∀ {k G H : Type u} [inst : CommRing k] [inst_1 : Monoid G] [inst_2 : Monoid H] (φ : G →* H) (X : Rep k G)
  (a : (Action.res (ModuleCat k) φ).obj (Rep.leftRegular k H) ⟶ X) (h : H),
  ↑((ModuleCat.Hom.hom ((Rep.coindFunctorIso φ).inv.app X).hom) a) h =
    (CategoryTheory.ConcreteCategory.hom a.hom) fun₀ | h => 1