reserve n   for Nat,
        r,s for Real,
        x,y for Element of REAL n,
        p,q for Point of TOP-REAL n,
        e   for Point of Euclid n;

theorem Th3:
  for x,y being Element of REAL,xe,ye being ExtReal st x <= xe & y <= ye holds
  x + y <= xe + ye
  proof
    let x,y be Element of REAL,xe,ye be ExtReal;
    assume that
A1: x <= xe and
A2: y <= ye;
    reconsider x1 = x,y1 = y as ExtReal;
    x1 + y1 <= xe + ye by A1,A2,XXREAL_3:36;
    hence x + y <= xe + ye by XXREAL_3:def 2;
  end;
