Step
*
2
1
1
of Lemma
q-not-limit-zero-diverges-2
1. f : ℕ+ ⟶ ℚ
2. ∀n:ℕ+. (0 ≤ f[n])
3. ∃q:ℚ. (0 < q ∧ (∀n:ℕ. ∃m:ℕ. (n < m ∧ (q ≤ f[m]))))
4. B : ℚ
5. n : ℕ
6. B ≤ Σ0 ≤ i < n. if (i =z 0) then 0 else f[i] fi
7. n = 0 ∈ ℤ
⊢ Σ1 ≤ i < 0. f[i] = Σ0 ≤ i < 0. if (i =z 0) then 0 else f[i] fi ∈ ℚ
BY
{ xxx((RW (AddrC [3] (LemmaC `sum_unroll_base_q`)) 0) THENA Auto)xxx }
1
1. f : ℕ+ ⟶ ℚ
2. ∀n:ℕ+. (0 ≤ f[n])
3. ∃q:ℚ. (0 < q ∧ (∀n:ℕ. ∃m:ℕ. (n < m ∧ (q ≤ f[m]))))
4. B : ℚ
5. n : ℕ
6. B ≤ Σ0 ≤ i < n. if (i =z 0) then 0 else f[i] fi
7. n = 0 ∈ ℤ
⊢ Σ1 ≤ i < 0. f[i] = 0 ∈ ℚ
Latex:
Latex:
1. f : \mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbQ{}
2. \mforall{}n:\mBbbN{}\msupplus{}. (0 \mleq{} f[n])
3. \mexists{}q:\mBbbQ{}. (0 < q \mwedge{} (\mforall{}n:\mBbbN{}. \mexists{}m:\mBbbN{}. (n < m \mwedge{} (q \mleq{} f[m]))))
4. B : \mBbbQ{}
5. n : \mBbbN{}
6. B \mleq{} \mSigma{}0 \mleq{} i < n. if (i =\msubz{} 0) then 0 else f[i] fi
7. n = 0
\mvdash{} \mSigma{}1 \mleq{} i < 0. f[i] = \mSigma{}0 \mleq{} i < 0. if (i =\msubz{} 0) then 0 else f[i] fi
By
Latex:
xxx((RW (AddrC [3] (LemmaC `sum\_unroll\_base\_q`)) 0) THENA Auto)xxx
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