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721 bytes removed , 14:58, 12 September 2010

→‎1.3.12.1. Syntactic Transformation Rules: del merged text

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=====1.3.12.1. Syntactic Transformation Rules=====

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~~======Value Rules======~~

<pre>

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E1d. (( f , g ))$(u). :$1b

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~~</pre>~~

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~~======Facts======~~

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~~Applying Rule 9, Rule 8, and the Logical Rules to the special case where S <=> (X = Y), one obtains the following general fact.~~

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~~<pre>~~

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~~Fact 1~~

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~~If X,Y c U,~~

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~~then the following are equivalent:~~

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~~F1a. S <=> X = Y. :R9a~~

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::

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~~F1b. S <=> {X} = {Y}. :R9b~~

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::

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~~F1c. S <=> {X}(u) = {Y}(u), for all u C U. :R9c~~

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::

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~~F1d. S <=> ConjUu ( {X}(u) = {Y}(u) ). :R9d~~

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~~:R8a~~

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::

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~~F1e. [S] = [ ConjUu ( {X}(u) = {Y}(u) ) ]. :R8b~~

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~~:???~~

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::

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~~F1f. [S] = ConjUu [ {X}(u) = {Y}(u) ]. :???~~

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::

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~~F1g. [S] = ConjUu (( {X}(u) , {Y}(u) )). :$1a~~

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::

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~~F1h. [S] = ConjUu (( {X} , {Y} ))$(u). :$1b~~

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~~///~~

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~~{u C U : (f, g)$(u)}~~

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~~= {u C U : (f(u), g(u))}~~

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~~= {u C~~

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~~///~~

</pre>

Jon Awbrey

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Revision as of 14:58, 12 September 2010