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Revision as of 12:40, 27 January 2009
, 12:40, 27 January 2009→Proof Schemata
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<pre>
{| align="center" cellpadding="2" 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%"
Rule 4
|- style="height:40px"
| width="2%" |
| width="18%" |
| width="60%" |
| align="center" width="20%" | <math>\text{Rule 4}\!</math>
|- style="height:40px"
| style="border-top:1px solid black" |
| style="border-top:1px solid black" | <math>\text{If}\!</math>
| style="border-top:1px solid black" | <math>Q \subseteq X ~\text{is fixed}</math>
| style="border-top:1px solid black" |
|- style="height:40px"
|
| <math>\text{and}\!</math>
| <math>x \in X ~\text{is varied}</math>
|
|- style="height:40px"
|
| <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
|
|- style="height:40px"
| style="border-top:1px solid black" |
| style="border-top:1px solid black" | <math>\text{R4a.}\!</math>
| style="border-top:1px solid black" | <math>x \in Q</math>
| style="border-top:1px solid black" |
|- style="height:40px"
|
| <math>\text{R4b.}\!</math>
| <math>\downharpoonleft x \in Q \downharpoonright</math>
|
|- style="height:40px"
|
| <math>\text{R4c.}\!</math>
| <math>\downharpoonleft x \in Q \downharpoonright (x)</math>
|
|- style="height:40px"
|
| <math>\text{R4d.}\!</math>
| <math>\upharpoonleft Q \upharpoonright (x)</math>
|
|- style="height:40px"
|
| <math>\text{R4e.}\!</math>
| <math>\upharpoonleft Q \upharpoonright (x) = \underline{1}</math>
|
|}
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