End Hall.
Section HallCorollaries.
Variable gT : finGroupType.

(* Specifications: *)
Corollary Hall_exists pi (G : {group gT}) :
solvable G -> exists H : {group gT}, pi.-Hall(G) H.
Corollary Hall_superset pi (G K : {group gT}) :
solvable G -> K \subset G -> pi.-group K ->
exists2 H : {group gT}, pi.-Hall(G) H & K \subset H.
Corollary Hall_subJ pi (G H K : {group gT}) :
solvable G -> pi.-Hall(G) H -> K \subset G -> pi.-group K ->
exists2 x, x \in G & K \subset H :^ x.
Corollary Hall_Jsub pi (G H K : {group gT}) :
solvable G -> pi.-Hall(G) H -> K \subset G -> pi.-group K ->
exists2 x, x \in G & K :^ x \subset H.
Lemma Hall_Frattini_arg pi (G K H : {group gT}) :
solvable K -> K <| G -> pi.-Hall(K) H -> K * 'N_G(H) = G.