
theorem Th7: :: 1.2.  LEMMA, p. 179
:: LowerAdj and UpperAdj preserve identities
  for L being complete LATTICE holds
  LowerAdj id L = id L & UpperAdj id L = id L
proof
  let L be complete LATTICE;
  [id L, id L] is Galois by Th6;
  hence thesis by Def1,Def2;
end;
