Changes

→‎Syntactic Transformation Rules: editing note + cleanup
Line 432: Line 432:  
'''Editing Note.'''  Need a transition here.  Give a brief description of the Tables of Translation Rules that have now been moved to the Appendices, and then move on to the rest of the Definitions and Proof Schemata.
 
'''Editing Note.'''  Need a transition here.  Give a brief description of the Tables of Translation Rules that have now been moved to the Appendices, and then move on to the rest of the Definitions and Proof Schemata.
   −
<br>
  −
  −
<pre>
  −
Value Rule 1
  −
  −
If v, w C B
  −
  −
then "v = w" is a sentence about <v, w> C B2,
  −
  −
[v = w] is a proposition : B2 -> B,
  −
  −
and the following are identical values in B:
  −
  −
V1a. [ v = w ](v, w)
  −
  −
V1b. [ v <=> w ](v, w)
  −
  −
V1c. ((v , w))
  −
</pre>
  −
  −
<br>
  −
  −
<pre>
  −
Value Rule 1
  −
  −
If v, w C B,
  −
  −
then the following are equivalent:
  −
  −
V1a. v = w.
  −
  −
V1b. v <=> w.
  −
  −
V1c. (( v , w )).
  −
</pre>
  −
  −
<br>
  −
  −
<pre>
   
A rule that allows one to turn equivalent sentences into identical propositions:
 
A rule that allows one to turn equivalent sentences into identical propositions:
   −
(S <=> T) <=> ([S] = [T])
+
{| align="center" cellpadding="8" width="90%"
 
+
| <math>(S \Leftrightarrow T) \quad \Leftrightarrow \quad (\downharpoonleft S \downharpoonright = \downharpoonleft T \downharpoonright)</math>
Consider [ v = w ](v, w) and [ v(u) = w(u) ](u)
+
|}
 
  −
Value Rule 1
  −
 
  −
If v, w C B,
  −
 
  −
then the following are identical values in B:
  −
 
  −
V1a. [ v = w ]
  −
 
  −
V1b. [ v <=> w ]
  −
 
  −
V1c. (( v , w ))
  −
</pre>
  −
 
  −
<br>
  −
 
  −
<pre>
  −
Value Rule 1
  −
 
  −
If f, g : U -> B,
  −
 
  −
and u C U
  −
 
  −
then the following are identical values in B:
  −
 
  −
V1a. [ f(u) = g(u) ]
  −
 
  −
V1b. [ f(u) <=> g(u) ]
  −
 
  −
V1c. (( f(u) , g(u) ))
  −
</pre>
  −
 
  −
<br>
  −
 
  −
<pre>
  −
Value Rule 1
  −
 
  −
If f, g : U -> B,
     −
then the following are identical propositions on U:
+
Compare:
   −
V1a. [ f = g ]
+
{| align="center" cellpadding="8" width="90%"
 +
| <math>\downharpoonleft v = w \downharpoonright (v, w)</math>
 +
|-
 +
| <math>\downharpoonleft v(u) = w(u) \downharpoonright (u)</math>
 +
|}
   −
V1b. [ f <=> g ]
+
'''Editing Note.'''  The last draft that I can find has 5 variants of the next box, for "Value&nbsp;Rule&nbsp;1", and I can't right off which one I meant to use.  Until I can get back to this, here is a link to the collection of variants:
   −
V1c. (( f , g ))$
+
* [http://mywikibiz.com/User:Jon_Awbrey/SCRATCHPAD#Value_Rule_1 Value Rule 1]
</pre>
      
<br>
 
<br>
12,080

edits