proposition: Lemma galois_radical E : w \in E -> (p > 0)%N -> x ^+ p \in E -> galois E <<E; x>>.
proof: Proof. by move=> + pp /(galois_cyclo_radical pp) => /(@Fadjoin_idP _)->. 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)