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 Th12:
  for V being set, C being finite set for A being Element of
  SubstitutionSet (V, C) holds mi (A ^ -A) = Bottom SubstLatt (V,C)
proof
  let V be set, C be finite set, A be Element of SubstitutionSet (V, C);
  mi (A ^ -A) = {} by Th9,SUBSTLAT:9
    .= Bottom SubstLatt (V,C) by SUBSTLAT:26;
  hence thesis;
end;
