reserve k for Element of NAT;
reserve r,r1 for Real;
reserve i for Integer;
reserve q for Rational;

theorem Th8:
  ex n being Element of NAT st r <= n
proof
  per cases;
  suppose
 [/ r \] >= 0;
    then reconsider n=[/ r \] as Element of NAT by INT_1:3;
    take n;
    thus thesis by INT_1:def 7;
  end;
  suppose
A1: [/ r \] < 0;
    take 0;
    thus thesis by A1,INT_1:def 7;
  end;
end;
