simple induction E'; intros A' f' r'; simple induction E'';
intros A'' f'' r''; simpl in |- *; simple induction 1;
intros e1 e2; simple induction 1; intros a' e'; elim (e1 a');
intros a'' e''; exists a''; apply EQ_tran with (f' a');
assumption.
Qed.
(* Inclusion is reflexive, transitive, extentional *)

Theorem INC_refl : forall E : Ens, INC E E.
unfold INC in |- *; auto with zfc.