induction ls; intuition.
simpl.
eapply comp_spec_eq_refl.
simpl.
prog_simp.
eapply comp_spec_eq_trans.
eapply comp_spec_seq_eq; intuition.
eapply IHls.
eapply comp_spec_eq_refl.
prog_simp.
eapply comp_spec_eq_refl.
Qed.

(* Specifications: *)
Lemma compFold_nop :
forall (A B : Set)(eqd : EqDec A)(c : A -> B -> Comp A)(ls : list B) init x,
In x (getSupport (compFold _ c init ls)) ->
(forall b a, In b ls -> In a (getSupport (c init b)) -> a = init) ->
x = init.