proposition: Lemma leq_bigmax_seq (I : eqType) r (P : pred I) F i0 : i0 \in r -> P i0 -> F i0 <= \max_(i <- r | P i) F i.
proof: Proof. move=> + Pi0; elim: r => // h t ih; rewrite inE big_cons. move=> /predU1P[<-|i0t]; first by rewrite Pi0 leq_maxl. by case: ifPn => Ph; [rewrite leq_max ih// orbT|rewrite ih]. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div fintype tuple finfun)