reserve x for object,
  a,b for Real,
  k,k1,i1,j1,w for Nat,
  m,m1,n,n1 for Integer;
reserve p,q for Rational;

theorem
  p <= -1 iff denominator(p) <= -numerator(p)
proof
  denominator(p)<=-numerator(p) iff -(-numerator(p))<=-denominator(p) by
XREAL_1:24;
  hence thesis by Th29;
end;
