proposition: Lemma mem_normal_Hall pi H G x : pi.-Hall(G) H -> H <| G -> x \in G -> (x \in H) = pi.-elt x.
proof: Proof. by rewrite -!cycle_subG; apply: sub_normal_Hall. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset prime fingroup morphism) mathcomp(gfunctor automorphism quotient action gproduct) mathcomp(cyclic)