Step
*
1
1
of Lemma
trivial-Taylor-approx
1. I : Interval
2. n : ℕ
3. F : ℕn + 1 ⟶ I ⟶ℝ
4. a : {x:ℝ| x ∈ I}
5. b : {x:ℝ| x ∈ I}
6. a = b
7. k : ℤ
8. (0 + 1) ≤ k
9. k ≤ n
10. v : ℝ
11. (F[k;a]/r((k)!)) = v ∈ ℝ
⊢ (v * b - a^k) = r0
BY
{ (RWO "6" 0 THEN Auto) }
1
1. I : Interval
2. n : ℕ
3. F : ℕn + 1 ⟶ I ⟶ℝ
4. a : {x:ℝ| x ∈ I}
5. b : {x:ℝ| x ∈ I}
6. a = b
7. k : ℤ
8. (0 + 1) ≤ k
9. k ≤ n
10. v : ℝ
11. (F[k;a]/r((k)!)) = v ∈ ℝ
⊢ (v * b - b^k) = r0
Latex:
Latex:
1. I : Interval
2. n : \mBbbN{}
3. F : \mBbbN{}n + 1 {}\mrightarrow{} I {}\mrightarrow{}\mBbbR{}
4. a : \{x:\mBbbR{}| x \mmember{} I\}
5. b : \{x:\mBbbR{}| x \mmember{} I\}
6. a = b
7. k : \mBbbZ{}
8. (0 + 1) \mleq{} k
9. k \mleq{} n
10. v : \mBbbR{}
11. (F[k;a]/r((k)!)) = v
\mvdash{} (v * b - a\^{}k) = r0
By
Latex:
(RWO "6" 0 THEN Auto)
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