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Step * of Lemma ni-selector-property

∀p:ℕ∞ ⟶ 𝔹. (∃x:ℕ∞. p x = ff ⇐⇒ p ni-selector(p) = ff)
BY
{ (Auto THEN SimpleBoolCase ⌜p ni-selector(p)⌝⋅ THEN Auto) }

1
1. p : ℕ∞ ⟶ 𝔹
2. ∃x:ℕ∞. p x = ff
3. p ni-selector(p) = tt
⊢ tt = ff

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Latex:

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Latex:
\mforall{}p:\mBbbN{}\minfty{}  {}\mrightarrow{}  \mBbbB{}.  (\mexists{}x:\mBbbN{}\minfty{}.  p  x  =  ff  \mLeftarrow{}{}\mRightarrow{}  p  ni-selector(p)  =  ff)


By

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Latex:
(Auto  THEN  SimpleBoolCase  \mkleeneopen{}p  ni-selector(p)\mkleeneclose{}\mcdot{}  THEN  Auto)

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