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 map_orthogonal M (nu : 'CF(G) -> 'CF(M)) S R (A : {pred 'CF(G)}) :
{in A &, isometry nu} -> {subset S <= A} -> {subset R <= A} ->
orthogonal (map nu S) (map nu R) = orthogonal S R.