proposition: Lemma lang_empty n (u: rmx 1 n) M v: u ≡0 -> lang M v u ≡ bot.
proof: Proof. intros Hu w. revert Hu. induction w; intro Hu. simpl; fold_regex. rewrite Hu, dot0x. intuition discriminate. simpl. rewrite <-IHw by assumption. now rewrite Hu, dot0x. Qed.
imports: positives comparisons kleene regex rmx sums matrix_ext prop normalisation