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
  (numerator(p) = p or denominator(p) = 1) & 0 <= p implies p is Element of NAT
proof
  assume that
A1: numerator(p)=p or denominator(p)=1 and
A2: 0<=p;
  p is Integer by A1,Th15;
  hence thesis by A2,INT_1:3;
end;
