∀ {α₁ : Type u_2} {α₂ : Type u_3} {β₁ : Type u_1} {β₂ : Type u_4} (e₁ : α₁ ≃ α₂) (e₂ : α₁ → β₁ ≃ β₂),
  Function.LeftInverse (fun y => (e₁.symm y.1, (e₂ (e₁.symm y.1)).symm y.2)) fun x => (e₁ x.1, (e₂ x.1) x.2)