Section InternalGroupAction.
Variable gT : finGroupType.
Implicit Types A B : {set gT}.
Implicit Types G H : {group gT}.
Implicit Type x : gT.
(*  Various identities for actions on groups. *)

Lemma astabQR A H : A \subset 'N(H) ->
'C(A / H | 'Q) = [set x in 'N(H) | [~: [set x], A] \subset H].