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Proofs in mathematics are what mathematics is all about. They are subject to entire books, created entire theories like Fermat’s last theorem, are hardly to understand like currently Mochizuki’s proof of the ABC conjecture, or need computer assistance like the 4-color-theorem. They are sometimes even missing, although everybody believes in the statement like the Riemann hypothesis or ##NP=P##. However, those are exceptions and events at the frontlines of mathematics. The daily mathematical life is cobblestoned by more or less easy deductions and conclusions. Some need detours like rather tricky integrals, a certain substitution or formula to solve them, and some need only modest calculations, or arguments along the line: What if not? The latter are the vast majority since they are required line by line when reading a proof: ##A\Longrightarrow B##. They are also subject to the exercises and problems collected under ‘homework’...