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, Lemma (6.24). *)
Lemma extend_to_cfdet G N s c0 u :
let theta := 'chi_s in let lambda := cfDet theta in let mu := 'chi_u in
N <| G -> coprime #|G : N| (truncC (theta 1%g)) ->
'Res[N, G] 'chi_c0 = theta -> 'Res[N, G] mu = lambda ->
exists2 c, 'Res 'chi_c = theta /\ cfDet 'chi_c = mu
& forall c1, 'Res 'chi_c1 = theta -> cfDet 'chi_c1 = mu -> c1 = c.