proposition: Lemma rootCV n x : 0 <= x -> n.-root x^-1 = (n.-root x)^-1.
proof: Proof. move=> x_ge0; have [->|n_gt0] := posnP n; first by rewrite !root0C invr0. apply/eqP. by rewrite -(eqrXn2 n_gt0) ?(invr_ge0, rootC_ge0) // !exprVn !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)