(* The matrix ring structure requires a strutural condition (dimension of the *)
(* form n.+1) to statisfy the nontriviality condition we have imposed.        *)
Variable n' : nat.
Local Notation n := n'.+1.

Lemma lift0_mx_is_perm s : is_perm_mx (lift0_mx (perm_mx s)).
Canonical matrix_countZmodType (M : countZmodType) m n :=
[countZmodType of 'M[M]_(m, n)].