  We report a single-neutron optical experiment to demonstrate the violation of
a Bell-like inequality. Entanglement is achieved not between particles, but
between the degrees of freedom, in this case, for a single-particle. The
spin-{\small 1/2} property of neutrons are utilized. The total wave function of
the neutron is described in a tensor product Hilbert space. A Bell-like
inequality is derived not by a non-locality but by a contextuality. Joint
measurements of the spinor and the path properties lead to the violation of a
Bell-like inequality. Manipulation of the wavefunction in one Hilbert space
influences the result of the measurement in the other Hilbert space. A
discussion is given on the quantum contextuality and an entanglement-induced
correlation in our experiment.
