(* Building a block matrix from 4 matrices :               *)
(*  up left, up right, down left and down right components *)

Definition block_mx Aul Aur Adl Adr : 'M_(m1 + m2, n1 + n2) :=
  col_mx (row_mx Aul Aur) (row_mx Adl Adr).

Lemma block_mx_const a : block_mx (const_mx a) (const_mx a) (const_mx a) (const_mx a) = const_mx a.