Quantum mechanical rules for observed observers and the consistency of quantum theory

I argue that the rules of unitary quantum mechanics imply that observers who will themselves be subject to measurements in a linear combination of macroscopic states (``cat" measurements) cannot make reliable predictions on the results of experiments performed after such measurements. This lifts the inconsistency in the interpretation of quantum mechanics recently identified by Frauchiger and Renner. The Born rules for calculating the probability of outcomes and for communicating with other observers do not generally apply for cat-measured observers, nor can they generally be amended to incorporate upcoming cat measurements. Quantum mechanical rules completed with these conditions become fully consistent.