proposition: Lemma diffUx x y z : (x `|` y) `\` z = (x `\` z) `|` (y `\` z).
proof: Proof. apply/eqP; rewrite eq_le leUx !leBl ?leUr ?leUl ?andbT //. by rewrite leBLR joinA diffKU joinAC diffKU joinAC -joinA leUr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)