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

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