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

theorem Th3:
  ||.x - y.|| <= ||.x.|| + ||.y.||
proof
  ||.x - y.|| <= ||.x.|| + ||.(-y).|| by Def1;
  hence thesis by Th2;
end;
