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User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 19:47, 11 February 2009

1,954 bytes removed ,  19:47, 11 February 2009
→‎Fact 2.2
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|- style="height:50px; text-align:center"
 
|- style="height:50px; text-align:center"
 
| style="width:80%" |  
 
| style="width:80%" |  
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| style="width:20%; border-left:1px solid black" | <math>\operatorname{Fact~2.1}</math>
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| style="width:20%; border-left:1px solid black" | <math>\operatorname{Fact~2.2}</math>
 
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|-
 
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| &nbsp;
 
| &nbsp;
 
| <math>\text{then}\!</math>
 
| <math>\text{then}\!</math>
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| <math>\text{the following are identical subsets of}~ S \times I :</math>
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| <math>\text{the following are equivalent:}\!</math>
 
| style="border-left:1px solid black" | &nbsp;
 
| style="border-left:1px solid black" | &nbsp;
 
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|- style="height:60px"
 
|- style="height:60px"
 
| width="2%"  style="border-top:1px solid black" | &nbsp;
 
| width="2%"  style="border-top:1px solid black" | &nbsp;
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| width="10%" style="border-top:1px solid black" | <math>\operatorname{F2.1a.}</math>
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| width="10%" style="border-top:1px solid black" | <math>\operatorname{F2.2a.}</math>
 
| width="68%" style="border-top:1px solid black" | <math>\operatorname{Der}^L</math>
 
| width="68%" style="border-top:1px solid black" | <math>\operatorname{Der}^L</math>
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| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{F2.1a~:~D13a}</math>
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| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{F2.2a~:~R11a}</math>
 
|- style="height:20px"
 
|- style="height:20px"
 
| &nbsp;
 
| &nbsp;
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|- style="height:40px"
 
|- style="height:40px"
 
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| valign="top" | <math>\operatorname{F2.1b.}</math>
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| valign="top" | <math>\operatorname{F2.2b.}</math>
 
| valign="top" | <math>\operatorname{Der}(L)</math>
 
| valign="top" | <math>\operatorname{Der}(L)</math>
 
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
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<math>\operatorname{F2.1b~:~D13b}</math>
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<math>\operatorname{F2.2b~:~R11b}</math>
 
|- style="height:20px"
 
|- style="height:20px"
 
| &nbsp;
 
| &nbsp;
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|- style="height:60px"
 
|- style="height:60px"
 
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| valign="top" | <math>\operatorname{F2.1c.}</math>
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| valign="top" | <math>\operatorname{F2.2c.}</math>
 
| valign="top" |
 
| valign="top" |
 
<math>\begin{array}{ll}
 
<math>\begin{array}{ll}
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\end{array}</math>
 
\end{array}</math>
 
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
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<p><math>\operatorname{F2.1c~:~D13c}</math></p>
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<math>\operatorname{F2.2c~:~R11c}</math></p>
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<p><math>\operatorname{F2.1c~:~R9a}</math></p>
   
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|- style="height:20px"
 
| &nbsp;
 
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|- style="height:60px"
 
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| valign="top" | <math>\operatorname{F2.1d.}</math>
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| valign="top" | <math>\operatorname{F2.2d.}</math>
 
| valign="top" |
 
| valign="top" |
 
<math>\begin{array}{ll}
 
<math>\begin{array}{ll}
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\end{array}</math>
 
\end{array}</math>
 
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
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<math>\operatorname{F2.1d~:~R9b}</math>
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<math>\operatorname{F2.2d~:~Log}</math>
 
|- style="height:20px"
 
|- style="height:20px"
 
| &nbsp;
 
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|- style="height:60px"
 
|- style="height:60px"
 
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| valign="top" | <math>\operatorname{F2.1e.}</math>
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| valign="top" | <math>\operatorname{F2.2e.}</math>
 
| valign="top" |
 
| valign="top" |
 
<math>\begin{array}{ll}
 
<math>\begin{array}{ll}
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\end{array}</math>
 
\end{array}</math>
 
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
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<math>\operatorname{F2.1e~:~R9c}</math>
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<math>\operatorname{F2.2e~:~Log}</math>
 
|- style="height:20px"
 
|- style="height:20px"
 
| &nbsp;
 
| &nbsp;
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|- style="height:60px"
 
|- style="height:60px"
 
| &nbsp;
 
| &nbsp;
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| valign="top" | <math>\operatorname{F2.1f.}</math>
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| valign="top" | <math>\operatorname{F2.2f.}</math>
 
| valign="top" |
 
| valign="top" |
 
<math>\begin{array}{ll}
 
<math>\begin{array}{ll}
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\end{array}</math>
 
\end{array}</math>
 
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
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<math>\operatorname{F2.1f~:~R9d}</math>
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<math>\operatorname{F2.2f~:~$~}</math>
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|- style="height:20px"
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| &nbsp;
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| &nbsp;
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| &nbsp;
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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|- style="height:60px"
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| &nbsp;
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| valign="top" | <math>\operatorname{F2.1g.}</math>
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| valign="top" |
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<math>\begin{array}{ll}
  −
\{ & (x, y) \in S \times I ~: \\
  −
  & \underset{o \in O}{\operatorname{Conj}}~ \underline{((}~ \upharpoonleft \operatorname{Den}(L, x) \upharpoonright (o) ~,~ \upharpoonleft \operatorname{Den}(L, y) \upharpoonright (o) ~\underline{))} \\
  −
\} & \\
  −
\end{array}</math>
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| style="border-left:1px solid black; text-align:center" |
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<math>\operatorname{F2.1g~:~R9e}</math>
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|- style="height:20px"
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| &nbsp;
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| &nbsp;
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| &nbsp;
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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|- style="height:60px"
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| &nbsp;
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| valign="top" | <math>\operatorname{F2.1h.}</math>
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| valign="top" |
  −
<math>\begin{array}{ll}
  −
\{ & (x, y) \in S \times I ~: \\
  −
  & \underset{o \in O}{\operatorname{Conj}}~ \underline{((}~ \upharpoonleft \operatorname{Den}(L, x) \upharpoonright ~,~ \upharpoonleft \operatorname{Den}(L, y) \upharpoonright ~\underline{))}^\$ (o) \\
  −
\} & \\
  −
\end{array}</math>
  −
| style="border-left:1px solid black; text-align:center" |
  −
<p><math>\operatorname{F2.1h~:~R9f}</math></p>
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<p><math>\operatorname{F2.1h~:~D12e}</math></p>
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|- style="height:20px"
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| &nbsp;
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| &nbsp;
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| &nbsp;
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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|- style="height:60px"
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| &nbsp;
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| valign="top" | <math>\operatorname{F2.1i.}</math>
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| valign="top" |
  −
<math>\begin{array}{ll}
  −
\{ & (x, y) \in S \times I ~: \\
  −
  & \underset{o \in O}{\operatorname{Conj}}~ \underline{((}~ \upharpoonleft L_{OS} \cdot x \upharpoonright ~,~ \upharpoonleft L_{OS} \cdot y \upharpoonright ~\underline{))}^\$ (o) \\
  −
\} & \\
  −
\end{array}</math>
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| style="border-left:1px solid black; text-align:center" |
  −
<math>\operatorname{F2.1i~:~D12a}</math>
   
|}
 
|}
 
|}
 
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Jon Awbrey
12,080

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