proposition: Lemma count_lt_ge x s : count (< x) s = size s - count (>= x) s.
proof: Proof. by rewrite -(count_predC (>= x)) addKn; apply: eq_count => y; rewrite /= ltNge. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)