induction ls; simpl in *; intuition.
destruct H; intuition.
apply in_app_or in H.
intuition.
exists a; intuition.
apply IHls in H0.
destruct H0.
intuition.
exists x; intuition.
apply in_or_app.
destruct H; intuition.
subst.
intuition.
right.
eapply IHls.
econstructor.
eauto.
Qed.

(* Specifications: *)
Theorem length_flatten_nz : forall (A : Type)(ls : list (list A)) ls',
In ls' ls ->
length ls' > 0 ->
length (flatten ls) > 0.