proposition: Lemma ler_eXnr x n : (0 < n)%N -> 1 <= x -> x <= x ^+ n.
proof: Proof. case: n => // n _ x_ge1. by rewrite exprS ler_peMr ?(le_trans _ x_ge1) // exprn_ege1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)