proposition: Lemma sdprod_normal_p'HallP pi K H G : K <| G -> pi^'.-Hall(G) H -> reflect (K ><| H = G) (pi.-Hall(G) K).
proof: Proof. move=> nsKG hallH; rewrite -(compl_p'Hall K hallH). exact: sdprod_normal_complP. 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)