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Step * 1 1 of Lemma boundary-singleton-complex

.....truecase..... 
1. k : ℕ
2. n : ℕ
3. c : {c:ℚCube(k)| dim(c) = n ∈ ℤ} 
4. ↑Inhabited(c)
⊢ rat-cube-sub-complex(λf.in-complex-boundary(k;f;[c]);remove-repeats(rc-deq(k);concat([rat-cube-faces(k;c)]))) 
~ remove-repeats(rc-deq(k);rat-cube-faces(k;c))
BY
{ ((RepUR ``concat`` 0 THEN (Subst' rat-cube-faces(k;c) @ [] ~ rat-cube-faces(k;c) 0 THENA Auto))
   THEN Unfold `rat-cube-sub-complex` 0
   THEN BLemma `filter_trivial`
   THEN Auto
   THEN RepUR ``so_apply`` 0
   THEN (GenConclTerm ⌜remove-repeats(rc-deq(k);rat-cube-faces(k;c))⌝⋅ THENA Auto)
   THEN (Assert v ∈ ℚCube(k) List BY
               Auto)
   THEN RWO "l_all_iff" 0
   THEN Auto) }

1
1. k : ℕ
2. n : ℕ
3. c : {c:ℚCube(k)| dim(c) = n ∈ ℤ} 
4. ↑Inhabited(c)
5. v : {f:ℚCube(k)| f ≤ c ∧ (dim(f) = (dim(c) - 1) ∈ ℤ)}  List
6. remove-repeats(rc-deq(k);rat-cube-faces(k;c)) = v ∈ ({f:ℚCube(k)| f ≤ c ∧ (dim(f) = (dim(c) - 1) ∈ ℤ)}  List)
7. v ∈ ℚCube(k) List
8. x : ℚCube(k)
9. (x ∈ v)
⊢ ↑in-complex-boundary(k;x;[c])

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Latex:

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Latex:
.....truecase..... 
1.  k  :  \mBbbN{}
2.  n  :  \mBbbN{}
3.  c  :  \{c:\mBbbQ{}Cube(k)|  dim(c)  =  n\} 
4.  \muparrow{}Inhabited(c)
\mvdash{}  rat-cube-sub-complex(\mlambda{}f.in-complex-boundary(k;f;[c]);remove-repeats(rc-deq(k);concat([...]))) 
\msim{}  remove-repeats(rc-deq(k);rat-cube-faces(k;c))


By

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Latex:
((RepUR  ``concat``  0  THEN  (Subst'  rat-cube-faces(k;c)  @  []  \msim{}  rat-cube-faces(k;c)  0  THENA  Auto))
  THEN  Unfold  `rat-cube-sub-complex`  0
  THEN  BLemma  `filter\_trivial`
  THEN  Auto
  THEN  RepUR  ``so\_apply``  0
  THEN  (GenConclTerm  \mkleeneopen{}remove-repeats(rc-deq(k);rat-cube-faces(k;c))\mkleeneclose{}\mcdot{}  THENA  Auto)
  THEN  (Assert  v  \mmember{}  \mBbbQ{}Cube(k)  List  BY
                          Auto)
  THEN  RWO  "l\_all\_iff"  0
  THEN  Auto)

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