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Revision as of 19:02, 31 January 2009
, 19:02, 31 January 2009→Rule 5
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px; text-align:right"
|- style="height:40px; text-align:center"
| width="98%" | <math>\text{Evaluation Rule 1}\!</math>
| width="80%" |
| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~3}</math>
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| width="2%" style="border-top:1px solid black" |
| width="2%" style="border-top:1px solid black" |
| width="14%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="14%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="84%" style="border-top:1px solid black" | <math>f, g ~:~ X \to \underline\mathbb{B}</math>
| width="64%" style="border-top:1px solid black" | <math>Q ~\subseteq~ X</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black" |
|- style="height:40px"
|- style="height:40px"
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| <math>\text{and}\!</math>
| <math>\text{and}\!</math>
| <math>x ~\in~ X</math>
| <math>x ~\in~ X</math>
| style="border-left:1px solid black" |
|- style="height:40px"
|- style="height:40px"
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| <math>\text{then}\!</math>
| <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
| <math>\text{the following are equivalent:}\!</math>
| style="border-left:1px solid black" |
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|- style="height:40px"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="2%" style="border-top:1px solid black" |
| width="14%" style="border-top:1px solid black" | <math>\operatorname{E1a.}</math>
| width="14%" style="border-top:1px solid black" | <math>\operatorname{R3a.}</math>
| width="64%" style="border-top:1px solid black" | <math>f(x) ~=~ g(x)</math>
| width="64%" style="border-top:1px solid black" | <math>x ~\in~ Q</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{E1a~:~V1a}</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{R3a~:~R1a}</math>
|- style="height:20px"
|- style="height:20px"
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|- style="height:60px"
|- style="height:60px"
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| <math>\operatorname{E1c.}</math>
| <math>\operatorname{R3b.}</math>
| <math>\underline{((}~ f(x) ~,~ g(x) ~\underline{))}</math>
| <math>\upharpoonleft Q \upharpoonright (x)</math>
| style="border-left:1px solid black; text-align:center" |
| style="border-left:1px solid black; text-align:center" |
<p><math>\operatorname{E1c~:~V1c}</math></p>
<p><math>\operatorname{R3b~:~R1b}</math></p>
<p><math>\operatorname{E1c~:~$1a}</math></p>
<p><math>\operatorname{R3b~:~R2a}</math></p>
|- style="height:20px"
|- style="height:20px"
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|- style="height:40px"
|- style="height:40px"
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| <math>\operatorname{E1d.}</math>
| <math>\operatorname{R3c.}</math>
| <math>\underline{((}~ f ~,~ g ~\underline{))}^\$ (x)</math>
| <math>\upharpoonleft Q \upharpoonright (x) ~=~ \underline{1}</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{E1d~:~$1b}</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R3c~:~R2b}</math></p>
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