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}.

Lemma cfun_onE phi A : (phi \in 'CF(G, A)) = (support phi \subset A).