Proof with auto.
intros.
induction H2.
simpl...
simpl...
rewrite app_length.
repeat rewrite map_length.
rewrite IHmerges_spec1. clear IHmerges_spec1.
rewrite IHmerges_spec2. clear IHmerges_spec2.
simpl @length...
Qed.
Definition me (ab: list T * list T): nat := length (fst ab) + length (snd ab).
Program Fixpoint merges_ex (ab: list T * list T) {measure (me ab)}: sig (merges_spec (fst ab) (snd ab)) :=
match ab with
| (nil, x) => x :: nil
| (x, nil) => x :: nil
| (x :: y, h :: t) => map (cons x) (merges_ex (y, h :: t)) ++ map (cons h) (merges_ex (x :: y, t))
end.
Next Obligation. unfold me. simpl. omega. Qed.
Next Obligation. repeat destruct_call merges_ex; auto. Qed.
Definition merges (a b: list T): list (list T) := proj1_sig (merges_ex (a, b)).

(* Specifications: *)
Lemma merges_real_eq a b: merges a b =
match a, b with
| nil, x => x :: nil
| x, nil => x :: nil
| x :: y, h :: t => map (cons x) (merges y (h :: t)) ++ map (cons h) (merges (x :: y) t)
end.