End ConsttIndExtendible.

(* This is Isaacs, Corollary (6.27). *)
Corollary extend_coprime_linear_char G N (lambda : 'CF(N)) :
N <| G -> lambda \is a linear_char -> G \subset 'I[lambda] ->
coprime #|G : N| 'o(lambda)%CF ->
exists u, [/\ 'Res 'chi[G]_u = lambda, 'o('chi_u)%CF = 'o(lambda)%CF
& forall v,
'Res 'chi_v = lambda -> coprime #|G : N| 'o('chi_v)%CF ->
v = u].