(* Note: 'nosimpl' MUST be used outside of a section -- the end of section   *)
(* "cooking" destroys it.                                                    *)
Definition derived_at := nosimpl derived_at_rec.Notation "G ^` ( n )" := (derived_at n G) : group_scope.Implicit Type A : {set gT}.Implicit Types G : {group gT}.

Lemma der_group_set G n : group_set G^`(n).