Definition asimple (K : {set rT}) := maxainv K 1.
Implicit Types (H K : {group rT}) (s : seq {group rT}).

Lemma asimpleP K :
reflect [/\ K :!=: 1
& forall H, H <| K -> [acts A, on H | to] -> H :=: 1 \/ H :=: K]
(asimple K).