(** ** Union of relations *)

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

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