proposition: Lemma prog_x_leq R S S': prog R S -> S ≦ S' -> prog R S'.
proof: Proof. intros H H' e f Hef. apply H in Hef as [? Hef]. split. assumption. split. now apply Hef. intros. now apply H', Hef. Qed.
imports: lset kat positives sums glang boolean comparisons powerfix ugregex