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).

Lemma cfun_on_sum A :
'CF(G, A) = (\sum_(xG in classes G | xG \subset A) <['1_xG]>)%VS.