Section MorphInduced.
Variables (aT rT : finGroupType) (D G H : {group aT}) (R S : {group rT}).
Variables (g : {morphism G >-> rT}) (h : {morphism H >-> rT}).
Hypotheses (isoG : isom G R g) (isoH : isom H S h) (eq_hg : {in H, h =1 g}).
Hypothesis sHG : H \subset G.

Lemma cfResIsom phi : 'Res[S] (cfIsom isoG phi) = cfIsom isoH ('Res[H] phi).