(* cfQuo is only linear on the class functions that have H in their kernel. *)

(* Specifications: *)
Lemma cfQuo_cfun1 : (1 / B)%CF = 1.
(* Cancellation properties *)
Lemma cfModK : B <| G -> cancel cfMod cfQuo.
Lemma cfQuoK :
B <| G -> forall phi, B \subset cfker phi -> (phi / B %% B)%CF = phi.
Lemma cfMod_eq1 psi : B <| G -> (psi %% B == 1)%CF = (psi == 1).
Lemma cfker_quo H phi :
H <| G -> H \subset cfker (phi) -> cfker (phi / H) = (cfker phi / H)%g.
Lemma cfQuoEker phi x :
x \in G -> (phi / cfker phi)%CF (coset (cfker phi) x) = phi x.
Lemma cfQuoInorm K phi :
K \subset cfker phi -> (phi / K)%CF = 'Res ('Res['N_G(K)] phi / K)%CF.
Lemma cforder_mod H (psi : 'CF(G / H)) : H <| G -> #[psi %% H]%CF = #[psi]%CF.
Lemma cfunM_on A phi psi :
phi \in 'CF(G, A) -> psi \in 'CF(G, A) -> phi * psi \in 'CF(G, A).
Lemma cfSdprodK : cancel cfSdprod 'Res[H].
Lemma sdprod_cfker phi : K ><| cfker phi = cfker (cfSdprod phi).
Lemma cforder_sdprod phi : #[cfSdprod phi]%CF = #[phi]%CF.
Definition cfDprodr := cfSdprod (dprodWsd KxH).