End MoreQuotientAction.
Section StableCompositionSeries.
Variables (aT rT : finGroupType).
Variables (D : {group rT})(A : {group aT}).
Variable to : groupAction A D.
Definition maxainv (B C : {set rT}) :=
[max C of H |
[&& (H <| B), ~~ (B \subset H) & [acts A, on H | to]]].
Section MaxAinvProps.
Variables K N : {group rT}.

(* Specifications: *)
Lemma maxainv_norm : maxainv K N -> N <| K.
Lemma maxainv_sub : maxainv K N -> N \subset K.
End MaxAinvProps.
Lemma maxainvM (G H K : {group rT}) :
H \subset D -> K \subset D -> maxainv G H -> maxainv G K ->
H :<>: K -> H * K = G.