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_joing A M N :
M \subset R -> N \subset R -> [acts A, on M | to] -> [acts A, on N | to] ->
[acts A, on M <*> N | to].