12,080
edits
Changes
User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 02:46, 2 February 2009
, 02:46, 2 February 2009→Rule 9
</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:40px; text-align:center"
| width="80%" |
| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~8}</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>s, t ~\text{are sentences about things in}~ 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{R8a.}</math>
| width="60%" style="border-top:1px solid black" | <math>s ~\Leftrightarrow~ t</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" |
<math>\operatorname{R8a~:~D7a}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|
| <math>\operatorname{R8b.}</math>
| <math>\downharpoonleft s \downharpoonright ~=~ \downharpoonleft t \downharpoonright</math>
| style="border-left:1px solid black; text-align:center" |
<p><math>\operatorname{R8b~:~D7b}</math></p>
<p><math>\operatorname{R8b~:~R7a}</math></p>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|
| <math>\operatorname{R8c.}</math>
| <math>\overset{X}{\underset{x}{\forall}}~ (\downharpoonleft s \downharpoonright (x) ~=~ \downharpoonleft t \downharpoonright (x))</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R8c~:~R7b}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|
| <math>\operatorname{R8d.}</math>
| <math>\operatorname{Conj_x^X}~ (\downharpoonleft s \downharpoonright (x) ~=~ \downharpoonleft t \downharpoonright (x))</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R8d~:~R7c}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|
| <math>\operatorname{R8e.}</math>
| <math>\operatorname{Conj_x^X}~ (\downharpoonleft s \downharpoonright (x) ~\Leftrightarrow~ \downharpoonleft t \downharpoonright (x))</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R8e~:~R7d}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|
| <math>\operatorname{R8f.}</math>
| <math>\operatorname{Conj_x^X}~ \underline{((}~ \downharpoonleft s \downharpoonright (x) ~,~ \downharpoonleft t \downharpoonright (x) ~\underline{))}</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R8f~:~R7e}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|
| <math>\operatorname{R8g.}</math>
| <math>\operatorname{Conj_x^X}~ \underline{((}~ \downharpoonleft s \downharpoonright ~,~ \downharpoonleft t \downharpoonright ~\underline{))}^\$ (x)</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R8g~:~R7f}</math>
|}
|}
<br>
===Rule 10===
===Rule 10===