---

Step * of Lemma rat-cube-face-dimension-equal

∀[k:ℕ]. ∀[c:ℚCube(k)].  ∀f:ℚCube(k). (f = c ∈ ℚCube(k)) supposing ((dim(f) = dim(c) ∈ ℤ) and f ≤ c) supposing ↑Inhabited\000C(c)
BY
{ (Auto
   THEN (InstLemma `inhabited-rat-cube-face` [⌜k⌝;⌜c⌝;⌜f⌝]⋅ THENA Auto)
   THEN (All (RWO "assert-inhabited-rat-cube") THENA Auto)) }

1
1. k : ℕ
2. c : ℚCube(k)
3. ∀i:ℕk. (↑Inhabited(c i))
4. f : ℚCube(k)
5. f ≤ c
6. dim(f) = dim(c) ∈ ℤ
7. ∀i:ℕk. (↑Inhabited(f i))
⊢ f = c ∈ ℚCube(k)

---

Latex:

---

Latex:
\mforall{}[k:\mBbbN{}].  \mforall{}[c:\mBbbQ{}Cube(k)].    \mforall{}f:\mBbbQ{}Cube(k).  (f  =  c)  supposing  ((dim(f)  =  dim(c))  and  f  \mleq{}  c)  supposing  \muparrow{}Inha\000Cbited(c)


By

---

Latex:
(Auto
  THEN  (InstLemma  `inhabited-rat-cube-face`  [\mkleeneopen{}k\mkleeneclose{};\mkleeneopen{}c\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (All  (RWO  "assert-inhabited-rat-cube")  THENA  Auto))

---

Home Index