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Step * of Lemma cu-cube-restriction-comp

∀[I:Cname List]. ∀[alpha:c𝕌(I)]. ∀[L,J,K:Cname List]. ∀[f:name-morph(L;J)]. ∀[g:name-morph(J;K)]. ∀[a:name-morph(I;L)].
∀[T:cu-cube-family(alpha;L;a)].
  (cu-cube-restriction(alpha;J;K;g;(a o f);cu-cube-restriction(alpha;L;J;f;a;T))
  = cu-cube-restriction(alpha;L;K;(f o g);a;T)
  ∈ cu-cube-family(alpha;K;(a o (f o g))))
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{}[L,J,K:Cname  List].  \mforall{}[f:name-morph(L;J)].  \mforall{}[g:name-morph(J;K)].
\mforall{}[a:name-morph(I;L)].  \mforall{}[T:cu-cube-family(alpha;L;a)].
    (cu-cube-restriction(alpha;J;K;g;(a  o  f);cu-cube-restriction(alpha;L;J;f;a;T))
    =  cu-cube-restriction(alpha;L;K;(f  o  g);a;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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