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Step * 2 of Lemma inhabited-half-cube


1. v : ℚInterval
2. v1 : ℚInterval
⊢ (↑Inhabited(v1)) ⇒ (↑is-half-interval(v;v1)) ⇒ (↑Inhabited(v))
BY
{ (D 1
   THEN D -1
   THEN RepUR ``inhabited-rat-interval is-half-interval`` 0
   THEN RW assert_pushdownC 0
   THEN Auto
   THEN D -1
   THEN ExRepD
   THEN RationalElim ⌜v2⌝⋅
   THEN RationalElim ⌜v3⌝⋅
   THEN All QavgSimp
   THEN Auto) }

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Latex:

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Latex:

1.  v  :  \mBbbQ{}Interval
2.  v1  :  \mBbbQ{}Interval
\mvdash{}  (\muparrow{}Inhabited(v1))  {}\mRightarrow{}  (\muparrow{}is-half-interval(v;v1))  {}\mRightarrow{}  (\muparrow{}Inhabited(v))


By

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Latex:
(D  1
  THEN  D  -1
  THEN  RepUR  ``inhabited-rat-interval  is-half-interval``  0
  THEN  RW  assert\_pushdownC  0
  THEN  Auto
  THEN  D  -1
  THEN  ExRepD
  THEN  RationalElim  \mkleeneopen{}v2\mkleeneclose{}\mcdot{}
  THEN  RationalElim  \mkleeneopen{}v3\mkleeneclose{}\mcdot{}
  THEN  All  QavgSimp
  THEN  Auto)

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