Changes

User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 16:28, 30 January 2009

318 bytes removed , 16:28, 30 January 2009

→‎Rule 3

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====Rule 3====

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=====Variant 1=====

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| style="border-left:1px solid black; text-align:center" | <math>\text{R3c : R2b}\!</math>

|}

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+

=====Variant 2=====

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{| align="center" cellpadding="0" cellspacing="0" width="100%"

|- style="height:48px; text-align:right"

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| width="98%" | <math>\text{~~Evaluation~~ Rule 1}\!</math>

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| width="98%" | <math>\text{Rule 3}\!</math>

| width="2%" |  

|}

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| width="2%" style="border-top:1px solid black" |  

| width="14%" style="border-top:1px solid black" | <math>\text{If}\!</math>

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| width="84%" style="border-top:1px solid black" | <math>~~f, g~~ ~:~ X ~~\to \underline\mathbb{B}~~</math>

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| width="84%" style="border-top:1px solid black" | <math>Q ~\subseteq~ X</math>

|- style="height:48px"

|  

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{| align="center" cellpadding="0" cellspacing="0" width="100%"

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|- style="height:~~56px~~"

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|- style="height:48px"

| width="2%" style="border-top:1px solid black" |  

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| width="14%" style="border-top:1px solid black" | <math>\operatorname{~~E1a~~.}</math>

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| width="14%" style="border-top:1px solid black" | <math>\operatorname{R3a.}</math>

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| width="64%" style="border-top:1px solid black" | <math>f(x) ~=~ ~~g(x)~~</math>

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| width="64%" style="border-top:1px solid black" | <math>x ~\in~ Q</math>

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| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{~~E1a~~~:~~~V1a~~}</math>

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| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{R3a~:~R1a}</math>

|- style="height:24px"

|  

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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>

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|- style="height:~~56px~~"

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|- style="height:48px"

|  

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| <math>\operatorname{~~E1b~~.}</math>

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| <math>\operatorname{R3b.}</math>

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~~| <math>f(x) ~\Leftrightarrow~ g(x)</math>~~

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| <math>\upharpoonleft Q \upharpoonright (x)</math>

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~~| style="border-left:1px solid black; text-align:center" | <math>\operatorname{E1b~:~V1b}</math>~~

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~~|- style="height:24px"~~

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~~|  ~~

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~~|  ~~

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~~|  ~~

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~~| style="border-left:1px solid black; text-align:center" | <math>::\!</math>~~

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~~|- style="height:56px"~~

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~~|  ~~

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| <math>\~~operatorname{E1c.}</math>~~

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~~| <math>~~\~~underline{((}~ f~~(x) ~~~,~ g(x) ~\underline{))}~~</math>

| style="border-left:1px solid black; text-align:center" |

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<math>\operatorname{~~E1c~~~:~~~V1c~~}</math>

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<math>\operatorname{R3b~:~R1b}</math>

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<math>\operatorname{~~E1c~~~:~~~$1a~~}</math>

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<math>\operatorname{R3b~:~R2a}</math>

|- style="height:24px"

|  

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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>

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|- style="height:~~56px~~"

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|- style="height:48px"

|  

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| <math>\operatorname{~~E1d~~.}</math>

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| <math>\operatorname{R3c.}</math>

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| <math>\~~underline{~~((}~ ~~f ~,~ g~~ ~\underline{))}~~^\$ (x)~~</math>

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| <math>\upharpoonleft Q \upharpoonright (x) ~=~ \underline{1}</math>

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| style="border-left:1px solid black; text-align:center" | <math>\operatorname{~~E1d~~~:~~~$1b~~}</math>

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| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R3c~:~R2b}</math>

|}

Jon Awbrey

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