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Step * 2 1 2 of Lemma es-prior-interface-cases-sq


1. [Info] : Type
2. X : EClass(Top)@i'
3. es : EO+(Info)@i'
4. e : E@i
5. ↑e ∈b prior(X)
6. ¬↑first(e)
7. ¬↑first(e)
8. ¬↑pred(e) ∈b X
⊢ prior(X)(e) ~ prior(X)(pred(e))
BY
{ (RepUR ``es-prior-interface local-pred-class eclass-val`` 0
   THEN RW (AddrC [1] (RecUnfoldC `es-local-pred`)) 0
   THEN Reduce 0
   THEN RepeatFor 2 (AutoSplit))⋅ }

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Latex:

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Latex:

1.  [Info]  :  Type
2.  X  :  EClass(Top)@i'
3.  es  :  EO+(Info)@i'
4.  e  :  E@i
5.  \muparrow{}e  \mmember{}\msubb{}  prior(X)
6.  \mneg{}\muparrow{}first(e)
7.  \mneg{}\muparrow{}first(e)
8.  \mneg{}\muparrow{}pred(e)  \mmember{}\msubb{}  X
\mvdash{}  prior(X)(e)  \msim{}  prior(X)(pred(e))


By

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Latex:
(RepUR  ``es-prior-interface  local-pred-class  eclass-val``  0
  THEN  RW  (AddrC  [1]  (RecUnfoldC  `es-local-pred`))  0
  THEN  Reduce  0
  THEN  RepeatFor  2  (AutoSplit))\mcdot{}

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