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 Th12:
  p = numerator(p)/denominator(p) & p = numerator(p)*denominator(p)"
proof
  set x=denominator(p);
  thus numerator(p)/denominator(p)=p*(x*x") .=p*1 by XCMPLX_0:def 7
    .=p;
  hence thesis;
end;
