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 Th9:
  A ^ -A = {}
proof
  assume A ^ -A <> {};
  then consider x be object such that
A1: x in A ^ -A by XBOOLE_0:def 1;
  x in { s \/ t where s, t is Element of PFuncs (V,C) : s in A & t in -A &
  s tolerates t } by A1,SUBSTLAT:def 3;
  then consider s1, t1 be Element of PFuncs (V,C) such that
  x = s1 \/ t1 and
A2: s1 in A and
A3: t1 in -A and
A4: s1 tolerates t1;
  ex f1 be Element of PFuncs (Involved A, C) st f1 = t1 & for g be
  Element of PFuncs (V, C) st g in A holds not f1 tolerates g by A3;
  hence thesis by A2,A4;
end;
