proposition: Lemma bigmax_eq_id P F : (forall i, P i -> x >= F i) -> \big[max/x]_(i <- r | P i) F i = x.
proof: Proof. by move=> x_ge; apply: le_anti; rewrite bigmax_ge_id bigmax_le. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)