 with the maximum occurring around \(\theta = 9\degr\). Inequality (33) asserts that for the specified angles there is a non-empty subensemble \(E'\) of pairs for which the results for a spin measurement along \(a\) for 1 and along \(b\) for 2 are both +. Eq. (30) implies the counterfactual proposition that if the spin of a 2 in \(E'\) had been measured along \(b'\) then with certainty the result would have been \(-\); and likewise Eq. (31) implies the counterfactual proposition that if the spin of a 1 in \(E'\) had been measured along \(a'\) then with certainty the result would have been \(-\). It is in this step that counterfactual reasoning is used in the argument. Since the subensemble \(E'\) is non-empty, we have reached a contradiction with Eq. (32), which asserts that if the spin of 1 is measured along \(a'\) and that of 2 is measured along \(b'\) then it is impossible that both results are \(-\). The incompatibility of a deterministic local theory with quantum mechanics is thereby demonstrated.