intuition.
eapply map_eq_nth_h; intuition.
Qed.

(* Specifications: *)
Theorem compFold_eq' :
forall (A1 A2 : Set) P (ls1 : list A1) (ls2 : list A2),
list_pred P ls1 ls2 ->
forall (B : Set)(eqd1 eqd2 : EqDec B) (c1 : B -> A1 -> Comp B) (c2: B -> A2 -> Comp B),
(forall acc a1 a2 x, P a1 a2 -> In a1 ls1 -> In a2 ls2 ->evalDist (c1 acc a1) x == evalDist (c2 acc a2) x) ->
forall init x,
evalDist (compFold eqd1 c1 init ls1) x == evalDist (compFold eqd2 c2 init ls2) x.