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 Th6:
  for A being antisymmetric RelStr, a1,a2 being Element of A holds
  a1 <= a2 implies not a2 < a1
by Th2;
