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.
Proof Bounded_th2 P A step1.
End Bounded_subprops2.

Theorem Bounded_subprops_th2 :
forall (P Q : Ens -> Prop) (s : SUBPROP P Q) (b : Bounded Q), Bounded P.