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 card_p1Elem_pnElem p n A E :
E \in 'E_p^n(A) -> #|'E_p^1(E)| = (\sum_(i < n) p ^ i)%N.