reserve V, C for set;
reserve A, B, D for Element of Fin PFuncs (V, C);
reserve s for Element of PFuncs (V,C);
reserve K, L, M for Element of SubstitutionSet (V,C);

theorem
  Top SubstLatt (V,C) = { {} }
proof
  { {} } in SubstitutionSet (V,C) by Th2;
  then reconsider Z = { {} } as Element of SubstLatt (V,C) by Def4;
  now
    let u be Element of SubstLatt (V,C);
    reconsider z = Z, u9 = u as Element of SubstitutionSet (V,C) by Def4;
    thus Z "/\" u = mi (z ^ u9) by Def4
      .= mi (u9 ^ z) by Th3
      .= mi u9 by Th4
      .= u by Th11;
  end;
  hence thesis by LATTICE2:16;
end;
