Lay summary
To assess the implications of the violation of Bell's inequality it is essential to have a minimal set of assumptions from which the inequality can be derived. To this end, we will analyze local causality and auxiliary assumptions of the existing derivations into precisely defined and clearly separated assumptions of causality and locality. To obtain a minimal set of assumptions we will also consider experimental setups that are different from the standard one. Drawing on our previous discovery of a minimal assumption derivation of a Bell-type inequality we will thus continue the quest for a yet more general set of assumptions that entail Bell's inequality. This will provide the appropriate basis for a substantial reductio ad absurdum since none of the assumptions will be redundant.