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Step * 2 of Lemma inhabited-iff-in-rat-cube


1. k : ℕ
2. c : ℚCube(k)
3. ∃p:ℝ^k. in-rat-cube(k;p;c)
⊢ ∀i:ℕk. (↑Inhabited(c i))
BY
{ (D -1
   THEN RepUR ``in-rat-cube`` -1
   THEN ParallelLast
   THEN MoveToConcl (-1)
   THEN (GenConclTerm ⌜c i⌝⋅ THENA Auto)
   THEN D -2
   THEN RepUR ``inhabited-rat-interval`` 0
   THEN EAuto 1) }

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Latex:

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Latex:

1.  k  :  \mBbbN{}
2.  c  :  \mBbbQ{}Cube(k)
3.  \mexists{}p:\mBbbR{}\^{}k.  in-rat-cube(k;p;c)
\mvdash{}  \mforall{}i:\mBbbN{}k.  (\muparrow{}Inhabited(c  i))


By

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Latex:
(D  -1
  THEN  RepUR  ``in-rat-cube``  -1
  THEN  ParallelLast
  THEN  MoveToConcl  (-1)
  THEN  (GenConclTerm  \mkleeneopen{}c  i\mkleeneclose{}\mcdot{}  THENA  Auto)
  THEN  D  -2
  THEN  RepUR  ``inhabited-rat-interval``  0
  THEN  EAuto  1)

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