Definition cfun_comp f f0 phi := Cfun 0 (@cfun_comp_subproof f phi f0).
Definition cfun_opp := cfun_comp (oppr0 _).
Fact cfun_add_subproof phi psi : is_class_fun G [ffun x => phi x + psi x].
Definition cfun_add phi psi := Cfun 0 (cfun_add_subproof phi psi).
Fact cfun_indicator_subproof (A : {set gT}) :
is_class_fun G [ffun x => ((x \in G) && (x ^: G \subset A))%:R].
Definition cfun_indicator A := Cfun 1 (cfun_indicator_subproof A).
Local Notation "''1_' A" := (cfun_indicator A) : ring_scope.

(* Specifications: *)
Lemma cfun1Egen x : '1_G x = (x \in G)%:R.
Definition cfun_mul phi psi := Cfun 0 (cfun_mul_subproof phi psi).