proposition: Lemma to_semiring_involutive N `{Naturals N} N2 `{Naturals N2} x : naturals_to_semiring N2 N (naturals_to_semiring N N2 x) = x.
proof: Proof. change (Compose (naturals_to_semiring N2 N) (naturals_to_semiring N N2) x = id x). apply to_semiring_unique_alt;apply _. 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