
theorem Th3:
  for X be ComplexNormSpace, x,y,z be Element of X holds ||.x-y.||
  = ||.(x-z)+(z-y).||
proof
  let X be ComplexNormSpace;
  let x,y,z be Element of X;
  thus ||.x-y.|| = ||.x-0.X-y.|| by RLVECT_1:13
    .= ||.x-(z-z)-y.|| by RLVECT_1:5
    .= ||.(x-z)+z-y.|| by RLVECT_1:29
    .= ||.(x-z)+(z-y).|| by RLVECT_1:def 3;
end;
