Section Domain_prop_bounded_proof_1.
Variable X : Ens.
Hypothesis p : Domain_prop R X.
Let Y := EV R X.
Let step1_1 : IN (PAIR X Y) R.
Proof EV_pr R X p.
Proof Relation_Total_th1 R X Y step1_1.
End Domain_prop_bounded_proof_1.
Let step1 : Bounded_By T (Domain_prop R).
Proof Domain_prop_bounded_proof_1_Out.
Proof Bounded_th2 (Domain_prop R) T step1.
End Domain_prop_bounded_proof.

Theorem Domain_prop_bounded : forall R : Ens, Bounded (Domain_prop R).