End ConsttIndExtendible.

(* This is Isaacs, Theorem (6.25). *)
Theorem solvable_irr_extendible_from_det G N s (theta := 'chi[N]_s) :
N <| G -> solvable (G / N) ->
G \subset 'I[theta] -> coprime #|G : N| (truncC (theta 1%g)) ->
[exists c, 'Res 'chi[G]_c == theta]
= [exists u, 'Res 'chi[G]_u == cfDet theta].