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Directory:Jon Awbrey/Papers/Syntactic Transformations (view source)
Revision as of 04:48, 3 February 2009
, 04:48, 3 February 2009→Syntactic Transformation Rules: format rule 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%"
Rule 6
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
If f, g : U -> V,
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then the following are equivalent:
| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~6}</math>
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R6a. f = g. :D3a
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R6b. f(u) = g(u), for all u C U. :D3b
{| align="center" cellpadding="0" cellspacing="0" width="100%"
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R6c. ConjUu (f(u) = g(u)). :D6e
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
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| width="60%" style="border-top:1px solid black" | <math>f, g ~:~ X \to Y</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black" |
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| <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{R6a.}</math>
| width="60%" style="border-top:1px solid black" | <math>f ~=~ g</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{R6a~:~D3a}</math>
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| <math>\operatorname{R6b.}</math>
| <math>\overset{X}{\underset{x}{\forall}}~ (f(x) ~=~ g(x))</math>
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<p><math>\operatorname{R6b~:~D3b}</math></p>
<p><math>\operatorname{R6b~:~D6a}</math></p>
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
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| <math>\operatorname{R6c.}</math>
| <math>\operatorname{Conj_x^X}~ (f(x) ~=~ g(x))</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R6c~:~D6e}</math>
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