Let rVabelemJmx v x : x \in G -> rV_E (v *m r x) = (rV_E v) ^ x.
Fact abelem_mx_repr : mx_repr G r.
Canonical abelem_repr := MxRepresentation abelem_mx_repr.
Let rG := abelem_repr.

Lemma mxsimple_abelem_subg U : mxsimple rHG U <-> mxsimple rH U.
End SubGroup.