proposition: Lemma plus_gt_compat : forall m n m' n', m >> m' -> n >> n' -> m + n >> m' + n'.
proof: Proof. intros. destruct m; destruct n; destruct m'; destruct n'; simpl; trivial; tropical_ord. apply min_gt_compat; hyp. unfold Peano.gt. apply lt_min_intro_l. hyp. unfold Peano.gt. apply lt_min_intro_r. hyp. Qed.
imports: Coq(Morphisms) CoLoR(RelDec RelUtil SN RelExtras NatUtil LogicUtil ZUtil)