End MaxNormalProps.
Section Simple.
Implicit Types gT rT : finGroupType.

(* Specifications: *)
Lemma simpleP gT (G : {group gT}) :
reflect (G :!=: 1 /\ forall H : {group gT}, H <| G -> H :=: 1 \/ H :=: G)
(simple G).
Lemma quotient_simple gT (G H : {group gT}) :
H <| G -> simple (G / H) = maxnormal H G G.
Lemma isog_simple gT rT (G : {group gT}) (M : {group rT}) :
G \isog M -> simple G = simple M.
Lemma simple_maxnormal gT (G : {group gT}) : simple G = maxnormal 1 G G.
End Simple.