proposition: Lemma DP_ph1_nonempty d : DP_ph1 d -> all (fun z => ~~ nilp z) d.
proof: Proof. elim:d => // a l Hr. rewrite DP_ph1_simp => /= /and3P [/Hr -> _]. by rewrite andbT;case/orP;[move => /eqP -> | move/andP => [] ]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype) mathcomp(ssrnat seq path div) mathcomp(fintype tuple finfun bigop finset binomial)