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