induction ls; intuition; simpl.
eapply comp_spec_eq_refl.
rewrite H.
prog_simp.
intuition.
Qed.

Lemma repeatMax_fold_in_support_false :
forall (A B : Set)(ls : list B)(eqd : EqDec A)(c : B -> Comp A)(P : A -> bool)(a : A),
(forall b, In b ls -> In a (getSupport (c b))) ->
P a = false ->
In a
(getSupport
(compFold eqd
(fun (a' : A) b => if P a' then ret a' else (c b)) a ls)).