Step
*
1
1
1
of Lemma
nearby-partition-choice
1. I : Interval@i
2. icompact(I)
3. p : partition(I)@i
4. q : partition(I)@i
5. e : {e:ℝ| r0 < e} @i
6. ||p|| = ||q|| ∈ ℤ
7. ∀i:ℕ||p||. (|p[i] - q[i]| ≤ e)
8. x : partition-choice(full-partition(I;p))@i
⊢ (||p @ [right-endpoint(I)]|| + 1) = (||q @ [right-endpoint(I)]|| + 1) ∈ ℤ
BY
{ Auto }
Latex:
Latex:
1. I : Interval@i
2. icompact(I)
3. p : partition(I)@i
4. q : partition(I)@i
5. e : \{e:\mBbbR{}| r0 < e\} @i
6. ||p|| = ||q||
7. \mforall{}i:\mBbbN{}||p||. (|p[i] - q[i]| \mleq{} e)
8. x : partition-choice(full-partition(I;p))@i
\mvdash{} (||p @ [right-endpoint(I)]|| + 1) = (||q @ [right-endpoint(I)]|| + 1)
By
Latex:
Auto
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