(** ** 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_trans {A} (R1 R2: rel A A): Transitive R1 -> Transitive R2 -> Transitive (R1 /\ R2).