Global Instance pointwise_relation_subrel A B:
  Monotonic (@pointwise_relation A B) (subrel ++> subrel).Global Instance pointwise_relation_params:
  Params (@pointwise_relation) 3.

(* Specifications: *)
Lemma pointwise_relation_rintro {A B} (R: relation B) f g: RIntro (forall a, R (f a) (g a)) (pointwise_relation A R) f g.
Lemma pointwise_relation_relim {A B} (R: relation B) f g a P Q: RElim R (f a) (g a) P Q -> RElim (pointwise_relation A R) f g P Q.