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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 16:48, 1 February 2009
, 16:48, 1 February 2009→Rule 8
R8g. ConjUu (( [S] , [T] ))$(u). :R7f
R8g. ConjUu (( [S] , [T] ))$(u). :R7f
</pre>
</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~7}</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 ~:~ X \to \underline\mathbb{B}</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{R7a.}</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{R7a~:~R6a}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|
| <math>\operatorname{R7b.}</math>
| <math>\overset{X}{\underset{x}{\forall}}~ (p(x) ~=~ q(x))</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R7b~:~R6b}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|
| <math>\operatorname{R7c.}</math>
| <math>\operatorname{Conj_x^X}~ (p(x) ~=~ q(x))</math>
| style="border-left:1px solid black; text-align:center" |
<p><math>\operatorname{R7c~:~R6c}</math></p>
<p><math>\operatorname{R7c~:~P1a}</math></p>
|- style="height:20px"
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|
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
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| <math>\operatorname{R7d.}</math>
| <math>\operatorname{Conj_x^X}~ (p(x) ~\Leftrightarrow~ q(x))</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R7d~:~P1b}</math>
|- style="height:20px"
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|
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
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| <math>\operatorname{R7e.}</math>
| <math>\operatorname{Conj_x^X}~ \underline{((}~ p(x) ~,~ q(x) ~\underline{))}</math>
| style="border-left:1px solid black; text-align:center" |
<p><math>\operatorname{R7e~:~P1c}</math></p>
<p><math>\operatorname{R7e~:~$1a}</math></p>
|- style="height:20px"
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|
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
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| <math>\operatorname{R7f.}</math>
| <math>\operatorname{Conj_x^X}~ \underline{((}~ p ~,~ q ~\underline{))}^\$ (x)</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R7f~:~$1b}</math>
|}
|}
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===Rule 9===
===Rule 9===