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Step * of Lemma inhabited-lower-rc-face

∀k:ℕ. ∀c:ℚCube(k). ∀j:ℕk.  ((↑Inhabited(c j)) ⇒ Inhabited(lower-rc-face(c;j)) = Inhabited(c))
BY
{ (Auto
   THEN (BLemma `iff_imp_equal_bool` THENA Auto)
   THEN (RWO "assert-inhabited-rat-cube" 0 THENA Auto)
   THEN RepUR ``lower-rc-face`` 0
   THEN Auto) }

1
1. k : ℕ
2. c : ℚCube(k)
3. j : ℕk
4. ↑Inhabited(c j)
5. ∀i:ℕk. (↑Inhabited(if (i =z j) then [fst((c i))] else c i fi ))
6. i : ℕk
⊢ ↑Inhabited(c i)

2
1. k : ℕ
2. c : ℚCube(k)
3. j : ℕk
4. ↑Inhabited(c j)
5. ∀i:ℕk. (↑Inhabited(c i))
6. i : ℕk
⊢ ↑Inhabited(if (i =z j) then [fst((c i))] else c i fi )

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Latex:

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Latex:
\mforall{}k:\mBbbN{}.  \mforall{}c:\mBbbQ{}Cube(k).  \mforall{}j:\mBbbN{}k.    ((\muparrow{}Inhabited(c  j))  {}\mRightarrow{}  Inhabited(lower-rc-face(c;j))  =  Inhabited(c))


By

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Latex:
(Auto
  THEN  (BLemma  `iff\_imp\_equal\_bool`  THENA  Auto)
  THEN  (RWO  "assert-inhabited-rat-cube"  0  THENA  Auto)
  THEN  RepUR  ``lower-rc-face``  0
  THEN  Auto)

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