x z : 0 < z <-> - z + x < x. Proof. split; intros ltz. - rewrite (commutativity (-z) x); apply pos_minus_lt_compat_r; assumption. - rewrite (commutativity (-z) x) in ltz. apply (snd (pos_minus_lt_compat_r x z)); assumption. Qed.
Require Import