End Bool.
Section Bool'.
Variable f:elt->bool.
Variable Comp: Proper (E.eq==>Logic.eq) f.
Local Definition Comp' : Proper (E.eq==>Logic.eq) (fun x => negb (f x)).

Lemma exists_mem_4:
forall s, exists_ f s=true -> {x:elt | (mem x s)=true /\ (f x)=true}.