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
A1: denominator(p)"<=1 by Th10;
  now
    assume not p is Integer;
    then denominator(p)" <> 1 by Lm7,Th15;
    hence denominator(p)"<1 by A1,XXREAL_0:1;
  end;
  hence thesis by Lm7,Th14;
end;
