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
  1 < denominator(p) iff p is not integer
proof
  now
    assume
A1: not p is Integer;
    denominator(p)>=1 by Th8;
    hence denominator(p)>1 by A1,Th15,XXREAL_0:1;
  end;
  hence thesis by Th14;
end;
