proposition: Lemma disjoint_lexUl z x y : x `&` z = \bot -> (x <= y `|` z) = (x <= y).
proof: Proof. move=> xz0; apply/idP/idP=> xy; last by rewrite lexU2 ?xy. by apply: (@leU2l_le x z); rewrite ?joinxx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)