theorem Th38:
  G is independent implies 'not' Ex(All(a,A,G),B,G) '<' Ex('not'
  All(a,B,G),A,G)
proof
  assume G is independent;
  then
A1: All('not' All(a,A,G),B,G) '<' 'not' All(All(a,B,G),A,G) by Th26;
  'not' Ex(All(a,A,G),B,G) = All('not' All(a,A,G),B,G) by BVFUNC_2:19;
  hence thesis by A1,BVFUNC_2:18;
end;
