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User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 16:50, 25 January 2009

197 bytes removed ,  16:50, 25 January 2009
→‎Proof Schemata
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{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black" width="90%"
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{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black; border-bottom:1px solid black" width="90%"
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| align="left"  style="border-left:1px solid black;"  width="50%" |
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<math>\mathfrak{C} (\mathfrak{P}) : \text{Grammar 1}\!</math>
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| align="right" style="border-right:1px solid black;" width="50%" |
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<math>\mathfrak{Q} = \varnothing</math>
   
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|-
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| colspan="2" style="border-top:1px solid black; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black" |
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| align="left" style="border-left:1px solid black;" width="50%" | &nbsp;
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<math>\begin{array}{rcll}
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| align="right" style="border-right:1px solid black;" width="50%" | <math>\text{Definition 1}\!</math>
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1.
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|-
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& S
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| colspan="2" style="border-left:1px solid black; border-right:1px solid black; border-top:1px solid black" |
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& :>
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<math>\begin{array}{ll}
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& m_1 \ = \ ^{\backprime\backprime} \operatorname{~} ^{\prime\prime}
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\text{If} & Q \subseteq X,
 
\\
 
\\
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2.
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& S
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& :>
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& p_j, \, \text{for each} \, j \in J
   
\\
 
\\
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3.
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\text{then} & \upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}
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& S
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& :>
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& \operatorname{Conc}^0 \ = \ ^{\backprime\backprime\prime\prime}
   
\\
 
\\
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4.
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& S
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& :>
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& \operatorname{Surc}^0 \ = \ ^{\backprime\backprime} \, \operatorname{()} \, ^{\prime\prime}
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\\
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5.
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& S
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& :>
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& S^*
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\\
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6.
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& S
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& :>
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& ^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, S \, \cdot \, ( \, ^{\backprime\backprime} \operatorname{,} ^{\prime\prime} \, \cdot \, S \, )^* \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}
   
\\
 
\\
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\text{such that:}
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\end{array}</math>
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|-
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| align="left" style="border-left:1px solid black; border-top:1px solid black" width="50%" |
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<math>\begin{array}{ll}
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\text{D1a.} & \upharpoonleft Q \upharpoonright (x) ~\Leftrightarrow~ x \in Q
 
\end{array}</math>
 
\end{array}</math>
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| align="right" style="border-right:1px solid black; border-top:1px solid black" width="50%" |
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<math>\forall x \in X</math>
 
|}
 
|}
Jon Awbrey
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