proposition: Lemma class_normal x G : x \in G -> x ^: G <| G.
proof: Proof. by move=> Gx; rewrite /normal class_norm class_subG. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)