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

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