Section DProd.
Variables (gT : finGroupType) (G K H : {group gT}).
Hypothesis KxH : K \x H = G.
Definition dprod_Iirr ij := cfIirr (cfDprod KxH 'chi_ij.1 'chi_ij.2).
Definition inv_dprod_Iirr i := iinv (dprod_Iirr_onto i).

Lemma cfBigdprod_Res_lin chi :
chi \is a linear_char -> cfBigdprod defG (fun i => 'Res[A i] chi) = chi.