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).

Lemma dprod_Iirr_eq0 i j : (dprod_Iirr (i, j) == 0) = (i == 0) && (j == 0).