End OrthogonalityRelations.
Prenex Implicits irr_class class_Iirr irr_classK.
Arguments class_IirrK {gT G%G} [xG%g] GxG : rename.
Arguments character_table {gT} G%g.
Section InnerProduct.
Variable (gT : finGroupType) (G : {group gT}).

Lemma eq_subZnat_irr (a b : nat) (i j r t : Iirr G) :
(a%:R *: 'chi_i - b%:R *: 'chi_j == a%:R *: 'chi_r - b%:R *: 'chi_t)
=   [|| a == 0%N | i == r] && [|| b == 0%N | j == t]
|| [&& i == j, r == t & a == b].