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 <> 0 implies denominator(p) = numerator(p)/p
proof
A1: (p"*p)*denominator(p)=p"*numerator(p);
  assume p<>0;
  then 1*denominator(p)=p"*numerator(p) by A1,XCMPLX_0:def 7;
  hence thesis;
end;
