unfold Symmetric, Complement in |- *.
intros U R H' x y H'0; red in |- *; intro H'1; apply H'0; auto.
Qed.

Theorem Equiv_from_preorder :
forall (U : Type) (R : Relation U),
Preorder U R -> Equivalence U (fun x y : U => R x y /\ R y x).