proposition: Lemma bigmax_sup j P m F : P j -> m <= F j -> m <= \big[max/x]_(i | P i) F i.
proof: Proof. by move=> Pj ?; apply: le_trans (le_bigmax_cond _ Pj). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)