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_pigeonhole l1 l2 : incl l1 l2 -> length l2 < length l1 ->
exists a l3, Permutation l1 (a :: a :: l3).