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 acts_gen A S :
S \subset R -> [acts A, on S | to] -> [acts A, on <<S>> | to].