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

Lemma qacts_cosetpre (H : {group rT}) (K' : {group coset_of H}) :
H \subset D -> [acts A, on H | to] ->
[acts qact_dom to H, on K' | to / H] ->
[acts A, on coset H @*^-1 K' | to].