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).

Lemma cfdotEl A phi psi :
phi \in 'CF(G, A) ->
'[phi, psi] = #|G|%:R^-1 * \sum_(x in A) phi x * (psi x)^*.