MyWikiBiz, Author Your Legacy — Saturday January 04, 2025
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, 17:48, 20 February 2009
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| '''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. |
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− | <pre>
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− | Value Rule 1
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− | If v, w C B
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− | then "v = w" is a sentence about <v, w> C B2,
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− | [v = w] is a proposition : B2 -> B,
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− | and the following are identical values in B:
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− | V1a. [ v = w ](v, w)
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− | V1b. [ v <=> w ](v, w)
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− | V1c. ((v , w))
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− | </pre>
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− | <br>
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− | <pre>
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− | Value Rule 1
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− |
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− | If v, w C B,
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− |
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− | then the following are equivalent:
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− |
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− | V1a. v = w.
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− |
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− | V1b. v <=> w.
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− | V1c. (( v , w )).
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− | </pre>
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− | <br>
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− | <pre>
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| A rule that allows one to turn equivalent sentences into identical propositions: | | A rule that allows one to turn equivalent sentences into identical propositions: |
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− | (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)
| + | |} |
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− | Value Rule 1
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− | | |
− | If v, w C B,
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− | then the following are identical values in B:
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− | V1a. [ v = w ]
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− | V1b. [ v <=> w ]
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− | V1c. (( v , w ))
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− | </pre>
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− | <br>
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− | <pre>
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− | Value Rule 1
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− | | |
− | If f, g : U -> B,
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− | and u C U
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− | then the following are identical values in B:
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− | V1a. [ f(u) = g(u) ]
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− | V1b. [ f(u) <=> g(u) ]
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− | V1c. (( f(u) , g(u) ))
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− | </pre> | |
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− | <br>
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− | <pre>
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− | Value Rule 1
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− | If f, g : U -> B,
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− | then the following are identical propositions on U:
| + | Compare: |
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− | 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> |
| + | |} |
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− | V1b. [ f <=> g ]
| + | '''Editing Note.''' The last draft that I can find has 5 variants of the next box, for "Value Rule 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: |
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− | V1c. (( f , g ))$
| + | * [http://mywikibiz.com/User:Jon_Awbrey/SCRATCHPAD#Value_Rule_1 Value Rule 1] |
− | </pre>
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| <br> | | <br> |