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Step * 1 2 1 of Lemma rat-complex-subdiv_wf


1. k : ℕ
2. n : ℕ
3. K : ℚCube(k) List
4. no_repeats(ℚCube(k);K)
5. (∀c,d∈K.  Compatible(c;d))
6. (∀c∈K.dim(c) = n ∈ ℤ)
7. K ∈ {c:ℚCube(k)| ↑Inhabited(c)}  List
8. (K)' ∈ ℚCube(k) List
9. l : ℚCube(k) List
10. y : {c:ℚCube(k)| ↑Inhabited(c)} 
11. (y ∈ K)
12. l = half-cubes-of(k;y) ∈ (ℚCube(k) List)
⊢ no_repeats(ℚCube(k);half-cubes-of(k;y))
BY
{ (GenConclTerm ⌜half-cubes-of(k;y)⌝⋅ THEN Auto) }

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Latex:

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Latex:

1.  k  :  \mBbbN{}
2.  n  :  \mBbbN{}
3.  K  :  \mBbbQ{}Cube(k)  List
4.  no\_repeats(\mBbbQ{}Cube(k);K)
5.  (\mforall{}c,d\mmember{}K.    Compatible(c;d))
6.  (\mforall{}c\mmember{}K.dim(c)  =  n)
7.  K  \mmember{}  \{c:\mBbbQ{}Cube(k)|  \muparrow{}Inhabited(c)\}    List
8.  (K)'  \mmember{}  \mBbbQ{}Cube(k)  List
9.  l  :  \mBbbQ{}Cube(k)  List
10.  y  :  \{c:\mBbbQ{}Cube(k)|  \muparrow{}Inhabited(c)\} 
11.  (y  \mmember{}  K)
12.  l  =  half-cubes-of(k;y)
\mvdash{}  no\_repeats(\mBbbQ{}Cube(k);half-cubes-of(k;y))


By

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Latex:
(GenConclTerm  \mkleeneopen{}half-cubes-of(k;y)\mkleeneclose{}\mcdot{}  THEN  Auto)

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