proposition: Lemma DP_splitb_race2 l (v:= (DP_splitb l).2): Dyck_path l -> ~~ nilp l -> (DP_splitb v).2 = v.
proof: Proof. move => h1 h2. move/andP:(DP_splitb_Dyck12 h1) => [_ d2]. have hb:= (DP_splitb_prop1 h1 h2). by move: (DP_splitb_race1 (DP_splitb l).1 d2 hb); rewrite(DP_splitb_recover). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype) mathcomp(ssrnat seq path div) mathcomp(fintype tuple finfun bigop finset binomial)