intros U R H'; elim H'; intros H'0 H'1.
apply Definition_of_equivalence.
red in H'0; auto 10.
2: red in |- *; intros x y h; elim h; intros H'3 H'4; auto 10.
red in H'1; red in |- *; auto 10.
intros x y z h; elim h; intros H'3 H'4; clear h.
intro h; elim h; intros H'5 H'6; clear h.
split; apply H'1 with y; auto 10.
Qed.
Hint Resolve Equiv_from_preorder.

(* Specifications: *)
Theorem Equiv_from_order :
forall (U : Type) (R : Relation U),
Order U R -> Equivalence U (fun x y : U => R x y /\ R y x).