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_length_2_inv : forall a1 a2 l, Permutation [a1;a2] l -> l = [a1;a2] \/ l = [a2;a1].