Definition acomps K s :=
((last K s) == 1%G) && path [rel x y : {group rT} | maxainv x y] K s.

(* Specifications: *)
Lemma acompsP K s :
reflect (last K s = 1%G /\  path [rel x y : {group rT} | maxainv x y] K s)
(acomps K s).
Lemma acomps_cons K H s : acomps K (H :: s) -> acomps H s.
Lemma exists_acomps K : exists s, acomps K s.
End StableCompositionSeries.