Definition: In mathematical logic, the concept of "pre-induction" refers to a set of rules that are necessary for the induction principle to work. These rules are typically used in conjunction with the initial condition (or base case) to ensure that the induction step is valid. A pre-induction rule states that if an object A has been proven to be true by a certain process, then it must also be true of any object B that it can produce from A through this same process. The proof for
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