Section CompositionSeries.
Variable gT : finGroupType.
Local Notation gTg := {group gT}.
Implicit Types (G : gTg) (s : seq gTg).
Local Notation compo := [rel x y : {set gT} | maxnormal y x x].
Definition comps G s := ((last G s) == 1%G) && compo.-series G s.

Lemma compsP G s :
reflect (last G s = 1%G /\  path [rel x y : gTg | maxnormal y x x] G s)
(comps G s).