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Step * of Lemma cu-cube-restriction-id

∀[I:Cname List]. ∀[alpha:c𝕌(I)]. ∀[K:Cname List]. ∀[a:name-morph(I;K)]. ∀[T:cu-cube-family(alpha;K;a)].
  (cu-cube-restriction(alpha;K;K;1;a;T) = T ∈ cu-cube-family(alpha;K;a))
BY
{ ((UnivCD THENA Auto)
   THEN (RWO "cubical-universe-I-cube" 2 THENA Auto)
   THEN RepeatFor 4 (D 2)
   THEN All Reduce
   THEN All (RepUR ``cu-cube-family cu-cube-restriction``)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[I:Cname  List].  \mforall{}[alpha:c\mBbbU{}(I)].  \mforall{}[K:Cname  List].  \mforall{}[a:name-morph(I;K)].
\mforall{}[T:cu-cube-family(alpha;K;a)].
    (cu-cube-restriction(alpha;K;K;1;a;T)  =  T)


By

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

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