Section OneRepresentation.
Variables (n : nat) (rG : mx_representation aF G n).
Local Notation rGf := (map_repr f rG).
End OneRepresentation.

Lemma map_regular_subseries U i (modU : mx_subseries (regular_repr aF G) U)
(modUf : mx_subseries (regular_repr rF G) [seq M^f | M <- U]) :
mx_rsim (map_repr f (subseries_repr i modU)) (subseries_repr i modUf).