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Step * 2 1 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)
⊢ ∃y:{c:ℚCube(k)| ↑Inhabited(c)} . ((y ∈ K) ∧ (half-cubes-of(k;a) = half-cubes-of(k;y) ∈ (ℚCube(k) List)))
BY
{ (D 0 With ⌜a⌝  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)
\mvdash{}  \mexists{}y:\{c:\mBbbQ{}Cube(k)|  \muparrow{}Inhabited(c)\}  .  ((y  \mmember{}  K)  \mwedge{}  (half-cubes-of(k;a)  =  half-cubes-of(k;y)))


By

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Latex:
(D  0  With  \mkleeneopen{}a\mkleeneclose{}    THEN  Auto)

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