(* foldBody_option is an adapter that allows you to fold a computation with signature B -> A -> Comp (option B) over a list of A, accumulating an option B. *)
Definition foldBody_option(A B : Set)(eqd : EqDec B)(f : B -> A -> Comp (option B))(b_opt : option B)(a : A) :=
  match b_opt with
      | None => ret None
      | Some b =>
        f b a
  end.Definition opt_pred(A B : Set)(P : A -> B -> Prop)(opt_a : option A)(opt_b : option B) :=
  match opt_a with
    | Some a =>
      match opt_b with
        | Some b => P a b
        | None => False
      end
    | None =>
      match opt_b with
        | Some _ => False
        | None => True
      end
  end.

Theorem foldBody_option_spec : forall (A B C D: Set)(eqda : EqDec A)(eqdb : EqDec B) (c1 : A -> C -> Comp (option A)) (c2 : B -> D -> Comp (option B)) (post : A -> B -> Prop) (pre1 : A -> B -> Prop) (pre2 : C -> D -> Prop), (forall a b c d, pre1 a b -> pre2 c d -> comp_spec (opt_pred post) (c1 a c) (c2 b d)) -> forall opt_a opt_b c d, opt_pred pre1 opt_a opt_b -> pre2 c d -> comp_spec (opt_pred post) (foldBody_option _ c1 opt_a c) (foldBody_option _ c2 opt_b d).