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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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| − | <pre>
| + | {| align="center" border="0" cellpadding="4" cellspacing="0" |
| − | o-----------------------------------------------------------o
| + | | [[Image:Logical_Graph_Figure_25.jpg]] || (25) |
| − | | C_1. Double Negation Theorem. Proof. |
| + | |} |
| − | o-----------------------------------------------------------o
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| − | | |
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| − | | a o |
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| − | | \ |
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| − | | \ |
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| − | | o |
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| − | | \ |
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| − | | \ |
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| − | | @ |
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| − | | |
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| − | o=============================< I2. Unfold "(())" >=========o
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| − | | |
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| − | | a o o |
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| − | | \ / |
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| − | | \ / |
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| − | | o o |
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| − | | \ / |
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| − | | \ / |
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| − | | @ |
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| − | | |
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| − | o=============================< J1. Insert "(a)" >==========o
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| − | | |
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| − | | a o |
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| − | | / |
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| − | | / |
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| − | | a o a o o |
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| − | | \ \ / |
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| − | | \ \ / |
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| − | | o o |
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| − | | \ / |
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| − | | \ / |
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| − | | @ |
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| − | | |
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| − | o=============================< J2. Distribute "((a))" >====o
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| − | | |
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| − | | a o a o |
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| − | | \ \ |
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| − | | \ \ |
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| − | | o o a o |
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| − | | \ \ / |
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| − | | \ \ / |
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| − | | a o o |
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| − | | \ / |
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| − | | \ / |
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| − | | o |
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| − | | / |
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| − | | / |
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| − | | @ |
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| − | | |
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| − | o=============================< J1. Delete "(a)" >==========o
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| − | | |
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| − | | a o |
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| − | | \ |
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| − | | \ |
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| − | | o o |
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| − | | \ \ |
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| − | | \ \ |
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| − | | a o o |
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| − | | \ / |
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| − | | \ / |
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| − | | o |
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| − | | / |
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| − | | / |
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| − | | @ |
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| − | | |
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| − | o=============================< J1. Insert "a" >============o
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| − | | |
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| − | | a o |
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| − | | \ |
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| − | | \ |
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| − | | o o a |
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| − | | \ \ |
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| − | | \ \ |
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| − | | a o o a |
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| − | | \ / |
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| − | | \ / |
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| − | | o |
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| − | | / |
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| − | | / |
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| − | | @ |
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| − | | |
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| − | o=============================< J2. Collect "a" >===========o
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| − | | |
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| − | | a o |
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| − | | \ |
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| − | | \ |
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| − | | o o a |
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| − | | \ \ |
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| − | | \ \ |
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| − | | o o |
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| − | | \ / |
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| − | | \ / |
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| − | | o |
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| − | | / |
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| − | | / | | |
| − | | a @ |
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| − | | |
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| − | o=============================< J1. Delete "((a))" >========o
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| − | | |
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| − | | o |
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| − | | \ |
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| − | | \ |
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| − | | o |
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| − | | / |
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| − | | / |
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| − | | a @ |
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| − | | | | |
| − | o=============================< I2. Refold "(())" >=========o
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| − | | |
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| − | | a |
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| − | | @ |
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| − | | | | |
| − | o=============================< QED >=======================o
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| − | </pre>
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| | | | |
| | ====C<sub>2</sub>. Generation theorem==== | | ====C<sub>2</sub>. Generation theorem==== |
