proposition: Lemma DP_ph1_simp a l: DP_ph1 (a:: l) = [&& DP_ph1 l, [|| size a == 2, nilp l | size (head nil l) == 2] & DP_ph1_aux2 a].
proof: Proof. by rewrite /DP_ph1 /= (andbC (DP_ph1_aux2 a)) andbACA. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype) mathcomp(ssrnat seq path div) mathcomp(fintype tuple finfun bigop finset binomial)