reserve n,i,k,m for Nat;

theorem
  for x1,x2,x3 being Element of REAL n holds
  |.x2 - x1.|- |.x2 - x3.| <= |.x3 - x1.|
proof
  let x1,x2,x3 be Element of REAL n;
  |.x2 - x1.|=|.x1 - x2.| by EUCLID:18;
  then |.x2 - x1.|- |.x2 - x3.| <= |.x1 - x3.| by Th3;
  hence thesis by EUCLID:18;
end;
