
theorem
  for L being non empty Poset, f being Function of L,L st f is closure
ex S being non empty Poset, g being Function of S,L, d being Function of L,S st
  [g,d] is Galois & f = g*d
proof
  let L be non empty Poset, f be Function of L,L;
  assume
A1: f is closure;
  reconsider S = Image f as non empty Poset;
  reconsider g = inclusion f as Function of S,L;
  reconsider d = corestr f as Function of L,S;
  take S,g,d;
  thus [g,d] is Galois by A1,Th36;
  thus thesis by Th32;
end;
