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.

(* Specifications: *)
Lemma cfResIsom phi : 'Res[S] (cfIsom isoG phi) = cfIsom isoH ('Res[H] phi).
Lemma cfIndIsom phi : 'Ind[R] (cfIsom isoH phi) = cfIsom isoG ('Ind[G] phi).
End MorphInduced.