proposition: Lemma bigmaxUl (A B : {set I}) F : \big[max/x]_(i in A) F i <= \big[max/x]_(i in A :|: B) F i.
proof: Proof. by apply: sub_bigmax => t; rewrite in_setU => ->. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)