
theorem
  for L being complete reflexive antisymmetric non empty RelStr for D
  being Subset of L, x being Element of L st x in D holds (sup D) "/\" x = x
proof
  let L be complete reflexive antisymmetric non empty RelStr, D be Subset of
  L, x be Element of L such that
A1: x in D;
  D is_<=_than sup D by YELLOW_0:32;
  then x <= sup D by A1;
  hence thesis by YELLOW_0:25;
end;
