End ExtremalStructure.
Section ExtremalClass.
Variables (gT : finGroupType) (G : {group gT}).
Inductive extremal_group_type :=
ModularGroup | Dihedral | SemiDihedral | Quaternion | NotExtremal.
Definition index_extremal_group_type c :=
match c with
| ModularGroup => 0
| Dihedral => 1
| SemiDihedral => 2
| Quaternion => 3
| NotExtremal => 4
end%N.
Definition enum_extremal_groups :=
[:: ModularGroup; Dihedral; SemiDihedral; Quaternion].

Lemma cancel_index_extremal_groups :
cancel index_extremal_group_type (nth NotExtremal enum_extremal_groups).