Definition cfDet_order_lin xi :
xi \is a linear_char -> cfDet_order xi = #[xi]%CF.

(* Specifications: *)
Lemma cfDetMorph aT rT (D G : {group aT}) (f : {morphism D >-> rT})
(phi : 'CF(f @* G)) :
phi \is a character -> cfDet (cfMorph phi) = cfMorph (cfDet phi).
Lemma cfDetIsom aT rT (G : {group aT}) (R : {group rT})
(f : {morphism G >-> rT}) (isoGR : isom G R f) phi :
cfDet (cfIsom isoGR phi) = cfIsom isoGR (cfDet phi).
Lemma cfDet_mul_lin gT (G : {group gT}) (lambda phi : 'CF(G)) :
lambda \is a linear_char -> phi \is a character ->
cfDet (lambda * phi) = lambda ^+ truncC (phi 1%g) * cfDet phi.