Context-independent mapping and free choice are equivalent: a general proof

Abstract Free choice (or statistical independence) assumption in a hidden variable model (HVM) means that the settings chosen by experimenters do not depend on values of variable. The context-independent (CI) mapping an HVM results measurement for other measurements. If measurements are spacelike separated, this is known as local causality. Both free and CI assumptions considered necessary derivation Bell-type criteria contextuality/nonlocality. It known, however, variety special cases, two logically independent. We show here, complete generality, any system random variables with or without disturbance/signaling, postulates equivalent to choice. one denies possibility given empirical scenario can be described which measurements’ settings, violations should denied too, vice versa.