Definition lex_pair {A B} (Ra: A -> A -> Prop) (Rb: B -> B -> Prop)
            (x: A*B) (y: A*B) : Prop :=
 Ra (fst x) (fst y) \/ (fst x = fst y /\ Rb (snd x) (snd y)).

Lemma well_founded_trans: forall A (Ra: A -> A -> Prop), well_founded Ra <-> well_founded (clos_trans _ Ra).