Step
*
1
of Lemma
exp-convex
1. a : ℕ
2. b : ℕ
3. c : ℕ
4. n : ℤ
5. 0 < n
6. |a - b| ≤ c supposing |a^n - b^n| ≤ c^n
7. |(a * a^n) - b * b^n| ≤ (c * c^n)
⊢ |a - b| ≤ c
BY
{ xxx(SupposeNot THEN D -3 THEN Auto THEN SupposeNot)xxx }
1
1. a : ℕ
2. b : ℕ
3. c : ℕ
4. n : ℤ
5. 0 < n
6. |(a * a^n) - b * b^n| ≤ (c * c^n)
7. ¬(|a - b| ≤ c)
8. ¬(|a^n - b^n| ≤ c^n)
⊢ |a^n - b^n| ≤ c^n
Latex:
Latex:
1. a : \mBbbN{}
2. b : \mBbbN{}
3. c : \mBbbN{}
4. n : \mBbbZ{}
5. 0 < n
6. |a - b| \mleq{} c supposing |a\^{}n - b\^{}n| \mleq{} c\^{}n
7. |(a * a\^{}n) - b * b\^{}n| \mleq{} (c * c\^{}n)
\mvdash{} |a - b| \mleq{} c
By
Latex:
xxx(SupposeNot THEN D -3 THEN Auto THEN SupposeNot)xxx
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