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Step * 1 of Lemma compact-nat-inf


1. p : ℕ∞ ⟶ 𝔹
2. p ni-selector(p) = tt
⊢ (∃x:ℕ∞. p x = ff) ∨ (∀x:ℕ∞. p x = tt)
BY
{ ((Assert ¬(∃x:ℕ∞. p x = ff) BY
          (RWO "ni-selector-property" 0 THEN Auto))
   THEN OrRight
   THEN Auto
   THEN SimpleBoolCase ⌜p x⌝⋅
   THEN Auto) }

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Latex:

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Latex:

1.  p  :  \mBbbN{}\minfty{}  {}\mrightarrow{}  \mBbbB{}
2.  p  ni-selector(p)  =  tt
\mvdash{}  (\mexists{}x:\mBbbN{}\minfty{}.  p  x  =  ff)  \mvee{}  (\mforall{}x:\mBbbN{}\minfty{}.  p  x  =  tt)


By

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Latex:
((Assert  \mneg{}(\mexists{}x:\mBbbN{}\minfty{}.  p  x  =  ff)  BY
                (RWO  "ni-selector-property"  0  THEN  Auto))
  THEN  OrRight
  THEN  Auto
  THEN  SimpleBoolCase  \mkleeneopen{}p  x\mkleeneclose{}\mcdot{}
  THEN  Auto)

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