Section ClassFun.
Variables (gT : finGroupType) (G : {group gT}).
Implicit Types (A B : {set gT}) (H K : {group gT}) (phi psi xi : 'CF(G)).
Local Notation "''1_' A" := (cfun_indicator G A).
Arguments cfun_onP {A phi}.
Canonical cfker_group phi := Group (cfker_is_group phi).
Canonical cfdotr_additive xi := Additive (cfdotr_is_linear xi).
Canonical cfdotr_linear xi := Linear (cfdotr_is_linear xi).
Arguments orthoPl {phi S}.

Lemma conjC_pair_orthogonal S chi :
cfConjC_closed S -> ~~ has cfReal S -> pairwise_orthogonal S -> chi \in S ->
pairwise_orthogonal (chi :: chi^*%CF).