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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 12:16, 26 January 2009
, 12:16, 26 January 2009→Proof Schemata
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===Proof Schemata===
===Proof Schemata : Old Versions===
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<math>\text{R3c : R2b}\!</math>
<math>\text{R3c : R2b}\!</math>
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===Proof Schemata : New Versions===
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| align="right" style="border-right:1px solid black" width="20%" | <math>\text{Definition 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>
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| style="border-left:1px solid black" | <math>\text{then}\!</math>
| <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}</math>
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| style="border-left:1px solid black" | <math>\text{such that:}\!</math>
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| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{D1a.}\!</math>
| style="border-top:1px solid black" | <math>\upharpoonleft Q \upharpoonright (x) ~\Leftrightarrow~ x \in Q</math>
| align="right" style="border-right:1px solid black; border-top:1px solid black" | <math>\forall x \in X</math>
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{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black; border-bottom:1px solid black" width="90%"
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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>
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| style="border-left:1px solid black" | <math>\text{then}\!</math>
| <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}</math>
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| style="border-left:1px solid black" | <math>\text{and if}\!</math>
| <math>x \in X</math>
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| style="border-left:1px solid black" | <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
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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>
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| style="border-left:1px solid black" | <math>\text{R1b.}\!</math>
| <math>\upharpoonleft Q \upharpoonright (x)</math>
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{| align="center" cellpadding="12" cellspacing="0" style="border-top:1px solid black; border-bottom:1px solid black" width="90%"
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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 2}\!</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>f : X \to \underline\mathbb{B}</math>
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| style="border-left:1px solid black" | <math>\text{and}\!</math>
| <math>x \in X</math>
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| style="border-left:1px solid black" | <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
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| style="border-left:1px solid black; border-top:1px solid black" | <math>\text{R2a.}\!</math>
| style="border-top:1px solid black" | <math>f(x)\!</math>
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| style="border-left:1px solid black" | <math>\text{R2b.}\!</math>
| <math>f(x) = \underline{1}</math>
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