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_vs_elt_inv : forall l l1 l2 a, Permutation l (l1 ++ a :: l2) -> exists l' l'', l = l' ++ a :: l''.