proposition: Lemma same_morphism: integers_to_ring Z R ∘ f⁻¹ = h.
proof: Proof. Proof with auto. intros x y F. rewrite <-F. transitivity ((h ∘ (f ∘ f⁻¹)) x). symmetry. unfold compose. apply (to_ring_unique (h ∘ f)). unfold compose. now rewrite jections.surjective_applied. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.naturals MathClasses.interfaces.abstract_algebra MathClasses.implementations.natpair_integers MathClasses.interfaces.integers