theorem
  G is independent implies 'not' All(Ex(a,A,G),B,G) '<' 'not' All(All(a,
  B,G),A,G)
proof
  assume G is independent;
  then
A1: Ex('not' Ex(a,A,G),B,G) '<' 'not' All(All(a,B,G),A,G) by Th31;
  Ex('not' Ex(a,A,G),B,G) = Ex(All('not' a,A,G),B,G) by BVFUNC_2:19;
  hence thesis by A1,Th19;
end;
