reserve X,Y,x,y for set;
reserve A for non empty Poset;
reserve a,a1,a2,a3,b,c for Element of A;
reserve S,T for Subset of A;

theorem Th21:
  not a in LowerCone{a}
proof
  a in {a} by TARSKI:def 1;
  hence thesis by Th20;
end;
