code: def test_internal_external_VT2T2_AT():
      ii, jj = symbols("i j", below_fermi=True)
      aa, bb = symbols("a b", above_fermi=True)
      k, l = symbols("k l", below_fermi=True, cls=Dummy)
      c, d = symbols("c d", above_fermi=True, cls=Dummy)
  
      exprs = [
          atv(k, l, c, d) * att(aa, c, ii, k) * att(bb, d, jj, l),
          atv(l, k, c, d) * att(aa, c, ii, l) * att(bb, d, jj, k),
          atv(k, l, d, c) * att(aa, d, ii, k) * att(bb, c, jj, l),
          atv(l, k, d, c) * att(aa, d, ii, l) * att(bb, c, jj, k),
      ]
      for permut in exprs[1:]:
          assert substitute_dummies(exprs[0]) == substitute_dummies(
              permut
          )
      exprs = [
          atv(k, l, c, d) * att(aa, c, ii, k) * att(d, bb, jj, l),
          atv(l, k, c, d) * att(aa, c, ii, l) * att(d, bb, jj, k),
          atv(k, l, d, c) * att(aa, d, ii, k) * att(c, bb, jj, l),
          atv(l, k, d, c) * att(aa, d, ii, l) * att(c, bb, jj, k),
      ]
      for permut in exprs[1:]:
          assert substitute_dummies(exprs[0]) == substitute_dummies(
              permut
          )
      exprs = [
          atv(k, l, c, d) * att(c, aa, ii, k) * att(bb, d, jj, l),
          atv(l, k, c, d) * att(c, aa, ii, l) * att(bb, d, jj, k),
          atv(k, l, d, c) * att(d, aa, ii, k) * att(bb, c, jj, l),
          atv(l, k, d, c) * att(d, aa, ii, l) * att(bb, c, jj, k),
      ]
      for permut in exprs[1:]:
          assert substitute_dummies(exprs[0]) == substitute_dummies(
              permut
          )
  
imports: from sympy.physics.secondquant import Dagger, Bd, VarBosonicBasis, BBra, B, BKet, FixedBosonicBasis, matrix_rep, apply_operators, InnerProduct, Commutator, KroneckerDelta, AnnihilateBoson, CreateBoson, BosonicOperator, F, Fd, FKet, BosonState, CreateFermion, AnnihilateFermion, evaluate_deltas, AntiSymmetricTensor, contraction, NO, wicks, PermutationOperator, simplify_index_permutations, _sort_anticommuting_fermions, _get_ordered_dummies, substitute_dummies, FockStateBosonKet, ContractionAppliesOnlyToFermions
  from sympy.concrete.summations import Sum
  from sympy.core.function import Function, expand
  from sympy.core.numbers import I, Rational
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy, Symbol, symbols
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.printing.repr import srepr
  from sympy.simplify.simplify import simplify
  from sympy.testing.pytest import slow, raises
  from sympy.printing.latex import latex
label_desc: Use image node_id 52 for calling a global function with example usage: test_internal_external_VT2T2_AT() without return types