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_onP A phi :
reflect (forall x, x \notin A -> phi x = 0) (phi \in 'CF(G, A)).