proposition: Lemma compl_p'Hall pi K H G : pi^'.-Hall(G) K -> (H \in [complements to K in G]) = pi.-Hall(G) H.
proof: Proof. by move/compl_pHall->; apply: eq_pHall (negnK pi). 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)