proposition: Lemma rootC_lt1 n x : (n > 0)%N -> 0 <= x -> (n.-root x < 1) = (x < 1).
proof: Proof. by move=> n_gt0 x_ge0; rewrite !lt_neqAle rootC_eq1 ?rootC_le1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)