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 compl_p'Hall pi K H G :
pi^'.-Hall(G) K -> (H \in [complements to K in G]) = pi.-Hall(G) H.