(** ** Define [includes] *)

Definition includes (x y:RegExp) : Prop := (x || y) =R= y.Notation "x <= y" := (includes x y) (at level 70).Definition prop_eq (p q:Prop) : Prop := (p <-> q).

Lemma includes_left_Cat_monotone : forall x y z, x <= y -> (z ++ x) <= (z ++ y).