theorem Th50:
  G is independent implies 'not' Ex(Ex(a,A,G),B,G) = All(All('not' a,B,G),A,G)
proof
  assume G is independent;
  then 'not' Ex(Ex(a,A,G),B,G) = All('not' Ex(a,B,G),A,G) by Th44;
  hence thesis by BVFUNC_2:19;
end;
