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

(* This does not depend on the (isoG : isom G R g) assumption. *)
Lemma cfConjgIsom phi y :
y \in G -> y \in 'N(H) -> (cfIsom isoH phi ^ g y)%CF = cfIsom isoH (phi ^ y).