∀ {k G H : Type u_1} [inst : CommRing k] [inst_1 : Monoid G] [inst_2 : Monoid H] (φ : G →* H) (A : Rep k G)
  (x : (Action.res (ModuleCat k) φ).obj (Rep.leftRegular k H) ⟶ A) (x_1 : H),
  ((CategoryTheory.ConcreteCategory.hom
        ((fun f => { hom := ModuleCat.ofHom (Finsupp.linearCombination k ↑f), comm := ⋯ })
            ((fun f => ⟨fun h => (CategoryTheory.ConcreteCategory.hom f.hom) fun₀ | h => 1, ⋯⟩) x)).hom)
      fun₀ | x_1 => 1) =
    (CategoryTheory.ConcreteCategory.hom x.hom) fun₀ | x_1 => 1