proposition: Lemma le_iff_lt_plus_1 x y : x ≤ y <-> x < y + 1.
proof: Proof. split; intros E. - apply lt_iff_plus_1_le. apply (order_preserving (+1)). trivial. - apply (order_reflecting (+1)), lt_iff_plus_1_le. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.naturals HoTT.Classes.theory.rings HoTT.Classes.orders.semirings