proposition: Lemma same_morphism x : (naturals_to_semiring N R ∘ f^-1) x = h x.
proof: Proof. transitivity ((h ∘ (f ∘ f^-1)) x). - symmetry. apply (to_semiring_unique (h ∘ f)). - unfold Compose. apply ap, eisretr. Qed.
imports: HoTT.Basics.Decidable HoTT.Classes.interfaces.orders HoTT.Classes.implementations.peano_naturals HoTT.Classes.theory.rings HoTT.Classes.isomorphisms.rings HoTT.Classes.interfaces.naturals