Proof
fun (F X : Ens) (h : EXISTS (fun U : Ens => nested_IN X U F)) =>
REPLACEMENT_pr1 (b_in_Union_a F) (Union_bounded F) X h.

Theorem Union_pr2 :
forall (F X : Ens) (i : IN X (Union F)),
EXISTS (fun U : Ens => nested_IN X U F).