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