Section ExponentAbelem.
Variable gT : finGroupType.
Implicit Types (p n : nat) (pi : nat_pred) (x : gT) (A B C : {set gT}).
Implicit Types E G H K P X Y : {group gT}.
Arguments exponentP {A n}.

Lemma pnElemI p n A B : 'E_p^n(A :&: B) = 'E_p^n(A) :&: subgroups B.