
theorem
  for L be complete transitive antisymmetric non empty RelStr for S be
sups-closed non empty Subset of L for X be Subset of S holds "\/"(X,subrelstr S
  ) = "\/"(X,L)
proof
  let L be complete transitive antisymmetric non empty RelStr;
  let S be sups-closed non empty Subset of L;
  let X be Subset of S;
  ex_sup_of X,L by YELLOW_0:17;
  hence thesis by Th22;
end;
