reserve x1, x2, x3, x4, x5, x6, x7 for set;

theorem Th13:
  for p, q being Element of RealSpace st q >= p holds dist (p, q) = q - p
proof
  let p, q be Element of RealSpace;
  assume p <= q;
  then
A1: q - p >= 0 by XREAL_1:48;
  dist (p, q) = |.q - p.| by TOPMETR:11
    .= q - p by A1,ABSVALUE:def 1;
  hence thesis;
end;
