proposition: Lemma DP_splitc_cat l1 l2: Dyck_path l1 -> Dyck_path l2 -> DP_splitc (l1 ++ l2) = DP_splitc l1 ++ DP_splitc l2.
proof: Proof. move => ha hb; apply:DP_splitc_unique. by rewrite all_cat (DP_splitc_correct ha) (DP_splitc_correct hb). by rewrite flatten_cat ! DP_splitc_recover. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype) mathcomp(ssrnat seq path div) mathcomp(fintype tuple finfun bigop finset binomial)