End ActBy.
Section Quotient.
Variable H : {group rT}.

(* Specifications: *)
Lemma acts_qact_dom_norm : {acts qact_dom to H, on 'N(H) | to}.
Lemma qact_is_groupAction : is_groupAction (R / H) (to / H).
Canonical quotient_groupAction := GroupAction qact_is_groupAction.
Lemma qact_domE : H \subset R -> qact_dom to H = 'N(H | to).
End Quotient.