proposition: Lemma sdprod_Hall_pcoreP H G : pi.-Hall(G) 'O_pi(G) -> reflect ('O_pi(G) ><| H = G) (pi^'.-Hall(G) H).
proof: Proof. move=> hallGpi; rewrite -(compl_pHall H hallGpi) complgC. exact: sdprod_normal_complP (pcore_normal G). 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)