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→Frequently used theorems: ASCII → JPEG
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The proof that follows is adapted from the one that was given by [[George Spencer Brown]] in his book ''Laws of Form'' (LOF), and credited to two of his students, John Dawes and D.A. Utting.
The proof that follows is adapted from the one that was given by [[George Spencer Brown]] in his book ''Laws of Form'' (LOF) and credited to two of his students, John Dawes and D.A. Utting.
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====C<sub>2</sub>. Generation theorem====
====C<sub>2</sub>. 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 What the WAST says is that a label can be freely distributed or freely erased (retracted or withdrawn) anywhere in a subtree whose root is labeled with that label.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 LOF, it goes by the name of ''Consequence 2'' (C<sub>2</sub>), or ''Generation''.
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 LOF, it goes by the name of ''Consequence 2'' (C<sub>2</sub>), or ''Generation''.
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| [[Image:Logical_Graph_Figure_27.jpg|500px]] || (27)
| C_2. Generation Theorem |
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| a(b) = a(ab) |
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Here is a proof of the Generation Theorem.
Here is a proof of the Generation Theorem.