
theorem Th50:
  for L being non empty RelStr, X being set holds (ex_sup_of X,L
iff ex_sup_of X /\ the carrier of L, L) & (ex_inf_of X,L iff ex_inf_of X /\ the
  carrier of L, L)
proof
  let L be non empty RelStr, X be set;
  set Y = X /\ the carrier of L;
  ( for x being Element of L holds x is_<=_than X iff x is_<=_than Y)& for
  x being Element of L holds x is_>=_than X iff x is_>=_than Y by Th5;
  hence thesis by Th46,Th48;
end;
