proposition: Lemma posz_dscore : exists x : G, dscore x > 0.
proof: Proof. apply/existsP; have: ~~ (0 <= - (120 : int)) by []; apply: contraR. rewrite negb_exists -dscore_roots -sumrN => /forallP-score_le0. by apply: sumr_ge0 => x _; rewrite oppr_ge0 leNgt. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype path fingraph) mathcomp(bigop order ssralg ssrnum ssrint) fourcolor(hypermap geometry part)