proposition: Lemma sdprod_normal_pHallP pi K H G : K <| G -> pi.-Hall(G) H -> reflect (K ><| H = G) (pi^'.-Hall(G) K).
proof: Proof. by move=> nsKG hallH; apply: sdprod_normal_p'HallP; rewrite ?pHallNK. 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)