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 Th14:
  p is Integer implies denominator(p) = 1 & numerator(p) = p
proof
  assume p is Integer;
  then reconsider m=p as Integer;
  p =m/1;
  then
A1: denominator(p)<=1 by Def3;
  1<=denominator(p) by Th8;
  hence denominator(p)=1 by A1,XXREAL_0:1;
  hence thesis;
end;
