∀ {R : Type u_2} {A₁ : Type u_3} {A₂ : Type u_1} [inst : CommSemiring R] [inst_1 : Semiring A₁] [inst_2 : Semiring A₂]
  [inst_3 : Algebra R A₁] [inst_4 : Algebra R A₂] (f : A₁ →ₐ[R] A₂) (g : A₂ →ₐ[R] A₁),
  f.comp g = AlgHom.id R A₂ → ∀ (x : A₂), (f.comp g) x = (AlgHom.id R A₂) x