proposition: Lemma add_S_r : forall a b, a + S b =N= S (a + b).
proof: Proof. induction a as [|a IHa];intros b. - reflexivity. - simpl_nat. apply (ap S),IHa. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.naturals HoTT.Classes.interfaces.orders HoTT.Classes.theory.rings HoTT.Classes.orders.semirings HoTT.Classes.theory.apartness