induction 1; intuition; simpl.
eapply comp_spec_ret; intuition.
eapply comp_spec_seq; eauto.
eapply foldBody_option_spec; eauto.
Qed.
(* Map a computation over a list. *)
Fixpoint compMap (A B : Set)(eqdb : EqDec B)(c : A -> Comp B)(ls : list A) : Comp (list B) :=
match ls with
| nil => ret nil
| a :: lsa' =>
b <-$ c a;
lsb' <-$ compMap _ c lsa';
ret (b :: lsb')
end.

Theorem compMap_cons:
forall (A B : Set)(eqdb : EqDec B) (ls : list A)(c : A -> Comp B) (a : A) x,
evalDist (compMap _ c (a :: ls)) x ==
evalDist (b <-$ c a; lsb <-$ compMap _ c ls; ret (b :: lsb)) x.