Line 4,292: |
Line 4,292: |
| )) :D10a | | )) :D10a |
| </pre> | | </pre> |
| + | |
| + | <br> |
| + | |
| + | {| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%" |
| + | | |
| + | {| align="center" cellpadding="0" cellspacing="0" width="100%" |
| + | |- style="height:50px; text-align:center" |
| + | | style="width:80%" | |
| + | | style="width:20%; border-left:1px solid black" | <math>\operatorname{Fact~2.2}</math> |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" cellpadding="0" cellspacing="0" width="100%" |
| + | |- style="height:50px" |
| + | | width="2%" style="border-top:1px solid black" | |
| + | | width="12%" style="border-top:1px solid black" | <math>\text{If}\!</math> |
| + | | width="66%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math> |
| + | | width="20%" style="border-top:1px solid black; border-left:1px solid black" | |
| + | |- style="height:50px" |
| + | | |
| + | | <math>\text{then}\!</math> |
| + | | <math>\text{the following are equivalent:}\!</math> |
| + | | style="border-left:1px solid black" | |
| + | |} |
| + | |- |
| + | | |
| + | {| align="center" cellpadding="0" cellspacing="0" width="100%" |
| + | |- style="height:10px" |
| + | | width="2%" style="border-top:1px solid black" | |
| + | | width="12%" style="border-top:1px solid black" | |
| + | | width="66%" style="border-top:1px solid black" | |
| + | | width="20%" style="border-top:1px solid black; border-left:1px solid black" | |
| + | |- style="height:100px" |
| + | | |
| + | | valign="top" | <math>\operatorname{F2.2a.}</math> |
| + | | valign="top" | |
| + | <math>\begin{array}{cccl} |
| + | \operatorname{Der}^L |
| + | & = & \{ & (x, y) \in S \times I ~: \\ |
| + | & & & \begin{array}{ccl} |
| + | \underset{o \in O}{\operatorname{Conj}} \\ |
| + | & ( & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\ |
| + | & = & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\ |
| + | & ) & \\ |
| + | \end{array} \\ |
| + | & & \} & \\ |
| + | \end{array}</math> |
| + | | style="border-left:1px solid black; text-align:center" | <math>\operatorname{F2.2a~:~R11a}</math> |
| + | |- style="height:20px" |
| + | | colspan="3" | |
| + | | style="border-left:1px solid black; text-align:center" | <math>::\!</math> |
| + | |- style="height:100px" |
| + | | |
| + | | valign="top" | <math>\operatorname{F2.2b.}</math> |
| + | | valign="top" | |
| + | <math>\begin{array}{ccccl} |
| + | \upharpoonleft \operatorname{Der}^L \upharpoonright |
| + | & = & \upharpoonleft & \{ & (x, y) \in S \times I ~: \\ |
| + | & & & & \begin{array}{ccl} |
| + | \underset{o \in O}{\operatorname{Conj}} \\ |
| + | & ( & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\ |
| + | & = & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\ |
| + | & ) & \\ |
| + | \end{array} \\ |
| + | & & & \} & \\ |
| + | & & \upharpoonright & & \\ |
| + | \end{array}</math> |
| + | | style="border-left:1px solid black; text-align:center" | |
| + | <math>\operatorname{F2.2b~:~R11b}</math> |
| + | |- style="height:20px" |
| + | | colspan="3" | |
| + | | style="border-left:1px solid black; text-align:center" | <math>::\!</math> |
| + | |- style="height:100px" |
| + | | |
| + | | valign="top" | <math>\operatorname{F2.2c.}</math> |
| + | | valign="top" | |
| + | <math>\begin{array}{cccl} |
| + | \upharpoonleft \operatorname{Der}^L \upharpoonright |
