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Step * of Lemma cu-cube-restriction_wf

∀[I:Cname List]. ∀[alpha:c𝕌(I)]. ∀[L,J:Cname List]. ∀[f:name-morph(L;J)]. ∀[a:name-morph(I;L)].
∀[T:cu-cube-family(alpha;L;a)].
  (cu-cube-restriction(alpha;L;J;f;a;T) ∈ cu-cube-family(alpha;J;(a o f)))
BY
{ (ProveWfLemma
   THEN (RWO "cubical-universe-I-cube" 2 THENA Auto)
   THEN RepeatFor 4 (D 2)
   THEN All (RepUR ``cu-cube-family``)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[I:Cname  List].  \mforall{}[alpha:c\mBbbU{}(I)].  \mforall{}[L,J:Cname  List].  \mforall{}[f:name-morph(L;J)].  \mforall{}[a:name-morph(I;L)].
\mforall{}[T:cu-cube-family(alpha;L;a)].
    (cu-cube-restriction(alpha;L;J;f;a;T)  \mmember{}  cu-cube-family(alpha;J;(a  o  f)))


By

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

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