
theorem
  for L being complete antisymmetric non empty RelStr for a being
Element of L, X being set holds a = "/\"(X,L) iff a is_<=_than X & for b being
  Element of L st b is_<=_than X holds a >= b
proof
  let L be complete non empty antisymmetric RelStr;
  let a be Element of L, X be set;
  ex_inf_of X,L by Th17;
  hence thesis by Th31;
end;
