Canonical lcn_gFun n := [gFun by lcn_cont n].
Canonical lcn_mgFun n := [mgFun by fun _ G H => @lcnS _ n G H].
Section UpperCentralFunctor.
Variable n : nat.
Implicit Type gT : finGroupType.

(* Now extract all the intermediate facts of the last proof. *)
Lemma ucn_group_set gT (G : {group gT}) : group_set 'Z_n(G).