reserve x, X, Y for set;
reserve L for complete LATTICE,
  a for Element of L;

theorem Th22:
  a in X implies a <= "\/"(X, L) & "/\"(X, L) <= a
proof
  assume
A1: a in X;
  X is_<=_than "\/"(X, L) by YELLOW_0:32;
  hence a <= "\/"(X, L) by A1;
  X is_>=_than "/\"(X, L) by YELLOW_0:33;
  hence thesis by A1;
end;
