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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 19:30, 25 January 2009
, 19:30, 25 January 2009→Proof Schemata
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<pre>
{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black; border-bottom:1px solid black" width="90%"
Rule 1
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| align="left" style="border-left:1px solid black" width="20%" |
| align="left" width="60%" |
| align="right" style="border-right:1px solid black" width="20%" | <math>\text{Rule 1}\!</math>
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| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{If}\!</math>
| style="border-top:1px solid black" | <math>Q \subseteq X</math>
| style="border-right:1px solid black; border-top:1px solid black" |
|-
| style="border-left:1px solid black" | <math>\text{then}\!</math>
| <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}</math>
| style="border-right:1px solid black" |
|-
| style="border-left:1px solid black" | <math>\text{and if}\!</math>
| <math>x \in X</math>
| style="border-right:1px solid black" |
|-
| style="border-left:1px solid black" | <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
| style="border-right:1px solid black" |
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| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{R1a.}\!</math>
| style="border-top:1px solid black" | <math>x \in Q</math>
| style="border-right:1px solid black; border-top:1px solid black" |
|-
| style="border-left:1px solid black" | <math>\text{R2a.}\!</math>
| <math>\upharpoonleft Q \upharpoonright (x)</math>
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|}
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then {X} : U -> B,
{| align="center" cellpadding="12" 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" width="60%" |
| align="right" style="border-right:1px solid black" width="20%" | <math>\text{Rule 1}\!</math>
|-
| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{If}\!</math>
| style="border-top:1px solid black" | <math>Q \subseteq X,</math>
| style="border-right:1px solid black; border-top:1px solid black" |
|-
| style="border-left:1px solid black" | <math>\text{then}\!</math>
| <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B},</math>
| style="border-right:1px solid black" |
|-
| style="border-left:1px solid black" | <math>\text{and if}\!</math>
| <math>x \in X,</math>
| style="border-right:1px solid black" |
|-
| style="border-left:1px solid black" | <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
| style="border-right:1px solid black" |
|-
| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{R1a.}\!</math>
| style="border-top:1px solid black" | <math>x \in Q.</math>
| style="border-right:1px solid black; border-top:1px solid black" |
|-
| style="border-left:1px solid black" | <math>\text{R2a.}\!</math>
| <math>\upharpoonleft Q \upharpoonright (x).</math>
| style="border-right:1px solid black" |
|}
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</pre>