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Step * 1 1 of Lemma not-all-int_seg


1. i : ℤ
2. j : ℤ
3. [P] : {i..j-} ⟶ ℙ
4. ∀x:{i..j-}. Dec(P[x])
5. ¬(∀x:{i..j-}. P[x])
6. i < j
⊢ ∃x:{i..j-}. (¬P[x])
BY
{ (InstLemma `not-all-int_seg2` [⌜i⌝;⌜j⌝;⌜P⌝;⌜λ2x.¬P[x]⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  i  :  \mBbbZ{}
2.  j  :  \mBbbZ{}
3.  [P]  :  \{i..j\msupminus{}\}  {}\mrightarrow{}  \mBbbP{}
4.  \mforall{}x:\{i..j\msupminus{}\}.  Dec(P[x])
5.  \mneg{}(\mforall{}x:\{i..j\msupminus{}\}.  P[x])
6.  i  <  j
\mvdash{}  \mexists{}x:\{i..j\msupminus{}\}.  (\mneg{}P[x])


By

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Latex:
(InstLemma  `not-all-int\_seg2`  [\mkleeneopen{}i\mkleeneclose{};\mkleeneopen{}j\mkleeneclose{};\mkleeneopen{}P\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.\mneg{}P[x]\mkleeneclose{}]\mcdot{}  THEN  Auto)

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