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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 12:58, 2 February 2009
, 12:58, 2 February 2009→Rule 10
R10h. ConjUu (( [u C X] , [u C Y] ))$(u). :R8g
R10h. ConjUu (( [u C X] , [u C Y] ))$(u). :R8g
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</pre>
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{| 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%"
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px; text-align:center"
| width="80%" |
| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~9}</math>
|}
|-
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="60%" style="border-top:1px solid black" | <math>P, Q ~\subseteq~ X</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black" |
|- style="height:40px"
|
| <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:40px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{R9a.}</math>
| width="60%" style="border-top:1px solid black" | <math>P ~=~ Q</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{R9a~:~R5a}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|
| <math>\operatorname{R9b.}</math>
| <math>\upharpoonleft P \upharpoonright ~=~ \upharpoonleft Q \upharpoonright</math>
| style="border-left:1px solid black; text-align:center" |
<p><math>\operatorname{R9b~:~R5e}</math></p>
<p><math>\operatorname{R9b~:~R7a}</math></p>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|
| <math>\operatorname{R9c.}</math>
| <math>\overset{X}{\underset{x}{\forall}}~ (\upharpoonleft P \upharpoonright (x) ~=~ \upharpoonleft Q \upharpoonright (x))</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R9c~:~R7b}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|
| <math>\operatorname{R9d.}</math>
| <math>\operatorname{Conj_x^X}~ (\upharpoonleft P \upharpoonright (x) ~=~ \upharpoonleft Q \upharpoonright (x))</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R9d~:~R7c}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|
| <math>\operatorname{R9e.}</math>
| <math>\operatorname{Conj_x^X}~ (\upharpoonleft P \upharpoonright (x) ~\Leftrightarrow~ \upharpoonleft Q \upharpoonright (x))</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R9e~:~R7d}</math>
|- style="height:20px"
|
|
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|
| <math>\operatorname{R9f.}</math>
| <math>\operatorname{Conj_x^X}~ \underline{((}~ \upharpoonleft P \upharpoonright (x) ~,~ \upharpoonleft Q \upharpoonright (x) ~\underline{))}</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R9f~:~R7e}</math>
|- style="height:20px"
|
|
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|
| <math>\operatorname{R9g.}</math>
| <math>\operatorname{Conj_x^X}~ \underline{((}~ \upharpoonleft P \upharpoonright ~,~ \upharpoonleft Q \upharpoonright ~\underline{))}^\$ (x)</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R9g~:~R7f}</math>
|}
|}
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===Rule 11===
===Rule 11===