unfold Union in |- *.
simpl in |- *.
simple induction E; intros A f r; simple induction E'; intros A' f' r'.
simpl in |- *.
intros.
elim X; intros.
split.
simple induction x.
intros.
elim (a x0).
intros.
elim (EQC_EXType (f x0) (f' x1) p0 p).
intros.
exists (dep_i A' (fun x : A' => pi1 (f' x)) x1 x2).
simpl in |- *.
auto with zfc.
simple induction y; intros.
elim (b x); intros.
cut (EQC (f' x) (f x0)); auto with zfc.
intros e.
elim (EQC_EXType (f' x) (f x0) e p); intros.
exists (dep_i A (fun x0 : A => pi1 (f x0)) x0 x1).
simpl in |- *; auto with zfc.
Qed.

Theorem Union_monC :
forall E E' : Ens, CINC E E' -> CINC (Union E) (Union E').