
theorem
  for L being non empty RelStr, X being set st ex_sup_of X,L or
ex_sup_of X /\ the carrier of L, L holds "\/"(X,L) = "\/"(X /\ the carrier of L
  , L)
proof
  let L be non empty RelStr, X be set;
  set Y = X /\ the carrier of L;
  assume
A1: ex_sup_of X,L or ex_sup_of Y,L;
  for x being Element of L holds x is_>=_than X iff x is_>=_than Y by Th5;
  hence thesis by A1,Th47;
end;
