Arguments maxainv {aT rT D%G A%G} to%gact B%g C%g.
Arguments asimple {aT rT D%G A%G} to%gact K%g.
Section StrongJordanHolder.
Section AuxiliaryLemmas.
Variables aT rT : finGroupType.
Variables (A : {group aT}) (D : {group rT}) (to : groupAction A D).

(* Specifications: *)
Lemma maxainv_asimple_quo (G H : {group rT}) :
H \subset D -> maxainv to G H -> asimple (to / H) (G / H).
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.
Lemma asimpleI (N1 N2 : {group rT}) :
N2 \subset 'N(N1) -> N1 \subset D ->
[acts A, on N1 | to] -> [acts A, on N2 | to] ->
asimple (to / N1) (N2 / N1) ->
asimple (to / (N2 :&: N1)) (N2 / (N2 :&: N1)).