Global Instance set_le_compose `(RCompose) :
  RCompose (set_le RAB) (set_le RBC) (set_le RAC).(** We define [set_ge] as well. *)

Definition set_ge {A B} (R: rel A B): rel (A -> Prop) (B -> Prop) :=
  fun sA sB => forall b, sB b -> exists a, sA a /\ R a b.Global Instance set_ge_subrel_params:
  Params (@set_ge) 3.

Lemma set_ge_refl {A} (R : relation A) : Reflexive R -> Reflexive (set_ge R).