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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 03:50, 28 January 2009
, 03:50, 28 January 2009→Geometric Translation Rule 1
===Geometric Translation Rule 1===
===Geometric Translation Rule 1===
<pre>
<br>
If X c U
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and P : U -> B, such that:
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G1a. {X} = P,
| width="98%" | <math>\text{Geometric Translation Rule 1}\!</math>
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then the following equations hold:
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| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="80%" style="border-top:1px solid black" | <math>Q \subseteq X</math>
|- style="height:48px"
</pre>
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| <math>\text{and}\!</math>
| <math>p ~:~ X \to \underline\mathbb{B}</math>
|- style="height:48px"
|
| <math>\text{such that:}\!</math>
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|- style="height:48px"
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| <math>\text{G1a.}\!</math>
| <math>\upharpoonleft Q \upharpoonright ~=~ p</math>
|- style="height:48px"
|
| <math>\text{then}\!</math>
| <math>\text{the following equations hold:}\!</math>
|}
|-
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|- style="height:52px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" align="left" | <math>\text{G1b}_{00}.\!</math>
| width="20%" style="border-top:1px solid black" |
<math>\upharpoonleft \varnothing \upharpoonright</math>
| width="5%" style="border-top:1px solid black" | <math>=\!</math>
| width="20%" style="border-top:1px solid black" | <math>(~)</math>
| width="5%" style="border-top:1px solid black" | <math>=\!</math>
| width="30%" style="border-top:1px solid black" |
<math>\underline{0} ~:~ X \to \underline\mathbb{B}</math>
|- style="height:52px"
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| align="left" | <math>\text{G1b}_{01}.\!</math>
| <math>\upharpoonleft {}^{_\sim} Q \upharpoonright</math>
| <math>=\!</math>
| <math>(\upharpoonleft Q \upharpoonright)</math>
| <math>=\!</math>
| <math>(p) ~:~ X \to \underline\mathbb{B}</math>
|- style="height:52px"
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| align="left" | <math>\text{G1b}_{10}.\!</math>
| <math>\upharpoonleft Q \upharpoonright</math>
| <math>=\!</math>
| <math>\upharpoonleft Q \upharpoonright</math>
| <math>=\!</math>
| <math>p ~:~ X \to \underline\mathbb{B}</math>
|- style="height:52px"
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| align="left" | <math>\text{G1b}_{11}.\!</math>
| <math>\upharpoonleft X \upharpoonright</math>
| <math>=\!</math>
| <math>((~))</math>
| <math>=\!</math>
| <math>\underline{1} ~:~ X \to \underline\mathbb{B}</math>
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