End CompositionSeries.
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(* Helper lemmas for group actions.                                           *)
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Section MoreGroupAction.
Variables (aT rT : finGroupType).
Variables (A : {group aT}) (D : {group rT}).
Variable to : groupAction A D.

(* Specifications: *)
Lemma gactsP (G : {set rT}) : reflect {acts A, on G | to} [acts A, on G | to].
Lemma gactsM (N1 N2 : {set rT}) :
N1 \subset D -> N2 \subset D ->
[acts A, on N1 | to] -> [acts A, on N2 | to] -> [acts A, on N1 * N2 | to].
Lemma gactsI (N1 N2 : {set rT}) :
[acts A, on N1 | to] -> [acts A, on N2 | to] -> [acts A, on N1 :&: N2 | to].
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)).