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Step * 2 2 of Lemma member-rat-complex-subdiv


1. k : ℕ
2. K : {c:ℚCube(k)| ↑Inhabited(c)}  List
3. c : ℚCube(k)
4. a : ℚCube(k)
5. (a ∈ K)
6. ↑is-half-cube(k;c;a)
7. ∃y:{c:ℚCube(k)| ↑Inhabited(c)} . ((y ∈ K) ∧ (half-cubes-of(k;a) = half-cubes-of(k;y) ∈ (ℚCube(k) List)))
⊢ (c ∈ half-cubes-of(k;a))
BY
{ ((GenConclTerm ⌜half-cubes-of(k;a)⌝⋅ THENA Auto) THEN D -2 THEN Unhide THEN Auto) }

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Latex:

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Latex:

1.  k  :  \mBbbN{}
2.  K  :  \{c:\mBbbQ{}Cube(k)|  \muparrow{}Inhabited(c)\}    List
3.  c  :  \mBbbQ{}Cube(k)
4.  a  :  \mBbbQ{}Cube(k)
5.  (a  \mmember{}  K)
6.  \muparrow{}is-half-cube(k;c;a)
7.  \mexists{}y:\{c:\mBbbQ{}Cube(k)|  \muparrow{}Inhabited(c)\}  .  ((y  \mmember{}  K)  \mwedge{}  (half-cubes-of(k;a)  =  half-cubes-of(k;y)))
\mvdash{}  (c  \mmember{}  half-cubes-of(k;a))


By

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Latex:
((GenConclTerm  \mkleeneopen{}half-cubes-of(k;a)\mkleeneclose{}\mcdot{}  THENA  Auto)  THEN  D  -2  THEN  Unhide  THEN  Auto)

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