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

Lemma asimple_quo_maxainv (G H : {group rT}) :
H \subset D -> G \subset D -> [acts A, on G | to] -> [acts A, on H | to] ->
H <| G -> asimple (to / H) (G / H) ->
maxainv to G H.