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Step * 1 2 1 1 1 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
⊢ Σ{full-partition(I;p)[i + 1] - full-partition(I;p)[i] | 0≤i≤||full-partition(I;p)|| - 2} = |I|
BY
{ (RWO "frs-non-dec-sum" 0 THEN Auto) }

1
.....rewrite subgoal..... 
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
⊢ frs-non-dec(full-partition(I;p))

2
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|

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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{}  \mSigma{}\{full-partition(I;p)[i  +  1]  -  full-partition(I;p)[i]  |  0\mleq{}i\mleq{}||full-partition(I;p)||  -  2\}  =  |I|


By

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Latex:
(RWO  "frs-non-dec-sum"  0  THEN  Auto)

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