proposition: Fact meet_YoungP sh sh1 sh2 : (sh <= meet_Young sh1 sh2)%O = (sh <= sh1)%O && (sh <= sh2)%O.
proof: Proof. apply/idP/andP => [Hinf |]. split; apply: (le_trans Hinf); first exact: meet_Young_le. by rewrite meet_YoungC meet_Young_le. move=> [/le_YoungP le1 /le_YoungP le2]. by apply/le_YoungP => i; rewrite nth_meet_Young leq_min le1 le2. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(div ssralg ssrint ssrnum binomial) tools combclass sorted ordtype