
theorem
  for W being with_non-empty_element set holds
  W-SUP(SO)_category, W-INF(SC)_category are_anti-isomorphic_under W UpperAdj
proof
  let W be with_non-empty_element set;
  W-SUP(SO)_category, W-INF(SC)_category
  are_anti-isomorphic_under (W LowerAdj)" by Th52,YELLOW20:51;
  hence thesis by Th18;
end;
