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Step * 1 1 of Lemma rat-complex-diameter-bound


1. k : ℕ
2. K : ℚCube(k) List
3. 0 < ||K||
4. i : ℕ
5. i < ||K||
⊢ rat-cube-diameter(k;K[i]) ≤ rat-complex-diameter(k;K)
BY
{ (Unfold `rat-complex-diameter` 0
   THEN (InstLemma `rmaximum_ub` [⌜i⌝;⌜0⌝;⌜||K|| - 1⌝]⋅ THENA Auto)
   THEN BHyp -1
   THEN Auto) }

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Latex:

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Latex:

1.  k  :  \mBbbN{}
2.  K  :  \mBbbQ{}Cube(k)  List
3.  0  <  ||K||
4.  i  :  \mBbbN{}
5.  i  <  ||K||
\mvdash{}  rat-cube-diameter(k;K[i])  \mleq{}  rat-complex-diameter(k;K)


By

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Latex:
(Unfold  `rat-complex-diameter`  0
  THEN  (InstLemma  `rmaximum\_ub`  [\mkleeneopen{}i\mkleeneclose{};\mkleeneopen{}0\mkleeneclose{};\mkleeneopen{}||K||  -  1\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  BHyp  -1
  THEN  Auto)

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