∀ {k G H : Type u_1} [inst : CommRing k] [inst_1 : Monoid G] [inst_2 : Monoid H] (φ : G →* H) (B : Rep k H)
  (A : Rep k G) (f : (Action.res (ModuleCat k) φ).obj B ⟶ A) (x : H),
  CategoryTheory.CategoryStruct.comp (B.ρ x)
      (ModuleCat.ofHom
        (LinearMap.codRestrict (Representation.coindV φ A.ρ) (LinearMap.pi fun h => ModuleCat.Hom.hom f.hom ∘ₗ B.ρ h)
          ⋯)) =
    CategoryTheory.CategoryStruct.comp
      (ModuleCat.ofHom
        (LinearMap.codRestrict (Representation.coindV φ A.ρ) (LinearMap.pi fun h => ModuleCat.Hom.hom f.hom ∘ₗ B.ρ h)
          ⋯))
      ((Rep.coind φ A).ρ x)