reserve X,X1 for set,
  r,s for Real,
  z for Complex,
  RNS for RealNormSpace,
  CNS, CNS1,CNS2 for ComplexNormSpace;

theorem
  for X be ComplexNormSpace, x, y be Point of X holds ||.x-y.|| = ||.y-x .||
proof
  let X be ComplexNormSpace;
  let x, y be Point of X;
  thus ||.x-y.|| = ||.-(x-y).|| by CLVECT_1:103
    .= ||.y-x.|| by RLVECT_1:33;
end;
