reserve V, C, x, a, b for set;
reserve A, B for Element of SubstitutionSet (V, C);
reserve C for finite set;
reserve A, B for Element of SubstitutionSet (V, C);

theorem
  for V being non empty set, C being finite non empty set for A being
  Element of SubstitutionSet (V, C) st A = {} holds mi -A = Top SubstLatt (V,C)
proof
  let V be non empty set, C be finite non empty set, A be Element of
  SubstitutionSet (V, C);
  assume A = {};
  then
A1: -A = { {} } by Th10;
  then -A in SubstitutionSet (V, C) by SUBSTLAT:2;
  then mi -A = { {} } by A1,SUBSTLAT:11;
  hence thesis by SUBSTLAT:27;
end;
