reserve x,y for set;
reserve s,r for Real;
reserve r1,r2 for Real;
reserve n for Nat;
reserve p,q,q1,q2 for Point of TOP-REAL 2;

theorem Th1:
  r<=s implies r <= (r+s)/2 & (r+s)/2 <= s
proof
  assume
A1: r<=s;
  per cases by A1,XXREAL_0:1;
  suppose r<s;
    hence thesis by XREAL_1:226;
  end;
  suppose r=s;
    hence thesis;
  end;
end;
