proposition: Lemma rootCX n x k : (n > 0)%N -> 0 <= x -> n.-root (x ^+ k) = n.-root x ^+ k.
proof: Proof. move=> n_gt0 x_ge0; apply/eqP. by rewrite -(eqrXn2 n_gt0) ?(exprn_ge0, rootC_ge0) // 1?exprAC !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)