intuition.
eapply eq_impl_comp_spec_eq.
intuition.
eapply evalDist_assoc; intuition.
Qed.

(* other facts *)
Theorem comp_spec_event_equiv :
forall (A B : Set){eqda : EqDec A}{eqdb : EqDec B}(c1 : Comp A)(c2 : Comp B)(f1 : A -> bool)(f2 : B -> bool)(P : bool -> bool -> Prop),
comp_spec (fun a b => P (f1 a) (f2 b)) c1 c2 ->
comp_spec P (x <-$ c1; ret (f1 x)) (x <-$ c2; ret (f2 x)).