proposition: Lemma nth_glueS b n (v : seq (vec n)) i k : nth false (nth [tuple of nseq n.+1 false] (glue b v) k) i.+1 = nth false (nth [tuple of nseq n false] v k) i.
proof: Proof. elim: k v b => [|k IH] [|v vs] [|b bs] //=. - by rewrite IH !nth_nil nth_nseq if_same. - case: (ltnP k (size vs)) => A. + by rewrite (nth_map [tuple of nseq n false]). + by rewrite ![_ _ _ k]nth_default ?size_map. Qed.
imports: mathcomp(all_ssreflect) RegLang(misc languages dfa nfa regexp)