proposition: Lemma exprCK n x : (0 < n)%N -> 0 <= x -> n.-root (x ^+ n) = x.
proof: Proof. move=> n_gt0 x_ge0; apply/eqP. by rewrite -(eqrXn2 n_gt0) ?rootC_ge0 ?exprn_ge0 ?rootCK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)