Frequently Used Theorems (cont.)

C₂.  Generation Theorem

One theorem of frequent use goes under the nickname of the weed and seed theorem (WAST).  The proof is just an exercise in mathematical induction, once a suitable basis is laid down, and it will be left as an exercise for the reader.  What the WAST says is that a label can be freely distributed or freely erased anywhere in a subtree whose root is labeled with that label.  The second in our list of frequently used theorems is in fact the base case of this weed and seed theorem.  In Laws of Form it goes by the names of Consequence 2 (C₂) or Generation.

Here is a proof of the Generation Theorem.

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