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Step * 1 2 1 1 1 1 2 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(full-partition(I;p)) - full-partition(I;p)[0]) = |I|
BY
{ (Unfold `full-partition` 0 THEN Reduce 0) }

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
⊢ (last([left-endpoint(I) / (p @ [right-endpoint(I)])]) - 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(full-partition(I;p))  -  full-partition(I;p)[0])  =  |I|


By

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Latex:
(Unfold  `full-partition`  0  THEN  Reduce  0)

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