Section Induction.
Definition matrix_rect := mx_ind.
Definition matrix_rec := mx_ind.
Definition matrix_ind := mx_ind.

Lemma ringmx_ind (P : forall n, 'M[R]_n.+1 -> Type) :
(forall x, P 0%N x) ->
(forall n x (r : 'rV_n.+1) (c : 'cV_n.+1) A,
P n A -> P (1 + n)%N (block_mx x r c A)) ->
forall n A, P n A.