∀ (k : Type u_2) (G : Type u_3) [inst : Ring k] [inst_1 : Monoid G] (A : Action (ModuleCat k) G),
  CategoryTheory.CategoryStruct.comp { hom := CategoryTheory.CategoryStruct.id A.V, comm := ⋯ }
      { hom := CategoryTheory.CategoryStruct.id ((Rep.RepToAction k G).obj ((Rep.ActionToRep k G).obj A)).V,
        comm := ⋯ } =
    CategoryTheory.CategoryStruct.id A