theorem Th21:
  len B1 in dom B1 implies Sum lmlt (Line(Jordan_block(L,len B1),
  len B1),B1)= L*(B1/.(len B1))
proof
  set N=len B1;
  assume
A1: N in dom B1;
  set J=Jordan_block(L,N);
  set ONE=1.(K,N);
  thus Sum lmlt (Line(J,N),B1) = Sum lmlt(L*Line(ONE,N),B1) by Th5
    .= L* Sum lmlt (Line(ONE,N),B1) by MATRLIN2:13
    .= L* (B1/.N) by A1,MATRLIN2:16;
end;
