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).

(* This is Isaacs, Corollary (6.17) (due to Gallagher). *)
Corollary constt_Ind_ext :
[/\ forall b : Iirr (G / N), 'chi_(mod_Iirr b) * chi \in irr G,
injective mul_mod_Iirr,
irr_constt ('Ind theta) =i codom mul_mod_Iirr
& 'Ind theta = \sum_b 'chi_b 1%g *: 'chi_(mul_mod_Iirr b)].