MHB Solving 10-14 Equivalence Arguments: R to neg(w v s)

chelseajjc95
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10.) neg[r\implies neg(w v s)] 13.) r\implies neg(w v s)
----------------------------- R
R^(wvs) --------------------------
neg(w v s)
11.) r\implies neg(w v s)
w v s 14.) r\implies neg(w v s)
------------------------- -------------------------
neg R (w v s)\implies neg r

12.) R
---------------
r v (w v s)
 
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Your post is hard to read. Please do the following to improve it.

  1. Use formula editor to typeset formulas.
  2. The editor does not support alignment in text (unless you use tags such as [m]code[/m] and [m]m[/m]), so you should not rely on it.
  3. Explain the meaning of horizontal lines.
  4. Write the problems in one column. It seems that the text was copied from a two-column PDF.
  5. Write the problem statement in the post body rather than the post title, following https://mathhelpboards.com/rules/.
  6. Show your attempts at solving the problems, or describe the difficulty you are having, following rule 11.
  7. Break the thread into two or three so that each one has one or two problems, foloowing rule 8.
  8. Explain the missing problem 14.
 
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Thread 'Detail of Diagonalization Lemma'
The following is more or less taken from page 6 of C. Smorynski's "Self-Reference and Modal Logic". (Springer, 1985) (I couldn't get raised brackets to indicate codification (Gödel numbering), so I use a box. The overline is assigning a name. The detail I would like clarification on is in the second step in the last line, where we have an m-overlined, and we substitute the expression for m. Are we saying that the name of a coded term is the same as the coded term? Thanks in advance.

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