induction l...
simpl.
rewrite IHl.
rewrite (merges_real_eq [a] (a0::l)).
rewrite (merges_real_eq [] (a0::l)).
simpl...
Qed.

(* Specifications: *)
Lemma merges_insert_everywhere' a l: Permutation (insert_everywhere a l) (merges l (a :: nil)).
Proof with auto.