Definition SUBPROP (P Q : Ens -> Prop) := forall X : Ens, P X -> Q X.Definition boundedsubprops1_Out : IN X A := h X step1.Definition Bounded_subprops1_Out : Bounded_By A P := boundedsubprops1_Out.

Theorem Bounded_subprops_th1 : forall (P Q : Ens -> Prop) (s : SUBPROP P Q) (A : Ens) (h : Bounded_By A Q), Bounded_By A P.