theorem Th24:
  |.w.| = 0 implies w = 0.TOP-REAL N
proof
  reconsider s = w as Element of REAL N by EUCLID:22;
  assume |.w.| = 0;
  then s = 0*N by EUCLID:8
    .= 0.TOP-REAL N by EUCLID:70;
  hence thesis;
end;
