theorem Th34:
  block_diagonal(<*M*>,d) = M
proof
  reconsider E=<*>(D**) as Matrix-yielding FinSequence of (D**) by Th12;
  set ME=<*M*>^E;
  set B=block_diagonal(<*M*>,d);
A1: len B = Sum Len <*M*> by Def5
    .= len M by Lm4;
A2: width B = Sum Width <*M*> by Def5
    .= width M by Lm5;
  ME = <*M*> by FINSEQ_1:34;
  hence M = Segm(B,Seg len M,Seg width M) by Th32
    .= B by A1,A2,MATRIX13:46;
end;
