Section MaxAinvProps.
Variables K N : {group rT}.
End MaxAinvProps.
Definition asimple (K : {set rT}) := maxainv K 1.
Implicit Types (H K : {group rT}) (s : seq {group rT}).
Definition acomps K s :=
((last K s) == 1%G) && path [rel x y : {group rT} | maxainv x y] K s.

Lemma acompsP K s :
reflect (last K s = 1%G /\  path [rel x y : {group rT} | maxainv x y] K s)
(acomps K s).