proposition: Lemma epsilon_iff_lang_nil e: epsilon e <-> (elang e) [].
proof: Proof. induction e; simpl. firstorder discriminate. firstorder. setoid_rewrite Bool.orb_true_iff. now apply cup_weq. setoid_rewrite Bool.andb_true_iff. setoid_rewrite lang_dot_nil. now apply cap_weq. split. now exists O. reflexivity. firstorder discriminate. Qed.
imports: syntax kleene boolean lang lset sums normalisation