(** ** Intersection of relations *)

Definition rel_inter {A B} (R1 R2: rel A B): rel A B :=
  fun x y => R1 x y /\ R2 x y.Infix "/\" := rel_inter : rel_scope.Global Instance rel_inter_params:
  Params (@rel_inter) 4.

Lemma rel_inter_subrel_rexists_r {A B} (R1 R2 R: rel A B): RExists (subrel R2 R) subrel (R1 /\ R2)%rel R.