proposition: Lemma sdprod_pcore_HallP H G : pi^'.-Hall(G) H -> reflect ('O_pi(G) ><| H = G) (pi.-Hall(G) 'O_pi(G)).
proof: Proof. exact: sdprod_normal_p'HallP (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)