Section Isomorphism.
Variables (aT rT : finGroupType) (G : {group aT}) (f : {morphism G >-> rT}).
Variable R : {group rT}.
Hypothesis isoGR : isom G R f.
Let defR := isom_im isoGR.
Local Notation G1 := (isom_inv isoGR @* R).
Let defG : G1 = G := isom_im (isom_sym isoGR).
Fact cfIsom_key : unit. Proof. by []. Qed.
Definition cfIsom :=
locked_with cfIsom_key (cfMorph \o 'Res[G1] : 'CF(G) -> 'CF(R)).
Canonical cfIsom_unlockable := [unlockable of cfIsom].

Lemma cfIsomE phi x : x \in G -> cfIsom phi (f x) = phi x.