code: def test_SubModulePolyRing_nontriv_local():
      R = QQ.old_poly_ring(x, y, z, order=ilex)
      F = R.free_module(1)
  
      def contains(I, f):
          return F.submodule(*[[g] for g in I]).contains([f])
  
      assert contains([x, y], x)
      assert contains([x, y], x + y)
      assert not contains([x, y], 1)
      assert not contains([x, y], z)
      assert contains([x**2 + y, x**2 + x], x - y)
      assert not contains(
          [x + y + z, x * y + x * z + y * z, x * y * z], x**2
      )
      assert contains([x * (1 + x + y), y * (1 + z)], x)
      assert contains([x * (1 + x + y), y * (1 + z)], x + y)
  
imports: from sympy.polys.agca.modules import FreeModule, ModuleOrder, FreeModulePolyRing
  from sympy.polys import CoercionFailed, QQ, lex, grlex, ilex, ZZ
  from sympy.abc import x, y, z
  from sympy.testing.pytest import raises
  from sympy.core.numbers import Rational
label_desc: Use image node_id 7 for calling a global function with example usage: test_SubModulePolyRing_nontriv_local() and returns: F