reserve N for Cardinal;
reserve M for Aleph;
reserve X for non empty set;
reserve Y,Z,Z1,Z2,Y1,Y2,Y3,Y4 for Subset of X;
reserve S for Subset-Family of X;
reserve x for set;
reserve F,Uf for Filter of X;

theorem Th5:
  X in F
proof
  set Y = the Element of F;
  Y in F & X c= X;
  hence thesis by Def1;
end;
