Canonical cfRes_lrmorphism := [lrmorphism of cfRes].
End Restrict.
Arguments cfRes {gT} A%g {B%g} phi%CF.
Notation "''Res[' H , G ]" := (@cfRes _ H G) (only parsing) : ring_scope.
Notation "''Res[' H ]" := 'Res[H, _] : ring_scope.
Notation "''Res'" := 'Res[_] (only parsing) : ring_scope.
Section MoreRestrict.
Variables (gT : finGroupType) (G H : {group gT}).
Implicit Types (A : {set gT}) (phi : 'CF(G)).

Lemma cfMorphE phi x : G \subset D -> x \in G -> cfMorph phi x = phi (f x).