proposition: Lemma Vmap_eq_nth : forall n (v1 : vector A n) (v2 : vector B n), (forall i (h : i<n), f (Vnth v1 h) = Vnth v2 h) -> Vmap v1 = v2.
proof: Proof. induction n; simpl; intros. VOtac. refl. VSntac v1. VSntac v2. simpl. apply Vcons_eq_intro. rewrite !Vhead_nth. apply H. apply IHn. intros. rewrite !Vnth_tail. apply H. Qed.
imports: Coq(Vector Program Structures.Equalities Morphisms) CoLoR(LogicUtil NatUtil EqUtil ListUtil BoolUtil RelUtil)