induction lsa; intuition; simpl in *.
destruct lsb; simpl in *; congruence.
destruct lsb; simpl in *; try omega.
f_equal.
eauto.
Qed.

Theorem Permutation_flatten :
forall (A : Set)(ls1 ls2 : list (list A)),
Permutation ls1 ls2 ->
Permutation (flatten ls1) (flatten ls2).