Section ConsttInertiaBijection.
Variables (gT : finGroupType) (H G : {group gT}) (t : Iirr H).
Hypothesis nsHG : H <| G.
Local Notation theta := 'chi_t.
Local Notation T := 'I_G[theta]%G.
Local Notation "` 'T'" := 'I_(gval G)[theta]
(at level 0, format "` 'T'") : group_scope.
Let calA := irr_constt ('Ind[T] theta).
Let calB := irr_constt ('Ind[G] theta).
Local Notation AtoB := (Ind_Iirr G).
End ConsttIndExtendible.

(* This is Isaacs, Theorem (6.25). *)
Theorem solvable_irr_extendible_from_det G N s (theta := 'chi[N]_s) :
N <| G -> solvable (G / N) ->
G \subset 'I[theta] -> coprime #|G : N| (truncC (theta 1%g)) ->
[exists c, 'Res 'chi[G]_c == theta]
= [exists u, 'Res 'chi[G]_u == cfDet theta].