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
  denominator p = denominator q & numerator p = numerator q implies p = q
proof
  assume that
A1: denominator(p)=denominator(q) and
A2: numerator(p)=numerator(q);
  thus p=numerator(q)/denominator(q) by A1,A2,Th12
    .=q by Th12;
end;
