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Step * 1 3 of Lemma rat-sub-div-diameter


1. k : ℕ
2. n : ℕ
3. K : n-dim-complex
4. 0 < ||K||
5. 0 < ||(K)'||
6. rmaximum(0;||(K)'|| - 1;i.rat-cube-diameter(k;(K)'[i])) ≤ ((r1/r(2))
* rmaximum(0;||K|| - 1;i.rat-cube-diameter(k;K[i])))
⊢ rmaximum(0;||(K)'|| - 1;i.rat-cube-diameter(k;(K)'[i])) ≤ ((r1/r(2))
* rmaximum(0;||K|| - 1;i.rat-cube-diameter(k;K[i])))
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Latex:

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Latex:

1.  k  :  \mBbbN{}
2.  n  :  \mBbbN{}
3.  K  :  n-dim-complex
4.  0  <  ||K||
5.  0  <  ||(K)'||
6.  rmaximum(0;||(K)'||  -  1;i.rat-cube-diameter(k;(K)'[i]))  \mleq{}  ((r1/r(2))
*  rmaximum(0;||K||  -  1;i.rat-cube-diameter(k;K[i])))
\mvdash{}  rmaximum(0;||(K)'||  -  1;i.rat-cube-diameter(k;(K)'[i]))  \mleq{}  ((r1/r(2))
*  rmaximum(0;||K||  -  1;i.rat-cube-diameter(k;K[i])))


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Latex:
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