proposition: Lemma le_bigmax_cond j P F : P j -> F j <= \big[max/x]_(i | P i) F i.
proof: Proof. by move=> Pj; rewrite (bigmaxD1 _ Pj) le_max lexx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)