
theorem Th39:
  for L being non empty Poset, f being Function of L,L st f is
  kernel holds [corestr f,inclusion f] is Galois
proof
  let L be non empty Poset, f be Function of L,L;
  assume that
A1: f is idempotent monotone and
A2: f <= id(L);
  set g = (corestr f), d = inclusion f;
  g*d = id(Image f) by A1,Th33;
  then
A3: id(Image f) <= g*d by Lm1;
  g is monotone & d*g <= id L by A1,A2,Th31,Th32;
  hence thesis by A3,Th19;
end;
