induction ls; intuition; simpl in *.
comp_simp; simpl; reflexivity.
inline_first; comp_skip; inline_first.
comp_swap_l.
(* comp_skip *)
(* *)
eapply comp_spec_eq_trans.
eapply (@comp_spec_seq (list C) (list C));
eauto with inhabited.
(* *)
intuition; subst.
eapply comp_spec_eq_refl.
inline_first; comp_skip; comp_simp; simpl.
comp_swap_r; comp_skip.
Qed.

(* Specifications: *)
Lemma list_pred_eq_gen :
forall (A : Set)(ls1 ls2 : list A),
ls1 = ls2 ->
list_pred eq ls1 ls2.