proposition: Lemma le_S_either : forall a b, a <= S b -> a <= b |_| a = S b.
proof: Proof. intros [|a] b. - intros;left;apply zero_least. - intros E. apply (snd (le_S_S _ _)) in E. destruct E as [|b E];auto. left. apply le_S_S. trivial. Defined.
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