reserve
  X for non empty set,
  FX for Filter of X,
  SFX for Subset-Family of X;

theorem Th28:
  for X being infinite set holds
    X in the set of all X\A where A is finite Subset of X
  proof
    let X be infinite set;
    set Z={};
    Z is finite Subset of X
    proof
      {} c= X;
      hence thesis;
    end;
    then reconsider Z as finite Subset of X;
    X\Z in {X\A where A is finite Subset of X:not contradiction};
    hence thesis;
  end;
