proposition: Lemma mon_apps_app_cons : forall u u', R u u' -> forall p (ts : Tes p) q (vs : Tes q) t, R (apps t (Vapp ts (Vcons u vs))) (apps t (Vapp ts (Vcons u' vs))).
proof: Proof. intros u u' uu'. induction ts; intros q vs t; simpl. apply mon_apps_l. apply mon_app_r; auto. refl. apply IHts. Qed.
imports: Coq(FSets Structures.OrderedType) CoLoR(LogicUtil BoolUtil VecUtil FSetUtil NatUtil RelUtil SN SetUtil)