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User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 20:43, 11 February 2009

94 bytes removed ,  20:43, 11 February 2009
→‎Fact 2.2
Line 4,025: Line 4,025:  
| width="2%"  style="border-top:1px solid black" |  
 
| width="2%"  style="border-top:1px solid black" |  
 
| width="10%" style="border-top:1px solid black" | <math>\operatorname{F2.2a.}</math>
 
| 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="16%" style="border-top:1px solid black" | <math>\operatorname{Der}^L</math>
 +
| width="4%"  style="border-top:1px solid black" | <math>=\!</math>
 +
| width="48%" style="border-top:1px solid black" | <math>\ldots</math>
 
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{F2.2a~:~R11a}</math>
 
| 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;
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| colspan="5" | &nbsp;
−
| &nbsp;
  −
| &nbsp;
   
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 
|- style="height:40px"
 
|- style="height:40px"
 
| &nbsp;
 
| &nbsp;
 
| valign="top" | <math>\operatorname{F2.2b.}</math>
 
| valign="top" | <math>\operatorname{F2.2b.}</math>
−
| valign="top" | <math>\operatorname{Der}(L)</math>
+
| valign="top" | <math>\upharpoonleft \operatorname{Der}(L) \upharpoonright</math>
 +
| valign="top" | <math>=\!</math>
 +
| valign="top" | <math>\ldots</math>
 
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
 
<math>\operatorname{F2.2b~:~R11b}</math>
 
<math>\operatorname{F2.2b~:~R11b}</math>
 
|- style="height:20px"
 
|- style="height:20px"
−
| &nbsp;
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| colspan="5" | &nbsp;
−
| &nbsp;
  −
| &nbsp;
   
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 
|- style="height:60px"
 
|- style="height:60px"
 
| &nbsp;
 
| &nbsp;
 
| valign="top" | <math>\operatorname{F2.2c.}</math>
 
| valign="top" | <math>\operatorname{F2.2c.}</math>
−
| valign="top" |
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| valign="top" | <math>\upharpoonleft \operatorname{Der}(L) \upharpoonright</math>
−
<math>\begin{array}{ll}
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| valign="top" | <math>=\!</math>
−
\{ & (x, y) \in S \times I ~: \\
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| valign="top" | <math>\ldots</math>
−
  & \operatorname{Den}(L, x) ~=~ \operatorname{Den}(L, y) \\
  −
\} & \\
  −
\end{array}</math>
   
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
 
<math>\operatorname{F2.2c~:~R11c}</math></p>
 
<math>\operatorname{F2.2c~:~R11c}</math></p>
 
|- style="height:20px"
 
|- style="height:20px"
−
| &nbsp;
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| colspan="5" | &nbsp;
−
| &nbsp;
  −
| &nbsp;
   
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 
|- style="height:60px"
 
|- style="height:60px"
 
| &nbsp;
 
| &nbsp;
 
| valign="top" | <math>\operatorname{F2.2d.}</math>
 
| valign="top" | <math>\operatorname{F2.2d.}</math>
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| valign="top" |
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| valign="top" | <math>\upharpoonleft \operatorname{Der}(L) \upharpoonright</math>
−
<math>\begin{array}{ll}
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| valign="top" | <math>=\!</math>
−
\{ & (x, y) \in S \times I ~: \\
+
| valign="top" | <math>\ldots</math>
−
  & \upharpoonleft \operatorname{Den}(L, x) \upharpoonright ~=~ \upharpoonleft \operatorname{Den}(L, y) \upharpoonright \\
  −
\} & \\
  −
\end{array}</math>
   
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
 
<math>\operatorname{F2.2d~:~Log}</math>
 
<math>\operatorname{F2.2d~:~Log}</math>
 
|- style="height:20px"
 
|- style="height:20px"
−
| &nbsp;
+
| colspan="5" | &nbsp;
−
| &nbsp;
  −
| &nbsp;
   
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 
|- style="height:60px"
 
|- style="height:60px"
 
| &nbsp;
 
| &nbsp;
 
| valign="top" | <math>\operatorname{F2.2e.}</math>
 
| valign="top" | <math>\operatorname{F2.2e.}</math>
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| valign="top" |
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| valign="top" | <math>\upharpoonleft \operatorname{Der}(L) \upharpoonright</math>
−
<math>\begin{array}{ll}
+
| valign="top" | <math>=\!</math>
−
\{ & (x, y) \in S \times I ~: \\
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| valign="top" | <math>\ldots</math>
−
  & \overset{O}{\underset{o}{\forall}}~ \upharpoonleft \operatorname{Den}(L, x) \upharpoonright (o) ~=~ \upharpoonleft \operatorname{Den}(L, y) \upharpoonright (o) \\
  −
\} & \\
  −
\end{array}</math>
   
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
 
<math>\operatorname{F2.2e~:~Log}</math>
 
<math>\operatorname{F2.2e~:~Log}</math>
 
|- style="height:20px"
 
|- style="height:20px"
−
| &nbsp;
+
| colspan="5" | &nbsp;
−
| &nbsp;
  −
| &nbsp;
   
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 
|- style="height:60px"
 
|- style="height:60px"
 
| &nbsp;
 
| &nbsp;
 
| valign="top" | <math>\operatorname{F2.2f.}</math>
 
| valign="top" | <math>\operatorname{F2.2f.}</math>
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| valign="top" |
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| valign="top" | <math>\upharpoonleft \operatorname{Der}(L) \upharpoonright</math>
−
<math>\begin{array}{ll}
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| valign="top" | <math>=\!</math>
−
\{ & (x, y) \in S \times I ~: \\
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| valign="top" | <math>\ldots</math>
−
  & \underset{o \in O}{\operatorname{Conj}}~ \upharpoonleft \operatorname{Den}(L, x) \upharpoonright (o) ~=~ \upharpoonleft \operatorname{Den}(L, y) \upharpoonright (o) \\
  −
\} & \\
  −
\end{array}</math>
   
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
 
<math>\operatorname{F2.2f~:~$~}</math>
 
<math>\operatorname{F2.2f~:~$~}</math>
Jon Awbrey
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