObjectProperty","IsSeparating","isSeparator_coproduct"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["CategoryTheory","Functor","category"],["CategoryTheory","Sheaf"],["CategoryTheory","Sheaf","freeYoneda"]]},{"isProp":true,"kind":"theorem","name":["CategoryTheory","Sheaf","hasSeparator"],"typeFallback":"forall {C : Type.{u}} [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.554182146._hygCtx._hyg.3 : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology.{v, u} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.554182146._hygCtx._hyg.3) (A : Type.{u'}) [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.554182146._hygCtx._hyg.9 : CategoryTheory.Category.{v', u'} A] [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.554182146._hygCtx._hyg.12 : CategoryTheory.Limits.HasCoproducts.{v, v', u'} A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.554182146._hygCtx._hyg.9] [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.554182146._hygCtx._hyg.15 : CategoryTheory.HasWeakSheafify.{v, v', u, u'} C inst._@.Mathlib.CategoryTheory.Generator.Sheaf.554182146._hygCtx._hyg.3 J A inst._@.Mathlib.CategoryTheory.Generator.Sheaf.554182146._hygCtx._hyg.9] [inst._@.Mathlib.CategoryTheory.Generator.Sheaf.554182146._hygCtx._hyg.19 : CategoryTheory.HasSeparator.{v', u'} A 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Combinatorics.Matroid.Init.sym.json

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