
theorem Th44:
  for L being non empty reflexive antisymmetric RelStr st for D1,
D2 being non empty directed Subset of L holds (sup D1) "/\" (sup D2) = sup (D1
  "/\" D2) holds L is satisfying_MC
proof
  let L be non empty reflexive antisymmetric RelStr such that
A1: for D1, D2 being non empty directed Subset of L holds (sup D1) "/\"
  (sup D2) = sup (D1 "/\" D2);
  let x be Element of L, D be non empty directed Subset of L;
A2: {x} is directed by WAYBEL_0:5;
  thus x "/\" sup D = sup {x} "/\" sup D by YELLOW_0:39
    .= sup ({x} "/\" D) by A1,A2;
end;
