reserve a, b for Real;
reserve RNS for RealNormSpace;
reserve x, y, z, g, g1, g2 for Point of RNS;

theorem Th4:
  0 <= ||.x.||
proof
  ||.x - x.|| = ||.09(RNS).|| by RLVECT_1:15
    .= 0;
  then 0 <= (||.x.|| + ||.x.||)/2 by Th3;
  hence thesis;
end;
