proposition: Lemma pHall_id pi H G : pi.-Hall(G) H -> pi.-group G -> H :=: G.
proof: Proof. by move=> hallH piG; rewrite (sub_pHall hallH piG) ?(pHall_sub hallH). 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)