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}.
Arguments nElemP {n G E}.

Lemma nt_pnElem p n E A : E \in 'E_p^n(A) -> n > 0 -> E :!=: 1.