Section ProdRepr.
Variables (n1 n2 : nat) (rG1 : reprG n1) (rG2 : reprG n2).
Definition prod_repr := MxRepresentation prod_mx_repr.
End ProdRepr.

Lemma prod_repr_lin n2 (rG1 : reprG 1) (rG2 : reprG n2) :
{in G, forall x, let cast_n2 := esym (mul1n n2) in
prod_repr rG1 rG2 x = castmx (cast_n2, cast_n2) (rG1 x 0 0 *: rG2 x)}.