
theorem
  for S,T being complete LATTICE for d being sups-preserving Function of S, T
  holds LowerAdj (d opp) = UpperAdj d
proof
  let S,T be complete LATTICE;
  let d be sups-preserving Function of S, T;
  [UpperAdj d, d] is Galois by Def2;
  then [d opp, (UpperAdj d) opp] is Galois by YELLOW_7:44;
  hence thesis by Def1;
end;
