12,089
edits
Changes
User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 13:42, 2 February 2009
, 13:42, 2 February 2009→Rule 10
|- style="height:40px; text-align:center"
|- style="height:40px; text-align:center"
| width="80%" |
| width="80%" |
| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~9}</math>
| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~10}</math>
|}
|}
|-
|-
|- style="height:40px"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{R9a.}</math>
| width="18%" style="border-top:1px solid black" | <math>\operatorname{R10a.}</math>
| width="60%" style="border-top:1px solid black" | <math>P ~=~ Q</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>
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{R9a~:~R5a}</math>
|- style="height:60px"
|- style="height:60px"
|
|
| <math>\operatorname{R9b.}</math>
| <math>\operatorname{R10b.}</math>
| <math>\upharpoonleft P \upharpoonright ~=~ \upharpoonleft Q \upharpoonright</math>
| <math>\upharpoonleft P \upharpoonright ~=~ \upharpoonleft Q \upharpoonright</math>
| style="border-left:1px solid black; text-align:center" |
| style="border-left:1px solid black; text-align:center" |
<p><math>\operatorname{R9b~:~R5e}</math></p>
<p><math>\operatorname{R10b~:~R5e}</math></p>
<p><math>\operatorname{R9b~:~R7a}</math></p>
<p><math>\operatorname{R10b~:~R7a}</math></p>
|- style="height:20px"
|- style="height:20px"
|
|
|- style="height:60px"
|- style="height:60px"
|
|
| <math>\operatorname{R9c.}</math>
| <math>\operatorname{R10c.}</math>
| <math>\overset{X}{\underset{x}{\forall}}~ (\upharpoonleft P \upharpoonright (x) ~=~ \upharpoonleft Q \upharpoonright (x))</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="border-left:1px solid black; text-align:center" | <math>\operatorname{R10c~:~R7b}</math>
|- style="height:20px"
|- style="height:20px"
|
|
|- style="height:40px"
|- style="height:40px"
|
|
| <math>\operatorname{R9d.}</math>
| <math>\operatorname{R10d.}</math>
| <math>\operatorname{Conj_x^X}~ (\upharpoonleft P \upharpoonright (x) ~=~ \upharpoonleft Q \upharpoonright (x))</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="border-left:1px solid black; text-align:center" | <math>\operatorname{R10d~:~R7c}</math>
|- style="height:20px"
|- style="height:20px"
|
|
|- style="height:40px"
|- style="height:40px"
|
|
| <math>\operatorname{R9e.}</math>
| <math>\operatorname{R10e.}</math>
| <math>\operatorname{Conj_x^X}~ (\upharpoonleft P \upharpoonright (x) ~\Leftrightarrow~ \upharpoonleft Q \upharpoonright (x))</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="border-left:1px solid black; text-align:center" | <math>\operatorname{R10e~:~R7d}</math>
|- style="height:20px"
|- style="height:20px"
|
|
| <math>\operatorname{R9f.}</math>
| <math>\operatorname{R9f.}</math>
| <math>\operatorname{Conj_x^X}~ \underline{((}~ \upharpoonleft P \upharpoonright (x) ~,~ \upharpoonleft Q \upharpoonright (x) ~\underline{))}</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="border-left:1px solid black; text-align:center" | <math>\operatorname{R10f~:~R7e}</math>
|- style="height:20px"
|- style="height:20px"
|
|
| <math>\operatorname{R9g.}</math>
| <math>\operatorname{R9g.}</math>
| <math>\operatorname{Conj_x^X}~ \underline{((}~ \upharpoonleft P \upharpoonright ~,~ \upharpoonleft Q \upharpoonright ~\underline{))}^\$ (x)</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>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R10g~:~R7f}</math>
|}
|}
|}
|}