"Looking at the rewritings used for the proofs of the four statements", it can be seen why the reasoning that combines the first three statements can lead to a conclusion (formula_37 gets "−" implies formula_39 gets "+") that is in contradiction with the constructed overall state, in which the combined probability for (formula_37 gets "−" and formula_39 gets "−"), is not zero, but equals formula_211 (see rewriting (4)). The reason is that the statements have implicit assumptions that contradict each other. For instance, statement (1) about a later formula_39 measurement, supposes that laboratory formula_81 is in a superposition of "up" and "down" states, ie that the observer formula_38 is in two states, namely thinking "the spin is up" and thinking "the spin is down". If formula_39 wants to measure with respect to the formula_216 basis, then formula_39 has two possibilities: Either (i) she constructs her projection-test-operator such that a "plus" state for formula_38 will become a superposition of "up" and "down", i.e. she does not leave a univocal formula_38 to stay univocal, or (ii) she changes the state of formula_38 to a single state not coupled any more to the "up" or "down" of the spin (the coupling was the result of a measurement as a unitary evolution, as described in the step at formula_194, and any measurement that is realized as a unitary transformation, can be undone in principle, if enough information is given to prevent entropy increase during the transformation). In both cases, the starting point of statement (2) is gone. So, the inference about a later formula_39 measurement, such as made in statement (1) can only be done, when the starting point of statement (2), namely formula_38 univocally thinks the spin formula_1 is formula_91, will be made unfullfilled.