Ltac InvAdd := repeat (match goal with
| H: Add ?x _ (_ :: _) |- _ => inversion H; clear H; subst
end).
Ltac finish_basic_perms H :=
try constructor; try rewrite perm_swap; try constructor; trivial;
(rewrite <- H; now apply Permutation_Add) ||
(rewrite H; symmetry; now apply Permutation_Add).

Lemma Permutation_app_inv_m l l1 l2 l3 l4 :
Permutation (l1 ++ l ++ l2) (l3 ++ l ++ l4) ->
Permutation (l1 ++ l2) (l3 ++ l4).