intros Id_u_X_V1_f isG_X_V1_R1_S1.
rewrite Gim_egal.
rewrite (Id_image_S Id_u_X_V1_f isG_X_V1_R1_S1).
rewrite (Id_image_R Id_u_X_V1_f isG_X_V1_R1_S1).
rewrite (Id_image_V Id_u_X_V1_f).
rewrite (Id_image_X Id_u_X_V1_f).
apply refl_equal.
Qed.

(* Specifications: *)
Lemma Derive_image :
forall u v : Word, Derive R1 u v -> Derive Rim (wef u) (wef v).