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 Th21:
  numerator(p) = -denominator(p) iff p = -1
proof
  hereby
    assume numerator(p)=-denominator(p);
    hence p=(-denominator(p))/denominator(p) by Th12
      .=-denominator(p)/denominator(p)
      .=-1 by XCMPLX_1:60;
  end;
  thus thesis;
end;
