Step
*
1
1
of Lemma
not-not-all-int_seg-xmiddle
1. d : ℤ
2. 0 < d
3. ∀a:ℤ. ∀P:{a..a + (d - 1)-} ⟶ ℙ. (¬¬(∀i:{a..a + (d - 1)-}. (P[i] ∨ (¬P[i]))))
4. a : ℤ
5. P : {a..a + d-} ⟶ ℙ
⊢ ¬¬(∀i:{a..a + d-}. (P[i] ∨ (¬P[i])))
BY
{ ((Assert ¬¬(∀i:{a..a + (d - 1)-}. (P[i] ∨ (¬P[i]))) BY
Auto)
THEN (Assert ¬¬(P[a + (d - 1)] ∨ (¬P[a + (d - 1)])) BY
(BLemma `not-not-1-xmiddle` THEN Auto))
) }
1
1. d : ℤ
2. 0 < d
3. ∀a:ℤ. ∀P:{a..a + (d - 1)-} ⟶ ℙ. (¬¬(∀i:{a..a + (d - 1)-}. (P[i] ∨ (¬P[i]))))
4. a : ℤ
5. P : {a..a + d-} ⟶ ℙ
6. ¬¬(∀i:{a..a + (d - 1)-}. (P[i] ∨ (¬P[i])))
7. ¬¬(P[a + (d - 1)] ∨ (¬P[a + (d - 1)]))
⊢ ¬¬(∀i:{a..a + d-}. (P[i] ∨ (¬P[i])))
Latex:
Latex:
1. d : \mBbbZ{}
2. 0 < d
3. \mforall{}a:\mBbbZ{}. \mforall{}P:\{a..a + (d - 1)\msupminus{}\} {}\mrightarrow{} \mBbbP{}. (\mneg{}\mneg{}(\mforall{}i:\{a..a + (d - 1)\msupminus{}\}. (P[i] \mvee{} (\mneg{}P[i]))))
4. a : \mBbbZ{}
5. P : \{a..a + d\msupminus{}\} {}\mrightarrow{} \mBbbP{}
\mvdash{} \mneg{}\mneg{}(\mforall{}i:\{a..a + d\msupminus{}\}. (P[i] \mvee{} (\mneg{}P[i])))
By
Latex:
((Assert \mneg{}\mneg{}(\mforall{}i:\{a..a + (d - 1)\msupminus{}\}. (P[i] \mvee{} (\mneg{}P[i]))) BY
Auto)
THEN (Assert \mneg{}\mneg{}(P[a + (d - 1)] \mvee{} (\mneg{}P[a + (d - 1)])) BY
(BLemma `not-not-1-xmiddle` THEN Auto))
)
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