Section MinMaxGroup.
Variable gT : finGroupType.
Implicit Types gP : pred {group gT}.
Definition maxgroup A gP := maxset (fun A => group_set A && gP <<A>>%G) A.
Definition mingroup A gP := minset (fun A => group_set A && gP <<A>>%G) A.
Variable gP : pred {group gT}.
Arguments gP _%G.
Variable G : {group gT}.
Hypothesis gPG : gP G.

Lemma maxgroup_exists : {H : {group gT} | maxgroup H gP & G \subset H}.