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Directory:Jon Awbrey/Papers/Syntactic Transformations (view source)
Revision as of 05:44, 9 February 2009
, 05:44, 9 February 2009→Derived Equivalence Relations: format definition box
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
Definition 9
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If R c OxSxI,
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then the following are identical subsets of IxS:
| width="20%" | <math>\operatorname{Definition~9}</math>
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D9a. RIS
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D9b. RSI^
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D9c. ConR^
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| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
D9d. Con(R)^
| width="80%" style="border-top:1px solid black" | <math>L ~\subseteq~ O \times S \times I</math>
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D9e. PrIS(R)
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| <math>\text{then}\!</math>
D9f. Conv(Con(R))
| <math>\text{the following are identical subsets of}~ I \times S \, :</math>
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D9g. {<i, s> C IxS : <o, s, i> C R for some o C O}
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:50px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{D9a.}</math>
| width="80%" style="border-top:1px solid black" | <math>L_{IS}\!</math>
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| <math>\operatorname{D9b.}</math>
| <math>\overset{\smile}{L_{SI}}</math>
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| <math>\operatorname{D9c.}</math>
| <math>\overset{\smile}{\operatorname{Con}^L}</math>
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| <math>\operatorname{D9d.}</math>
| <math>\overset{\smile}{\operatorname{Con}(L)}</math>
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| <math>\operatorname{D9e.}</math>
| <math>\operatorname{proj}_{IS}(L)</math>
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| <math>\operatorname{D9f.}</math>
| <math>\operatorname{Conv}(\operatorname{Con}(L))</math>
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| <math>\operatorname{D9g.}</math>
| <math>\{ (i, s) \in I \times S ~:~ (o, s, i) \in L ~\operatorname{for~some}~ o \in O \}</math>
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