(x y z : R) : 0 ≤ z -> x ≤ y -> x - z ≤ y. Proof. intros E1 E2. rewrite plus_comm, (plus_conjugate_alt y (- z)), involutive. apply (order_preserving (-(z) +)). transitivity y; trivial. pattern y at 1;apply (transport _ (plus_0_r y)). apply (order_preserving (y +)). trivial. Qed.
Require Import