proposition: Lemma nat_le_plus {x y: N}: x ≤ y <-> exists z, y = x + z.
proof: Proof. split; intros E. - destruct (decompose_le E) as [z [Ez1 Ez2]]. exists z. trivial. - destruct E as [z Ez]. apply compose_le with z; [solve_propholds | trivial]. Qed.
imports: HoTT.Types.Sigma HoTT.Classes.theory.naturals HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.rings HoTT.Classes.orders.rings HoTT.Classes.implementations.peano_naturals HoTT.Classes.orders.nat_int