intros C; simple induction 1; intros a ea; elim (e1 a); intros a' ea';
exists a'.
apply EQ_tran with (f a); assumption.
Qed.
Hint Resolve EQ_sym EQ_refl EQ_INC: zfc.
(* easy lemma *)

(* Specifications: *)
Theorem INC_EQ : forall E E' : Ens, INC E E' -> INC E' E -> EQ E E'.
simple induction E; intros A f r; simple induction E'; intros A' f' r';
unfold INC in |- *; simpl in |- *; intros I1 I2; split.
Theorem INC_EQ : forall E E' : Ens, INC E E' -> INC E' E -> EQ E E'.
simple induction E; intros A f r; simple induction E'; intros A' f' r';
unfold INC in |- *; simpl in |- *; intros I1 I2; split.