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Revision as of 17:30, 2 February 2009
, 17:30, 2 February 2009→Rule 11
===Rule 11===
===Rule 11===
====Variant 1====
====Variant 1====
|- style="height:40px; text-align:center"
|- style="height:40px; text-align:center"
| width="80%" |
| width="80%" |
| width="20%" | <math>\text{Definition 5}\!</math>
| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~11}</math>
|}
|}
|-
|-
| 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="80%" style="border-top:1px solid black" | <math>Q ~\subseteq~ X</math>
| width="60%" style="border-top:1px solid black" | <math>Q ~\subseteq~ X</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black" |
|- style="height:40px"
|- style="height:40px"
|
|
| <math>\text{then}\!</math>
| <math>\text{then}\!</math>
| <math>\text{the following are identical propositions:}\!</math>
| <math>\text{the following are equivalent:}\!</math>
| style="border-left:1px solid black" |
|}
|}
|-
|-
|- 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{D5a.}</math>
| width="18%" style="border-top:1px solid black" | <math>\operatorname{R11a.}</math>
| width="80%" style="border-top:1px solid black" | <math>\upharpoonleft Q \upharpoonright</math>
| width="60%" style="border-top:1px solid black" | <math>Q ~=~ \{ x \in X ~:~ s \}</math>
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{R11a~:~R5a}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|
| <math>\operatorname{R11b.}</math>
| <math>\upharpoonleft Q \upharpoonright ~=~ \upharpoonleft \{ x \in X ~:~ s \} \upharpoonright</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R11b~:~R5e}</math>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|
| <math>\operatorname{R11c.}</math>
|
<math>\begin{array}{lcl}
\upharpoonleft Q \upharpoonright
& \subseteq &
X \times \underline\mathbb{B}
\\
\upharpoonleft Q \upharpoonright
& = &
\{ (x, y) \in X \times \underline\mathbb{B} ~:~ y = \, \downharpoonleft s \downharpoonright (x) \}
\end{array}</math>
| style="border-left:1px solid black; text-align:center" |
<p><math>\operatorname{R11c~:~\_\_?\_\_}</math></p>
<p><math>\operatorname{R11c~:~\_\_?\_\_}</math></p>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:60px"
|- style="height:60px"
|
|
| <math>\operatorname{D5b.}</math>
| <math>\operatorname{R11d.}</math>
|
|
<math>\begin{array}{ccccl}
<math>\begin{array}{ccccl}
\upharpoonleft Q \upharpoonright & : & X & \to & \underline\mathbb{B}
\\
\\
\upharpoonleft Q \upharpoonright & : & x & \mapsto & \downharpoonleft s \downharpoonright (x)
\end{array}</math>
\end{array}</math>
| style="border-left:1px solid black; text-align:center" |
<p><math>\operatorname{R11d~:~\_\_?\_\_}</math></p>
<p><math>\operatorname{R11d~:~\_\_?\_\_}</math></p>
|- style="height:20px"
|
|
|
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
|- style="height:40px"
|
| <math>\operatorname{R11e.}</math>
| <math>\upharpoonleft Q \upharpoonright ~=~ \downharpoonleft s \downharpoonright</math>
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R11e~:~\_\_?\_\_}</math>
|}
|}
|}
|}
