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Step * 1 2 of Lemma nearby-partition-mesh


1. I : Interval
2. icompact(I)
3. e : {e:ℝ| r0 < e} 
4. p : partition(I)
5. p' : partition(I)
6. nearby-partitions((e/r(2));p;p')
7. nearby-partitions((e/r(2));full-partition(I;p);full-partition(I;p'))
⊢ frs-mesh(full-partition(I;p')) ≤ (frs-mesh(full-partition(I;p)) + e)
BY
{ (FLemma `nearby-frs-mesh` [-1] THENA Auto) }

1
.....wf..... 
1. I : Interval
2. icompact(I)
3. e : {e:ℝ| r0 < e} 
4. p : partition(I)
5. p' : partition(I)
6. nearby-partitions((e/r(2));p;p')
7. nearby-partitions((e/r(2));full-partition(I;p);full-partition(I;p'))
⊢ (e/r(2)) ∈ {e:ℝ| r0 < e} 

2
1. I : Interval
2. icompact(I)
3. e : {e:ℝ| r0 < e} 
4. p : partition(I)
5. p' : partition(I)
6. nearby-partitions((e/r(2));p;p')
7. nearby-partitions((e/r(2));full-partition(I;p);full-partition(I;p'))
8. frs-mesh(full-partition(I;p')) ≤ (frs-mesh(full-partition(I;p)) + (r(2) * (e/r(2))))
⊢ frs-mesh(full-partition(I;p')) ≤ (frs-mesh(full-partition(I;p)) + e)

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Latex:

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Latex:

1.  I  :  Interval
2.  icompact(I)
3.  e  :  \{e:\mBbbR{}|  r0  <  e\} 
4.  p  :  partition(I)
5.  p'  :  partition(I)
6.  nearby-partitions((e/r(2));p;p')
7.  nearby-partitions((e/r(2));full-partition(I;p);full-partition(I;p'))
\mvdash{}  frs-mesh(full-partition(I;p'))  \mleq{}  (frs-mesh(full-partition(I;p))  +  e)


By

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Latex:
(FLemma  `nearby-frs-mesh`  [-1]  THENA  Auto)

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