∀ {D₁ : Type u_3} {Q₁ : Type u_4} {D₂ : Type u_1} {Q₂ : Type u_2} [inst : Group D₁] [inst_1 : Group Q₁]
  [inst_2 : Group D₂] [inst_3 : Group Q₂] (f : D₁ ≃* D₂) (g : Q₁ ≃* Q₂) (x : D₂ ≀ᵣ Q₂),
  (fun x => { left := ⇑f ∘ x.left ∘ ⇑g.symm, right := g x.right })
      ((fun x => { left := (⇑f.symm ∘ x.left) ∘ ⇑g, right := g.symm x.right }) x) =
    x