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Step * 2 of Lemma equal-rat-cube-complexes


1. k : ℕ
2. [n] : ℕ
3. K : n-dim-complex
4. L : n-dim-complex
5. [%] : permutation(ℚCube(k);K;L)
6. c : {c:ℚCube(k)| (↑Inhabited(c)) ∧ (dim(c) = n ∈ ℤ)} 
7. (c ∈ L)
⊢ (c ∈ K)
BY
{ ((Unhide THENA Auto) THEN InstLemma `l_member_functionality_wrt_permutation` [⌜ℚCube(k)⌝;⌜L⌝;⌜K⌝;⌜c⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  k  :  \mBbbN{}
2.  [n]  :  \mBbbN{}
3.  K  :  n-dim-complex
4.  L  :  n-dim-complex
5.  [\%]  :  permutation(\mBbbQ{}Cube(k);K;L)
6.  c  :  \{c:\mBbbQ{}Cube(k)|  (\muparrow{}Inhabited(c))  \mwedge{}  (dim(c)  =  n)\} 
7.  (c  \mmember{}  L)
\mvdash{}  (c  \mmember{}  K)


By

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Latex:
((Unhide  THENA  Auto)
  THEN  InstLemma  `l\_member\_functionality\_wrt\_permutation`  [\mkleeneopen{}\mBbbQ{}Cube(k)\mkleeneclose{};\mkleeneopen{}L\mkleeneclose{};\mkleeneopen{}K\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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