
theorem lemma1:
  for L being Lattice,
      A being Subset of L
    st L = BooleLatt {{}} holds
      A = {} or A = {{}} or A = {{},{{}}} or A = {{{}}}
   proof
     let L be Lattice,
         A be Subset of L;
     assume L = BooleLatt {{}}; then
A2:  the carrier of L = bool {{}} by LATTICE3:def 1;
     bool {{}} = {{}, {{}}} by ZFMISC_1:24;
     hence thesis by ZFMISC_1:36,A2;
   end;
