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, Corollary (6.28). *)
Corollary extend_solvable_coprime_irr G N t (theta := 'chi[N]_t) :
N <| G -> solvable (G / N) -> G \subset 'I[theta] ->
coprime #|G : N| ('o(theta)%CF * truncC (theta 1%g)) ->
exists c, [/\ 'Res 'chi[G]_c = theta, 'o('chi_c)%CF = 'o(theta)%CF
& forall d,
'Res 'chi_d = theta -> coprime #|G : N| 'o('chi_d)%CF ->
d = c].