Section Lemmas_on_partial_orders.
Variable U : Type.
Variable B : Ensemble U.
Variable D : PO U.
elim D; simpl in |- *; auto.
intros C R H' H'0; elim H'0; auto 10.
Qed.
Hint Resolve Rel_of_reflexive.
elim D; simpl in |- *; auto.
intros C R H' H'0; elim H'0; auto 10.
Qed.
Hint Resolve Rel_of_antisymmetric.

Theorem Rel_of_transitive : Transitive U (Rel_of U D).