12,089
edits
Changes
MyWikiBiz, Author Your Legacy — Thursday September 11, 2025
Jump to navigationJump to searchUser:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 21:28, 3 February 2009
, 21:28, 3 February 2009→Fact 1
| style="border-top:1px solid black; width:2%" |
| style="border-top:1px solid black; width:2%" |
| style="border-top:1px solid black; width:18%" | <math>\operatorname{F1a.}</math>
| style="border-top:1px solid black; width:18%" | <math>\operatorname{F1a.}</math>
| style="border-top:1px solid black; width:60%" | <math>P ~=~ Q</math>
| style="border-top:1px solid black; width:60%" | <math>s \quad \Leftrightarrow \quad P ~=~ Q</math>
| style="border-top:1px solid black; border-left:1px solid black; text-align:center" |
| style="border-top:1px solid black; border-left:1px solid black; text-align:center" |
<math>\operatorname{F1a~:~R5a}</math>
<math>\operatorname{F1a~:~R9a}</math>
|- style="height:20px"
|- style="height:20px"
|
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|- style="height:40px"
|
|
| <math>\operatorname{F1b.}</math>
| <math>\operatorname{F1b.}</math>
| <math>\upharpoonleft P \upharpoonright ~=~ \upharpoonleft Q \upharpoonright</math>
| <math>s \quad \Leftrightarrow \quad \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" |
<math>\operatorname{F1b~:~R9b}</math>
|- style="height:20px"
|- style="height:20px"
|
|
|
|
| <math>\operatorname{F1c.}</math>
| <math>\operatorname{F1c.}</math>
| <math>\overset{X}{\underset{x}{\forall}}~ (\upharpoonleft P \upharpoonright (x) ~=~ \upharpoonleft Q \upharpoonright (x))</math>
| <math>s \quad \Leftrightarrow \quad \overset{X}{\underset{x}{\forall}}~ (\upharpoonleft P \upharpoonright (x) ~=~ \upharpoonleft Q \upharpoonright (x))</math>
| style="border-left:1px solid black; text-align:center" |
| style="border-left:1px solid black; text-align:center" |
<math>\operatorname{F1c~:~R7b}</math>
<math>\operatorname{F1c~:~R9c}</math>
|- style="height:20px"
|- style="height:20px"
|
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|- style="height:60px"
|
|
| <math>\operatorname{F1d.}</math>
| <math>\operatorname{F1d.}</math>
| <math>\operatorname{Conj_x^X}~ (\upharpoonleft P \upharpoonright (x) ~=~ \upharpoonleft Q \upharpoonright (x))</math>
| <math>s \quad \Leftrightarrow \quad \operatorname{Conj_x^X}~ (\upharpoonleft P \upharpoonright (x) ~=~ \upharpoonleft Q \upharpoonright (x))</math>
| style="border-left:1px solid black; text-align:center" |
| style="border-left:1px solid black; text-align:center" |
<math>\operatorname{F1d~:~R7c}</math>
<p><math>\operatorname{F1d~:~R9d}</math></p>
<p><math>\operatorname{F1d~:~R8a}</math></p>
|- style="height:20px"
|- style="height:20px"
|
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|- style="height:60px"
|
|
| <math>\operatorname{F1e.}</math>
| <math>\operatorname{F1e.}</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" |
| style="border-left:1px solid black; text-align:center" |
<math>\operatorname{F1e~:~R7d}</math>
<p><math>\operatorname{F1e~:~R8b}</math></p>
<p><math>\operatorname{F1e~:~\_\_?\_\_}</math></p>
|- style="height:20px"
|- style="height:20px"
|
|
| <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" |
| style="border-left:1px solid black; text-align:center" |
<math>\operatorname{F1f~:~R7e}</math>
<math>\operatorname{F1f~:~\_\_?\_\_}</math>
|- style="height:20px"
|- style="height:20px"
|
|
| <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" |
| style="border-left:1px solid black; text-align:center" |
<math>\operatorname{F1g~:~R7f}</math>
<math>\operatorname{F1g~:~~\_\_?\_\_}</math>
|}
|}
|}
|}
<br>
<br>
