reserve A, B for non empty preBoolean set,
  x, y for Element of [:A,B:];
reserve X for set,
  a,b,c for Element of [:A,B:];
reserve a for Element of [:Fin X, Fin X:];
reserve A for set;
reserve x,y for Element of [:Fin X, Fin X:],
  a,b for Element of DISJOINT_PAIRS X;
reserve A for set,
  x for Element of [:Fin A, Fin A:],
  a,b,c,d,s,t for Element of DISJOINT_PAIRS A,
  B,C,D for Element of Fin DISJOINT_PAIRS A;
reserve K,L,M for Element of Normal_forms_on A;
reserve K, L, M for Element of Normal_forms_on A;

theorem
  Bottom NormForm A = {}
proof
  {} in Normal_forms_on A by Lm4;
  then reconsider Z = {} as Element of NormForm A by Def12;
  now
    let u be Element of NormForm A;
    reconsider z = Z, u9 = u as Element of Normal_forms_on A by Def12;
    thus Z "\/" u = mi (z \/ u9) by Def12
      .= u by Th42;
  end;
  hence thesis by LATTICE2:14;
end;
