Section QuoMax.
Variables (gT : finGroupType) (K G H : {group gT}).

(* Specifications: *)
Lemma cosetpre_maximal (Q R : {group coset_of K}) :
maximal (coset K @*^-1 Q) (coset K @*^-1 R) = maximal Q R.
Lemma maximal_eqJ x : maximal_eq (G :^ x) (H :^ x) = maximal_eq G H.
Lemma maxnormal_proper A B C : maxnormal A B C -> A \proper B.
Lemma maxnormal_sub A B C : maxnormal A B C -> A \subset B.
Lemma ex_maxnormal_ntrivg G : G :!=: 1-> {N : {group gT} | maxnormal N G G}.
Lemma maxnormalM G H K :
maxnormal H G G -> maxnormal K G G -> H :<>: K -> H * K = G.
Lemma maxnormal_minnormal G L M :
G \subset 'N(M) -> L \subset 'N(G) ->  maxnormal M G L ->
minnormal (G / M) (L / M).
Lemma minnormal_maxnormal G L M :
M <| G -> L \subset 'N(M) -> minnormal (G / M) (L / M) -> maxnormal M G L.