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 gacent_cycle a : a \in D -> 'C_(|to)(<[a]>) = 'C_(|to)[a].