Proof fun F : Ens => REPLACEMENT_pr2 (b_in_Union_a F) (Union_bounded F).
Definition Union_intermediate (F X : Ens) (i : IN X (Union F)) : Ens :=
CHOICE (fun U : Ens => nested_IN X U F).

Theorem Union_intermediate_pr :
forall (F X : Ens) (i : IN X (Union F)),
nested_IN X (Union_intermediate F X i) F.