Section MoreQuotientAction.
Variables (aT rT : finGroupType).
Variables (A : {group aT})(D : {group rT}).
Variable to : groupAction A D.

Lemma qacts_coset (H K : {group rT}) :
H \subset D -> [acts A, on K | to] ->
[acts qact_dom to H, on (coset H) @* K | to / H].