proposition: Lemma merge_is_part l k : is_part l -> is_part k -> is_part (merge geq l k).
proof: Proof. rewrite !is_part_sortedE => /andP[sortl l0] /andP[sortk k0]. apply/andP; split; first exact: merge_sorted. by rewrite mem_merge mem_cat negb_or l0 k0. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(div ssralg ssrint ssrnum binomial) tools combclass sorted ordtype