Section Bool.
(** Properties of [filter] *)
Variable f:elt->bool.
Variable Comp: Proper (E.eq==>Logic.eq) f.
Let Comp' : Proper (E.eq==>Logic.eq) (fun x =>negb (f x)).
(** Properties of [for_all] *)

Lemma for_all_mem_3:
forall s x,(mem x s)=true -> (f x)=false -> (for_all f s)=false.