simple induction E''; intros A'' f'' r'' e; simpl in |- *; simple induction 1;
intros a'' p; exists a''; apply EQ_tran with E; auto with zfc.
Qed.

(* Specifications: *)
Theorem IN_sound_right :
forall E E' E'' : Ens, EQ E' E'' -> IN E E' -> IN E E''.
Theorem IN_sound_right :
forall E E' E'' : Ens, EQ E' E'' -> IN E E' -> IN E E''.