(******************)
intros. generalize H0. rewrite app_eq2. intros. injection H1. intro. apply H. exact H2.
Qed.

Lemma app_v_nil_sym : forall v1 v2 : list A, v1 = nil -> v1 ++ v2 = v2 ++ v1.
simple induction v2. intro. rewrite H. trivial with arith.