reserve x, X, Y for set;
reserve L for complete LATTICE,
  a for Element of L;
reserve J for non empty set,
  j for Element of J;

theorem
  for F being Function of J, the carrier of L holds F.j <= Sup F & Inf F <= F.j
proof
  let F be Function of J, the carrier of L;
  F.j in rng F by FUNCT_2:4;
  hence thesis by Th22;
end;
