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_eq1 phi :
(forall i, P i -> phi i \is a character) ->
(cfBigdprod defG phi == 1) = [forall (i | P i), phi i == 1].