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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 15:48, 1 February 2009
, 15:48, 1 February 2009→Rule 7
|- style="height:40px; text-align:center"
|- style="height:40px; text-align:center"
| width="80%" |
| width="80%" |
| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~6}</math>
| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~7}</math>
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| width="2%" style="border-top:1px solid black" |
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="60%" style="border-top:1px solid black" | <math>f, g ~:~ X \to Y</math>
| width="60%" style="border-top:1px solid black" | <math>p, q ~:~ X \to \underline\mathbb{B}</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black" |
| width="20%" style="border-top:1px solid black; border-left:1px solid black" |
|- style="height:40px"
|- style="height:40px"
|- style="height:40px"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="2%" style="border-top:1px solid black" |
| width="18%" style="border-top:1px solid black" | <math>\operatorname{R6a.}</math>
| width="18%" style="border-top:1px solid black" | <math>\operatorname{R7a.}</math>
| width="60%" style="border-top:1px solid black" | <math>f ~=~ g</math>
| width="60%" style="border-top:1px solid black" | <math>p ~=~ q</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{R6a~:~D3a}</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{R7a~:~R6a}</math>
|- style="height:20px"
|- style="height:20px"
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|- style="height:60px"
|- style="height:60px"
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| <math>\operatorname{R6b.}</math>
| <math>\operatorname{R7b.}</math>
| <math>\overset{X}{\underset{x}{\forall}}~ (f(x) ~=~ g(x))</math>
| <math>\overset{X}{\underset{x}{\forall}}~ (p(x) ~=~ q(x))</math>
| style="border-left:1px solid black; text-align:center" |
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R7b~:~R6b}</math>
|- style="height:20px"
|- style="height:20px"
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| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|- style="height:60px"
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| <math>\operatorname{R6c.}</math>
| <math>\operatorname{R7c.}</math>
| <math>\operatorname{Conj_x^X}~ (f(x) ~=~ g(x))</math>
| <math>\operatorname{Conj_x^X}~ (p(x) ~=~ q(x))</math>
| style="border-left:1px solid black; text-align:center" |<math>\operatorname{R6c~:~D6e}</math>
| style="border-left:1px solid black; text-align:center" |
<p><math>\operatorname{R7c~:~R6c}</math></p>
<p><math>\operatorname{R7c~:~P1a}</math></p>
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