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 (6.19). *)
Corollary cfRes_prime_irr_cases G N s p (chi := 'chi[G]_s) :
N <| G -> #|G : N| = p -> prime p ->
[\/ 'Res[N] chi \in irr N
|  exists2 c, injective c & 'Res[N] chi = \sum_(i < p) 'chi_(c i)].