Section SomeHall.
Variable gT : finGroupType.
Implicit Types (p : nat) (pi : nat_pred) (G H K P R : {group gT}).

Lemma coprime_mulG_setI_norm H G K R :
K * R = G -> G \subset 'N(H) -> coprime #|K| #|R| ->
(K :&: H) * (R :&: H) = G :&: H.