proposition: Lemma le_iff_lt_S x y : x ≤ y <-> x < 1 + y.
proof: Proof. rewrite plus_comm. apply le_iff_lt_plus_1. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.naturals HoTT.Classes.theory.rings HoTT.Classes.orders.semirings