Definition submod_mx of mxmodule U :=
fun x => in_submod (val_submod 1%:M *m rG x).
Definition factmod_mx of mxmodule U :=
fun x => in_factmod (val_factmod 1%:M *m rG x).
Hypothesis Umod : mxmodule U.

Lemma submod_mx_repr : mx_repr G (submod_mx Umod).
Canonical submod_repr := MxRepresentation submod_mx_repr.