Section RawGroupAction.
Variables (aT rT : finGroupType) (D : {set aT}) (R : {set rT}).
Variable to : groupAction D R.
Canonical gacent_group A := Group (group_set_gacent A).

Lemma gacentC A S :
A \subset D -> S \subset R ->
(S \subset 'C_(|to)(A)) = (A \subset 'C(S | to)).