reserve a,b,c,d for Real;
reserve r,s for Real;

theorem
  ex c st c < a & c < b
proof
  per cases;
  suppose
A1: a <= b;
    take z = a+-1;
    z < a+0 by Lm10;
    hence thesis by A1,XXREAL_0:2;
  end;
  suppose
A2: b <= a;
    take z = b+-1;
    z < b+0 by Lm10;
    hence thesis by A2,XXREAL_0:2;
  end;
end;
