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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 22:35, 25 January 2009
, 22:35, 25 January 2009→Proof Schemata
R3c. {X}(u) = 1. :R2b
R3c. {X}(u) = 1. :R2b
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{| align="center" cellpadding="8" cellspacing="0" style="border-top:1px solid black; border-bottom:1px solid black" width="90%"
|-
| align="left" style="border-left:1px solid black" width="20%" |
| align="left" style="border-right:1px solid black" width="60%" |
| align="center" style="border-right:1px solid black" width="20%" | <math>\text{Rule 3}\!</math>
|-
| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{If}\!</math>
| style="border-top:1px solid black; border-right:1px solid black" | <math>Q \subseteq X</math>
| style="border-top:1px solid black; border-right:1px solid black" |
|-
| style="border-left:1px solid black" | <math>\text{and}\!</math>
| style="border-right:1px solid black" | <math>x \in X</math>
| style="border-right:1px solid black" |
|-
| style="border-left:1px solid black" | <math>\text{then}\!</math>
| style="border-right:1px solid black" | <math>\text{the following are equivalent:}\!</math>
| style="border-right:1px solid black" |
|-
| align="left" style="border-left:1px solid black; border-top:1px solid black" |
<math>\text{R3a.}\!</math>
| align="left" style="border-top:1px solid black; border-right:1px solid black" |
<math>x \in Q</math>
| align="center" style="border-top:1px solid black; border-right:1px solid black" |
<math>\text{R3a : R1a}\!</math>
|-
| align="left" style="border-left:1px solid black" |
| align="left" style="border-right:1px solid black" |
| align="center" style="border-right:1px solid black" | <math>::\!</math>
|-
| align="left" style="border-left:1px solid black" |
<math>\text{R3b.}\!</math>
| align="left" style="border-right:1px solid black" |
<math>\upharpoonleft Q \upharpoonright (x)</math>
| align="center" style="border-right:1px solid black" |
<p><math>\text{R3b : R1b}\!</math></p>
<p><math>\text{R3b : R2a}\!</math></p>
|-
| align="left" style="border-left:1px solid black" |
| align="left" style="border-right:1px solid black" |
| align="center" style="border-right:1px solid black" | <math>::\!</math>
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| align="left" style="border-left:1px solid black" |
<math>\text{R3c.}\!</math>
| align="left" style="border-right:1px solid black" |
<math>\upharpoonleft Q \upharpoonright (x) = \underline{1}</math>
| align="center" style="border-right:1px solid black" |
<math>\text{R3c : R2b}\!</math>
|}
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