proposition: Lemma nhomo_ltn_lt_in : {in D, forall i, i.+1 \in D -> f i > f i.+1} -> {in D &, {homo f : i j /~ i < j}}.
proof: Proof. move=> f_dec; apply: homo_sym_in. by apply: homo_ltn_in Dconvex f_dec => ? ? ? ? /lt_trans->. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)