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MyWikiBiz, Author Your Legacy — Monday November 04, 2024
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Line 4,384: Line 4,384:  
| valign="top" | <math>\operatorname{F2.3d.}</math>
 
| valign="top" | <math>\operatorname{F2.3d.}</math>
 
| valign="top" |
 
| valign="top" |
<math>\begin{array}{cccl}
+
<math>\begin{array}{ccccl}
\upharpoonleft \operatorname{Der}^L \upharpoonright
+
\upharpoonleft \operatorname{Der}^L \upharpoonright (x, y)
& = & \{ & (x, y, z) \in S \times I \times \underline\mathbb{B} ~:~ z = \\
+
& = & \underset{o \in O}{\operatorname{Conj}} \\
&   &   & \begin{array}{cccl}
+
&   & & \begin{array}{ccl}
          \underset{o \in O}{\operatorname{Conj}} \\
+
        \downharpoonleft  & ( & \upharpoonleft \operatorname{Den}^L \upharpoonright (o, x) \\
          & \downharpoonleft  & ( & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\
+
                          & = & \upharpoonleft \operatorname{Den}^L \upharpoonright (o, y) \\
          &                  & = & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\
+
                          & ) & \\
          &                  & ) & \\
+
        \downharpoonright &  & \\
          & \downharpoonright &  & \\
+
        \end{array} \\
          \end{array} \\
+
&  & & \\
&  & \} & \\
   
\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
+
\upharpoonleft \operatorname{Der}^L \upharpoonright (x, y)
& = & \{ & (x, y, z) \in S \times I \times \underline\mathbb{B} ~:~ z = \\
+
& = & \underset{o \in O}{\operatorname{Conj}} \\
&   &    & \begin{array}{ccl}
+
&   & & \begin{array}{cl}
          \underset{o \in O}{\operatorname{Conj}} \\
+
        \underline{((} & \upharpoonleft \operatorname{Den}^L \upharpoonright (o, x) \\
          & \underline{((} & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\
+
        ,              & \upharpoonleft \operatorname{Den}^L \upharpoonright (o, y) \\
          & ,              & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\
+
        \underline{))} & \\
          & \underline{))} & \\
+
        \end{array} \\
          \end{array} \\
+
&  & & \\
&  & \} & \\
   
\end{array}</math>
 
\end{array}</math>
 
| style="border-left:1px solid black; text-align:center" |
 
| style="border-left:1px solid black; text-align:center" |
Line 4,425: Line 4,423:  
| valign="top" | <math>\operatorname{F2.2f.}</math>
 
| valign="top" | <math>\operatorname{F2.2f.}</math>
 
| valign="top" |
 
| valign="top" |
<math>\begin{array}{cccl}
+
<math>\begin{array}{ccccl}
\upharpoonleft \operatorname{Der}^L \upharpoonright
+
\upharpoonleft \operatorname{Der}^L \upharpoonright (x, y)
& = & \{ & (x, y, z) \in S \times I \times \underline\mathbb{B} ~:~ z = \\
+
& = & \underset{o \in O}{\operatorname{Conj}} \\
&   &   & \begin{array}{cll}
+
&  & & \begin{array}{cl}
          \underset{o \in O}{\operatorname{Conj}} \\
+
        \underline{((} & \upharpoonleft L_{OS} \upharpoonright (o, x) \\
          & \underline{((}   & \upharpoonleft \operatorname{Den}^L x \upharpoonright \\
+
        ,             & \upharpoonleft L_{OS} \upharpoonright (o, y) \\
          & ,                 & \upharpoonleft \operatorname{Den}^L y \upharpoonright \\
+
        \underline{))} & \\
          & \underline{))}^\$ & (o) \\
+
        \end{array} \\
          \end{array} \\
+
&  & & \\
&  & \} & \\
   
\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>
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