proposition: Lemma in_conj_part sh : is_part sh -> forall r c, in_shape sh (r, c) = in_shape (conj_part sh) (c, r).
proof: Proof. move=> Hpart r c; apply/idP/idP; first exact: in_conj_part_impl. rewrite -{2}(conj_partK Hpart). by apply in_conj_part_impl; exact: is_part_conj. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(div ssralg ssrint ssrnum binomial) tools combclass sorted ordtype