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Step * 1 of Lemma boundary-singleton-complex


1. k : ℕ
2. n : ℕ
3. c : {c:ℚCube(k)| dim(c) = n ∈ ℤ} 
⊢ ∂(singleton-complex(c)) ~ remove-repeats(rc-deq(k);rat-cube-faces(k;c))
BY
{ (RepUR ``rat-complex-boundary singleton-complex face-complex`` 0 THEN (SplitOnConclITE THENA Auto)) }

1
.....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))

2
.....falsecase..... 
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([[]]))) 
~ remove-repeats(rc-deq(k);rat-cube-faces(k;c))

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Latex:

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Latex:

1.  k  :  \mBbbN{}
2.  n  :  \mBbbN{}
3.  c  :  \{c:\mBbbQ{}Cube(k)|  dim(c)  =  n\} 
\mvdash{}  \mpartial{}(singleton-complex(c))  \msim{}  remove-repeats(rc-deq(k);rat-cube-faces(k;c))


By

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Latex:
(RepUR  ``rat-complex-boundary  singleton-complex  face-complex``  0  THEN  (SplitOnConclITE  THENA  Auto))

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