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 cfBigdprodKabelian Iphi (phi := fun i => 'chi_(Iphi i)) :
abelian G -> forall i, P i -> 'Res (cfBigdprod defG phi) = 'chi_(Iphi i).