
theorem Th9:
  for x,y being Element of REAL holds real_dist.(x,y) = real_dist.(y,x)
proof
  let x,y be Element of REAL;
  thus real_dist.(x,y)=|.x-y.| by Def12
    .=|.-(x-y).| by COMPLEX1:52
    .=|.y-x.|
    .=real_dist.(y,x) by Def12;
end;
