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Step * 1 2 1 1 1 1 2 1 of Lemma partition-sum-bound-no-mc


1. I : Interval
2. icompact(I)
3. p : partition(I)
4. y : partition-choice(full-partition(I;p))
5. ||full-partition(I;p)|| = (||p|| + 2) ∈ ℤ
⊢ (last([left-endpoint(I) / (p @ [right-endpoint(I)])]) - left-endpoint(I)) = |I|
BY
{ (RWO "last-cons" 0 THENA Auto) }

1
1. I : Interval
2. icompact(I)
3. p : partition(I)
4. y : partition-choice(full-partition(I;p))
5. ||full-partition(I;p)|| = (||p|| + 2) ∈ ℤ
⊢ (if null(p @ [right-endpoint(I)]) then left-endpoint(I) else last(p @ [right-endpoint(I)]) fi  - left-endpoint(I))
= |I|

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Latex:

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Latex:

1.  I  :  Interval
2.  icompact(I)
3.  p  :  partition(I)
4.  y  :  partition-choice(full-partition(I;p))
5.  ||full-partition(I;p)||  =  (||p||  +  2)
\mvdash{}  (last([left-endpoint(I)  /  (p  @  [right-endpoint(I)])])  -  left-endpoint(I))  =  |I|


By

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Latex:
(RWO  "last-cons"  0  THENA  Auto)

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