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

Lemma gastabsP (S : {set rT}) (a : aT) :
a \in A -> reflect (forall x, (to x a \in S) = (x \in S)) (a \in 'N(S | to)).