
theorem :: 1.3 THEOREM, p. 179
  for W being with_non-empty_element set holds
  (W LowerAdj)*(W UpperAdj) = id (W-SUP_category) &
  (W UpperAdj)*(W LowerAdj) = id (W-INF_category)
proof
  let W be with_non-empty_element set;
A1: W LowerAdj" = W UpperAdj by Th18;
  W UpperAdj" = W LowerAdj by Th18;
  hence thesis by A1,FUNCTOR1:18;
end;
