Proof with simpl; auto.
intros H1 H2 H3. revert c0 H2. induction l... intros c0 H2.
inversion H1; apply IHl...
Qed.

(* put this lemma elsewhere *)
Lemma var_eq_join_sub e1 e2 (x y s : state) :
sepalg.join x y s -> ((e1 === e2) s <-> (e1 === e2) x).