Arguments gen_prodgP {gT A x}.
Arguments joing_idPl {gT G A}.
Arguments joing_idPr {gT A G}.
Arguments mulGsubP {gT K H G}.
Arguments joing_subP {gT A B G}.
Section Cycles.
(* Elementary properties of cycles and order, needed in perm.v.  *)
(* More advanced results on the structure of cyclic groups will  *)
(* be given in cyclic.v.                                         *)
Variable gT : finGroupType.
Implicit Types x y : gT.
Implicit Types G : {group gT}.

Lemma memJ_norm x y A : x \in 'N(A) -> (y ^ x \in A) = (y \in A).