---

Step * 1 of Lemma rat-cube-complex-polyhedron-compact1


1. k : ℕ
2. K : ℚCube(k) List
3. 0 < ||K||
4. (∀c∈K.↑Inhabited(c))
5. i : ℕ||K||
⊢ mcompact({x:ℝ^k| in-rat-cube(k;x;K[i])} ;rn-prod-metric(k))
BY
{ (D -2 With ⌜i⌝  THEN EAuto 1) }

---

Latex:

---

Latex:

1.  k  :  \mBbbN{}
2.  K  :  \mBbbQ{}Cube(k)  List
3.  0  <  ||K||
4.  (\mforall{}c\mmember{}K.\muparrow{}Inhabited(c))
5.  i  :  \mBbbN{}||K||
\mvdash{}  mcompact(\{x:\mBbbR{}\^{}k|  in-rat-cube(k;x;K[i])\}  ;rn-prod-metric(k))


By

---

Latex:
(D  -2  With  \mkleeneopen{}i\mkleeneclose{}    THEN  EAuto  1)

---

Home Index