proposition: Theorem le_add_le_sub_r : forall n m p, n + p <= m -> n <= m - p.
proof: Proof. intros n m p LE. apply (add_le_mono_r _ _ p). rewrite sub_add. - assumption. - apply le_trans with (n+p); trivial. rewrite <- (add_0_l p) at 1. rewrite <- add_le_mono_r. apply le_0_l. Qed.
imports: NMulOrder