Step
*
of Lemma
boundary-singleton-complex
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∀[k,n:ℕ]. ∀[c:{c:ℚCube(k)| dim(c) = n ∈ ℤ} ].  (∂(singleton-complex(c)) ~ remove-repeats(rc-deq(k);rat-cube-faces(k;c)))
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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))
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\mforall{}[k,n:\mBbbN{}].  \mforall{}[c:\{c:\mBbbQ{}Cube(k)|  dim(c)  =  n\}  ].
    (\mpartial{}(singleton-complex(c))  \msim{}  remove-repeats(rc-deq(k);rat-cube-faces(k;c)))
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