Definition gen_mx g := \matrix_i in_gen (row (gen_base 0 i) (rG g)).
Let val_genJmx m :
{in G, forall g, {morph @val_gen m : W / W *m gen_mx g >-> W *m rG g}}.

(* Specifications: *)
Lemma gen_mx_repr : mx_repr G gen_mx.
Canonical gen_repr := MxRepresentation gen_mx_repr.