Global Instance pointwise_subrelation `(sub : subrelation B R R') :
    subrelation (pointwise_relation A R) (pointwise_relation A R') | 4.

Lemma forall_subrelation (R S : forall x : A, relation (P x)) : (forall a, subrelation (R a) (S a)) -> subrelation (forall_relation R) (forall_relation S).