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Step * of Lemma center-point-in-cube-interior

No Annotations
∀[k:ℕ]. ∀[a:ℚCube(k)].  rat-point-in-cube-interior(k;λj.qavg(fst((a j));snd((a j)));a) supposing ↑Inhabited(a)
BY
{ (Auto
   THEN (RWO "assert-inhabited-rat-cube" (-1) THENA Auto)
   THEN D 0
   THEN Reduce 0
   THEN Auto
   THEN QavgSimp 0
   THEN Try (Trivial)
   THEN (D 3 With ⌜i⌝  THENA Auto)
   THEN MoveToConcl (-1)
   THEN (GenConclTerm ⌜a i⌝⋅ THENA Auto)
   THEN All Thin
   THEN D 1
   THEN RepUR ``inhabited-rat-interval`` 0
   THEN RW assert_pushdownC 0
   THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}[k:\mBbbN{}].  \mforall{}[a:\mBbbQ{}Cube(k)].
    rat-point-in-cube-interior(k;\mlambda{}j.qavg(fst((a  j));snd((a  j)));a)  supposing  \muparrow{}Inhabited(a)


By

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Latex:
(Auto
  THEN  (RWO  "assert-inhabited-rat-cube"  (-1)  THENA  Auto)
  THEN  D  0
  THEN  Reduce  0
  THEN  Auto
  THEN  QavgSimp  0
  THEN  Try  (Trivial)
  THEN  (D  3  With  \mkleeneopen{}i\mkleeneclose{}    THENA  Auto)
  THEN  MoveToConcl  (-1)
  THEN  (GenConclTerm  \mkleeneopen{}a  i\mkleeneclose{}\mcdot{}  THENA  Auto)
  THEN  All  Thin
  THEN  D  1
  THEN  RepUR  ``inhabited-rat-interval``  0
  THEN  RW  assert\_pushdownC  0
  THEN  Auto)

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