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_signed_irr (s t : bool) i j :
((-1) ^+ s *: 'chi[G]_i == (-1) ^+ t *: 'chi_j) = (s == t) && (i == j).