Section PgroupProps.
Variable gT : finGroupType.
Implicit Types (pi rho : nat_pred) (p : nat).
Implicit Types (x y z : gT) (A B C D : {set gT}) (G H K P Q R : {group gT}).

Lemma coprime_mulGp_Hall pi G K R :
K * R = G -> pi^'.-group K -> pi.-group R ->
pi^'.-Hall(G) K /\ pi.-Hall(G) R.