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 Th4:
  for A being antisymmetric RelStr, a1,a2 being Element of A holds
  not(a1 < a2 & a2 < a1)
by Th2;
