Section MorphInduced.
Variables (aT rT : finGroupType) (D G H : {group aT}) (R S : {group rT}).

Lemma cfIndMorph (f : {morphism D >-> rT}) (phi : 'CF(f @* H)) :
'ker f \subset H -> H \subset G -> G \subset D ->
'Ind[G] (cfMorph phi) = cfMorph ('Ind[f @* G] phi).