intros A B P S f H' l H'0; elim H'0; simpl in |- *; auto.
Qed.

Lemma subRelGoodR :
forall (A B : Set) (R : Rel A) (S : Rel B) (f : A -> B),
(forall a b : A, R a b -> S (f a) (f b)) ->
forall l : list A, GoodR A R l -> GoodR B S (map f l).