proposition: Lemma lt_iff_S_le x y : x < y <-> 1 + x ≤ y.
proof: Proof. rewrite plus_comm. apply lt_iff_plus_1_le. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.naturals HoTT.Classes.theory.rings HoTT.Classes.orders.semirings