proposition: Lemma sdprod_p'core_HallP pi H G : pi.-Hall(G) H -> reflect ('O_pi^'(G) ><| H = G) (pi^'.-Hall(G) 'O_pi^'(G)).
proof: Proof. by rewrite -(pHallNK pi G H); apply: sdprod_pcore_HallP. 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)