---

Step * of Lemma cu-cube-filler_wf

∀[I:Cname List]. ∀[alpha:c𝕌(I)].
  (cu-cube-filler(alpha) ∈ L:(Cname List)
   ⟶ f:name-morph(I;L)
   ⟶ J:(nameset(L) List)
   ⟶ x:nameset(L)
   ⟶ i:ℕ2
   ⟶ A-open-box(unit-cube(I);Kan-type(alpha);L;f;J;x;i)
   ⟶ cu-cube-family(alpha;L;f))
BY
{ (ProveWfLemma
   THEN (RWO "cubical-universe-I-cube" 2 THENA Auto)
   THEN RepeatFor 4 (D 2)
   THEN All (RepUR ``cu-cube-family cu-cube-filler Kan-type``)
   THEN Auto) }

---

Latex:

---

Latex:
\mforall{}[I:Cname  List].  \mforall{}[alpha:c\mBbbU{}(I)].
    (cu-cube-filler(alpha)  \mmember{}  L:(Cname  List)
      {}\mrightarrow{}  f:name-morph(I;L)
      {}\mrightarrow{}  J:(nameset(L)  List)
      {}\mrightarrow{}  x:nameset(L)
      {}\mrightarrow{}  i:\mBbbN{}2
      {}\mrightarrow{}  A-open-box(unit-cube(I);Kan-type(alpha);L;f;J;x;i)
      {}\mrightarrow{}  cu-cube-family(alpha;L;f))


By

---

Latex:
(ProveWfLemma
  THEN  (RWO  "cubical-universe-I-cube"  2  THENA  Auto)
  THEN  RepeatFor  4  (D  2)
  THEN  All  (RepUR  ``cu-cube-family  cu-cube-filler  Kan-type``)
  THEN  Auto)

---

Home Index