End ConsttIndExtendible.

(* This is Isaacs, Theorem (6.19). *)
Theorem invariant_chief_irr_cases G K L s (theta := 'chi[K]_s) :
chief_factor G L K -> abelian (K / L) -> G \subset 'I[theta] ->
let t := #|K : L| in
[\/ 'Res[L] theta \in irr L,
exists2 e, exists p, 'Res[L] theta = e%:R *: 'chi_p & (e ^ 2)%N = t
|  exists2 p, injective p & 'Res[L] theta = \sum_(i < t) 'chi_(p i)].