proposition: Lemma order_galois_pradical : #|G| = p.
proof: Proof. rewrite -galois_dim 1?galois_radical// -adjoin_degreeE. by have := size_minPoly E x; rewrite size_minPoly_pradical// => -[]. 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)