proposition: Lemma radical_ext_Fadjoin (n : nat) (x : L) (E : {subfield L}) : (0 < n)%N -> x ^+ n \in E -> radical.-ext E <<E; x>>%VS.
proof: Proof. by move=> n_gt0 xnE; apply/rext_r/(radical_Fadjoin n_gt0 xnE). Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field polyrcf) Abel(various classic_ext map_gal algR) Abel(char0 cyclotomic_ext real_closed_ext)