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

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)).