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 Th23:
  m <> 0 implies p = (numerator(p)*m) / (denominator(p)*m)
proof
  assume m<>0;
  then numerator(p)/denominator(p)=(numerator(p)*m)/(denominator(p)*m) by
XCMPLX_1:91;
  hence thesis by Th12;
end;
