proposition: Lemma decompose_le {x y} : x ≤ y -> exists z, 0 ≤ z /\ y = x + z.
proof: Proof. intros E. destruct (srorder_partial_minus x y E) as [z Ez]. exists z. split; [| trivial]. apply (order_reflecting (x+)). rewrite plus_0_r, <-Ez. trivial. Qed.
imports: HoTT.Classes.theory.apartness HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.rings HoTT.Classes.orders.orders HoTT.Classes.orders.maps