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_2:
forall s, exists_ f s=false -> forall x, mem x s=true -> f x=false.