Section MoreRestrict.
Variables (gT : finGroupType) (G H : {group gT}).
Implicit Types (A : {set gT}) (phi : 'CF(G)).
Definition cfMorph phi := Cfun 1 (cfMorph_subproof phi).
Fact cfMorph_is_linear : linear cfMorph.
Canonical cfMorph_additive := Additive cfMorph_is_linear.
Canonical cfMorph_linear := Linear cfMorph_is_linear.
Fact cfMorph_is_multiplicative : multiplicative cfMorph.
Canonical cfMorph_rmorphism := AddRMorphism cfMorph_is_multiplicative.
Canonical cfMorph_lrmorphism := [lrmorphism of cfMorph].
Hypothesis sGD : G \subset D.

Lemma sub_morphim_cfker phi (A : {set aT}) :
A \subset G -> (f @* A \subset cfker phi) = (A \subset cfker (cfMorph phi)).