| + | & = & \{ & (x, y, z) \in S \times I \times \underline\mathbb{B} ~:~ z = \\ |
| + | & & & \begin{array}{cccl} |
| + | \downharpoonleft & \underset{o \in O}{\operatorname{Conj}} \\ |
| + | & & ( & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\ |
| + | & & = & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\ |
| + | & & ) & \\ |
| + | \downharpoonright & & \\ |
| + | \end{array} \\ |
| + | & & \} & \\ |
| + | \end{array}</math> |
| + | | style="border-left:1px solid black; text-align:center" | |
| + | <math>\operatorname{F2.2c~:~R11c}</math></p> |
| + | |- style="height:20px" |
| + | | colspan="3" | |
| + | | style="border-left:1px solid black; text-align:center" | <math>::\!</math> |
| + | |- style="height:100px" |
| + | | |
| + | | valign="top" | <math>\operatorname{F2.2d.}</math> |
| + | | valign="top" | |
| + | <math>\begin{array}{cccl} |
| + | \upharpoonleft \operatorname{Der}^L \upharpoonright |
| + | & = & \{ & (x, y, z) \in S \times I \times \underline\mathbb{B} ~:~ z = \\ |
| + | & & & \begin{array}{cccl} |
| + | \underset{o \in O}{\operatorname{Conj}} \\ |
| + | & \downharpoonleft & ( & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\ |
| + | & & = & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\ |
| + | & & ) & \\ |
| + | & \downharpoonright & & \\ |
| + | \end{array} \\ |
| + | & & \} & \\ |
| + | \end{array}</math> |
| + | | style="border-left:1px solid black; text-align:center" | |
| + | <math>\operatorname{F2.2d~:~Log}</math> |
| + | |- style="height:20px" |
| + | | colspan="3" | |
| + | | style="border-left:1px solid black; text-align:center" | <math>::\!</math> |
| + | |- style="height:100px" |
| + | | |
| + | | valign="top" | <math>\operatorname{F2.2e.}</math> |
| + | | valign="top" | |
| + | <math>\begin{array}{cccl} |
| + | \upharpoonleft \operatorname{Der}^L \upharpoonright |
| + | & = & \{ & (x, y, z) \in S \times I \times \underline\mathbb{B} ~:~ z = \\ |
| + | & & & \begin{array}{ccl} |
| + | \underset{o \in O}{\operatorname{Conj}} \\ |
| + | & \underline{((} & \upharpoonleft \operatorname{Den}^L x \upharpoonright (o) \\ |
| + | & , & \upharpoonleft \operatorname{Den}^L y \upharpoonright (o) \\ |
| + | & \underline{))} & \\ |
| + | \end{array} \\ |
| + | & & \} & \\ |
| + | \end{array}</math> |
| + | | style="border-left:1px solid black; text-align:center" | |
| + | <math>\operatorname{F2.2e~:~Log}</math> |
| + | |- style="height:20px" |
| + | | colspan="3" | |
| + | | style="border-left:1px solid black; text-align:center" | <math>::\!</math> |
| + | |- style="height:100px" |
| + | | |
| + | | valign="top" | <math>\operatorname{F2.2f.}</math> |
| + | | valign="top" | |
| + | <math>\begin{array}{cccl} |
| + | \upharpoonleft \operatorname{Der}^L \upharpoonright |
| + | & = & \{ & (x, y, z) \in S \times I \times \underline\mathbb{B} ~:~ z = \\ |
| + | & & & \begin{array}{cll} |
| + | \underset{o \in O}{\operatorname{Conj}} \\ |
| + | & \underline{((} & \upharpoonleft \operatorname{Den}^L x \upharpoonright \\ |
| + | & , & \upharpoonleft \operatorname{Den}^L y \upharpoonright \\ |
| + | & \underline{))}^\$ & (o) \\ |
| + | \end{array} \\ |
| + | & & \} & \\ |
| + | \end{array}</math> |
| + | | style="border-left:1px solid black; text-align:center" | |
| + | <math>\operatorname{F2.2f~:~$~}</math> |
| + | |} |
| + | |} |
| + | |
| + | <br> |