proposition: Lemma DP_splita_pos1 l: DP_pos l = nilp ((DP_splita l).1).
proof: Proof. by elim:l => // a l /= <-;case ha: (DP_pos l) => //; case:leqP. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype) mathcomp(ssrnat seq path div) mathcomp(fintype tuple finfun bigop finset binomial)