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Step * 1 1 of Lemma inhabited-iff-in-rat-cube


1. [k] : ℕ
2. c : ℚCube(k)
3. ∀i:ℕk. (↑Inhabited(c i))
4. i : ℕk
⊢ (rat2real(fst((c i))) ≤ rat2real(fst((c i)))) ∧ (rat2real(fst((c i))) ≤ rat2real(snd((c i))))
BY
{ ((D -2 With ⌜i⌝  THENA Auto)
   THEN MoveToConcl (-1)
   THEN (GenConclTerm ⌜c i⌝⋅ THENA Auto)
   THEN D -2
   THEN RepUR ``inhabited-rat-interval`` 0
   THEN RW assert_pushdownC 0
   THEN Auto
   THEN EAuto 1) }

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Latex:

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Latex:

1.  [k]  :  \mBbbN{}
2.  c  :  \mBbbQ{}Cube(k)
3.  \mforall{}i:\mBbbN{}k.  (\muparrow{}Inhabited(c  i))
4.  i  :  \mBbbN{}k
\mvdash{}  (rat2real(fst((c  i)))  \mleq{}  rat2real(fst((c  i))))  \mwedge{}  (rat2real(fst((c  i)))  \mleq{}  rat2real(snd((c  i))))


By

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

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