12,089
edits
Changes
User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 15:39, 30 January 2009
, 15:39, 30 January 2009→Rule 3
| <math>\upharpoonleft Q \upharpoonright (x) = \underline{1}</math>
| <math>\upharpoonleft Q \upharpoonright (x) = \underline{1}</math>
| style="border-left:1px solid black; text-align:center" | <math>\text{R3c : R2b}\!</math>
| style="border-left:1px solid black; text-align:center" | <math>\text{R3c : R2b}\!</math>
|}
<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:48px; text-align:right"
| width="98%" | <math>\text{Evaluation Rule 1}\!</math>
| width="2%" |
|}
|-
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:48px"
| width="2%" style="border-top:1px solid black" |
| 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>
|- style="height:48px"
|
| <math>\text{and}\!</math>
| <math>x ~\in~ X</math>
|- style="height:48px"
|
| <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
|}
|-
|
{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:56px"
| width="2%" style="border-top:1px solid black" |
| width="14%" style="border-top:1px solid black" | <math>\operatorname{E1a.}</math>
| width="64%" style="border-top:1px solid black" | <math>f(x) ~=~ g(x)</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{E1a~:~V1a}</math>
|- style="height:24px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:56px"
|
| <math>\operatorname{E1b.}</math>
| <math>f(x) ~\Leftrightarrow~ g(x)</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{E1b~:~V1b}</math>
|- style="height:24px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:56px"
|
| <math>\operatorname{E1c.}</math>
| <math>\underline{((}~ f(x) ~,~ g(x) ~\underline{))}</math>
| style="border-left:1px solid black; text-align:center" |
<p><math>\operatorname{E1c~:~V1c}</math></p>
<p><math>\operatorname{E1c~:~$1a}</math></p>
|- style="height:24px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:56px"
|
| <math>\operatorname{E1d.}</math>
| <math>\underline{((}~ f ~,~ g ~\underline{))}^\$ (x)</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{E1d~:~$1b}</math>
|}
|}
|}