{x y} : x ≤ y -> exists z, 0 ≤ z /\ y = x + z. 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.
Require Import