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====C<sub>3</sub>.  Dominant form theorem====
 
====C<sub>3</sub>.  Dominant form theorem====
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The third of the frequently used theorems of service to this survey is one that Spencer-Brown annotates as ''Consequence&nbsp;3'' (C<sub>3</sub>), or ''Integration''.  A better mnemonic might be ''dominance and recession theorem'' (DART), but perhaps the brevity of ''dominant form theorem'' (DFT) is sufficient reminder of its double-edged role in proofs.
 
The third of the frequently used theorems of service to this survey is one that Spencer-Brown annotates as ''Consequence&nbsp;3'' (C<sub>3</sub>), or ''Integration''.  A better mnemonic might be ''dominance and recession theorem'' (DART), but perhaps the brevity of ''dominant form theorem'' (DFT) is sufficient reminder of its double-edged role in proofs.
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<pre>
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o-----------------------------------------------------------o
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| [[Image:Logical_Graph_Figure_29.jpg|500px]] || (29)
| C_3.  Dominant Form Theorem                              |
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o-----------------------------------------------------------o
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|                                                          |
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|                  o                  o                  |
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|                  |                  |                  |
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|                a @        =         @                  |
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|                                                           |
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o-----------------------------------------------------------o
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|                                                           |
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|                 a( )       =        ( )                  |
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|                                                           |
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o-----------------------------------------------------------o
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|                Remark <---- | ----> Recess                |
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o-----------------------------------------------------------o
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</pre>
      
Here is a proof of the Dominant Form Theorem.
 
Here is a proof of the Dominant Form Theorem.
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