induction ls1; intuition.
rewrite app_nil_l.
unfold compFold.
fold compFold.
comp_simp.
intuition.
rewrite <- app_comm_cons.
unfold compFold.
fold compFold.
inline_first.
comp_skip.
Qed.

Theorem comp_fold_ext :
forall (A B : Set)(eqd : EqDec A)(c1 c2 : A -> B -> Comp A)(ls : list B)(init : A),
(forall a b,
comp_spec eq (c1 a b) (c2 a b)) ->
comp_spec eq (compFold _ c1 init ls) (compFold _ c2 init ls).