
theorem Th1:
  for L being RelStr, X being set, a being Element of L st a in X &
  ex_sup_of X,L holds a <= "\/"(X,L)
proof
  let L be RelStr, X be set, a be Element of L such that
A1: a in X and
A2: ex_sup_of X,L;
  X is_<=_than "\/"(X, L) by A2,YELLOW_0:def 9;
  hence thesis by A1;
end;
