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 Th12:
  for A being reflexive antisymmetric RelStr, a1,a2 being Element
of A holds (ex C being Chain of A st a1 in C & a2 in C) iff (a1 < a2 iff not a2
  <= a1)
by Th6,Th11;
