End ConsttIndExtendible.

(* This is Isaacs, Theorem (6.26). *)
Theorem extend_linear_char_from_Sylow G N (lambda : 'CF(N)) :
N <| G -> lambda \is a linear_char -> G \subset 'I[lambda] ->
(forall p, p \in \pi('o(lambda)%CF) ->
exists2 Hp : {group gT},
[/\ N \subset Hp, Hp \subset G & p.-Sylow(G / N) (Hp / N)%g]
& exists u, 'Res 'chi[Hp]_u = lambda) ->
exists u, 'Res[N, G] 'chi_u = lambda.