End AuxiliaryLemmas.
Variables (aT rT : finGroupType).
Variables (A : {group aT}) (D : {group rT}) (to : groupAction A D).
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(* The factors associated to two A-stable composition series of the same      *)
(* group are the same up to isomorphism and permutation                       *)
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Lemma StrongJordanHolderUniqueness (G : {group rT}) (s1 s2 : seq {group rT}) :
G \subset D -> acomps to G s1 -> acomps to G s2 ->
perm_eq (mkfactors G s1) (mkfactors G s2).