reserve i,j,m,n,k for Nat,
  x,y for set,
  K for Field,
  a,a1,a2 for Element of K,
  D for non empty set,
  d,d1,d2 for Element of D,
  M,M1,M2 for (Matrix of D),
  A,A1,A2,B1,B2 for (Matrix of K),
  f,g for FinSequence of NAT;
reserve F,F1,F2 for FinSequence_of_Matrix of D,
  G,G9,G1,G2 for FinSequence_of_Matrix of K;

theorem
  for F be FinSequence_of_Matrix of D st F={} holds block_diagonal(F,d)= {}
proof
  let F be FinSequence_of_Matrix of D;
  assume F={};
  then len Len F=0;
  then Len F=<*>REAL;
  then 0 =len block_diagonal(F,d) by Def5,RVSUM_1:72;
  hence thesis;
end;
