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A proposition is a formula that is claimed to be true. However, a claim is only as good as the substantiating argument is. Since different people may disagree on the quality of an argument, we need some objective criteria whether an argument is correct or not. Surprisingly, there exist a number of structural rules such that any proposition is true that has a correspondingly formed argument. We call such an argument a proof (Beweis).
It is always possible to decide whether a given argument represents a proof or not; once a proof is given, there is therefore no more dispute about the validity of a proposition. Proving is thus at the heart of any critical discourse and the knowledge about the correct application of proof rules is a must for a scientist or engineer: if we derive new knowledge, we must be able to proof it; if we are given some knowledge, we must able to check it (i.e., its proof).
To invent a proof is a creative activity. The proof rules give some guiding principles that help in the first steps; however, from a certain point on, some insight is required to discover the "killer argument" that "slays" the proposition. To check a proof is simply craft; everybody who understands "proof terminology" is able to read a proof and judge its correctness.
This chapter is dedicated to the demonstration of formal proof rules and the various forms of their appearance. The application of these rules is demonstrated by the various proofs given throughout this document.