Proof Bounded_subprops1_Out.
Section Bounded_subprops2.
Variable P : Ens -> Prop.
Variable Q : Ens -> Prop.
Hypothesis s : SUBPROP P Q.
Hypothesis b : Bounded Q.
Let A : Ens := Bounded_CHOICE Q.
Let h : Bounded_By A Q. Proof Bounded_CHOICE_pr Q b.
Let step1 : Bounded_By A P.
Proof Bounded_subprops_th1 P Q s A h.

Lemma Bounded_sub2_Out : Bounded P.
Proof Bounded_th2 P A step1.