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User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 04:00, 13 February 2009

323 bytes removed ,  04:00, 13 February 2009
→‎Fact 2.3
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| valign="top" | <math>\operatorname{F2.3d.}</math>
 
| valign="top" | <math>\operatorname{F2.3d.}</math>
 
| valign="top" |
 
| valign="top" |
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<math>\begin{array}{cccl}
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<math>\begin{array}{ccccl}
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\upharpoonleft \operatorname{Der}^L \upharpoonright
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\upharpoonleft \operatorname{Der}^L \upharpoonright (x, y)
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& = & \{ & (x, y, z) \in S \times I \times \underline\mathbb{B} ~:~ z = \\
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& = & \underset{o \in O}{\operatorname{Conj}} \\
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&   &   & \begin{array}{cccl}
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&   & & \begin{array}{ccl}
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          \underset{o \in O}{\operatorname{Conj}} \\
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        \downharpoonleft  & ( & \upharpoonleft \operatorname{Den}^L \upharpoonright (o, x) \\
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          & \downharpoonleft  & ( & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\
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                          & = & \upharpoonleft \operatorname{Den}^L \upharpoonright (o, y) \\
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          &                  & = & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\
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                          & ) & \\
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          &                  & ) & \\
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        \downharpoonright &  & \\
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          & \downharpoonright &  & \\
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        \end{array} \\
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          \end{array} \\
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&  & & \\
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&  & \} & \\
   
\end{array}</math>
 
\end{array}</math>
 
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.3d~:~Def}</math>
 
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.3d~:~Def}</math>
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| valign="top" | <math>\operatorname{F2.3e.}</math>
 
| valign="top" | <math>\operatorname{F2.3e.}</math>
 
| valign="top" |
 
| valign="top" |
−
<math>\begin{array}{cccl}
+
<math>\begin{array}{ccccl}
−
\upharpoonleft \operatorname{Der}^L \upharpoonright
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\upharpoonleft \operatorname{Der}^L \upharpoonright (x, y)
−
& = & \{ & (x, y, z) \in S \times I \times \underline\mathbb{B} ~:~ z = \\
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& = & \underset{o \in O}{\operatorname{Conj}} \\
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&   &    & \begin{array}{ccl}
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&   & & \begin{array}{cl}
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          \underset{o \in O}{\operatorname{Conj}} \\
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        \underline{((} & \upharpoonleft \operatorname{Den}^L \upharpoonright (o, x) \\
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          & \underline{((} & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\
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        ,              & \upharpoonleft \operatorname{Den}^L \upharpoonright (o, y) \\
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          & ,              & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\
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        \underline{))} & \\
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          & \underline{))} & \\
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        \end{array} \\
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          \end{array} \\
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&  & & \\
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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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| valign="top" | <math>\operatorname{F2.2f.}</math>
 
| valign="top" | <math>\operatorname{F2.2f.}</math>
 
| valign="top" |
 
| valign="top" |
−
<math>\begin{array}{cccl}
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<math>\begin{array}{ccccl}
−
\upharpoonleft \operatorname{Der}^L \upharpoonright
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\upharpoonleft \operatorname{Der}^L \upharpoonright (x, y)
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& = & \{ & (x, y, z) \in S \times I \times \underline\mathbb{B} ~:~ z = \\
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& = & \underset{o \in O}{\operatorname{Conj}} \\
−
&   &   & \begin{array}{cll}
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&  & & \begin{array}{cl}
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          \underset{o \in O}{\operatorname{Conj}} \\
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        \underline{((} & \upharpoonleft L_{OS} \upharpoonright (o, x) \\
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          & \underline{((}   & \upharpoonleft \operatorname{Den}^L x \upharpoonright \\
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        ,             & \upharpoonleft L_{OS} \upharpoonright (o, y) \\
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          & ,                 & \upharpoonleft \operatorname{Den}^L y \upharpoonright \\
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        \underline{))} & \\
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          & \underline{))}^\$ & (o) \\
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        \end{array} \\
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          \end{array} \\
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&  & & \\
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&  & \} & \\
   
\end{array}</math>
 
\end{array}</math>
 
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.3f~:~D10a}</math>
 
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.3f~:~D10a}</math>
Jon Awbrey
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