Changes

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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| ~~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%" |  

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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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5.

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~~& S~~

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~~& :>~~

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& S^*

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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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| 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>

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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>

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Jon Awbrey

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edits