Section InvMorphism.
Variables (aT rT : finGroupType) (G : {group aT}) (f : {morphism G >-> rT}).
Variable R : {group rT}.
Hypothesis isoGR : isom G R f.
Definition cfQuo phi := Cfun 1 (cfQuo_subproof phi).
Local Notation "phi /  'B'" := (cfQuo phi) (at level 40) : cfun_scope.
Local Notation "phi %%  'B'" := (cfMod phi) (at level 40) : cfun_scope.
(* We specialize the cfMorph lemmas to cfMod by strengthening the domain      *)
(* condition G \subset 'N(H) to H <| G; the cfMorph lemmas can be used if the *)
(* stronger results are needed.                                               *)
(* Note that cfQuo is nondegenerate even when G does not normalize B.         *)

Lemma cfQuoE (phi : 'CF(G)) x :
B <| G -> B \subset cfker phi -> x \in G -> (phi / B)%CF (coset B x) = phi x.