Section Induction.

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