reserve x, y for object, X, X1, X2 for set;

theorem Th4:
  Q_Funcs(X) is Subset of Q_PFuncs(X)
proof
  Q_Funcs(X) c= Q_PFuncs(X)
  proof
    let x be object;
    assume x in Q_Funcs(X);
    then x is Function of X,RAT by Def15;
    hence thesis by Def14;
  end;
  hence thesis;
end;
