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 Th15:
  numerator(p) = p or denominator(p) = 1 implies p is Integer
proof
  assume
A1: numerator(p)=p or denominator(p)=1;
  per cases by A1;
  suppose
    numerator(p)=p;
    hence thesis;
  end;
  suppose
    denominator(p)=1;
    then numerator(p)=p;
    hence thesis;
  end;
end;
