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Step * of Lemma cu-cube-family-comp

∀[I:Cname List]. ∀[alpha:c𝕌(I)]. ∀[J,L,f,g:Top].  (cu-cube-family(alpha;L;(f o g)) ~ cu-cube-family(f(alpha);L;g))
BY
{ ((UnivCD THENA Auto)
   THEN (RWO "cubical-universe-I-cube" 2 THENA Auto)
   THEN RepeatFor 4 (D 2)
   THEN All Reduce
   THEN RepUR ``cu-cube-family cube-set-restriction cubical-universe`` 0⋅
   THEN RepUR ``csm-Kan-cubical-type csm-ap-type unit-cube-map csm-ap`` 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[I:Cname  List].  \mforall{}[alpha:c\mBbbU{}(I)].  \mforall{}[J,L,f,g:Top].
    (cu-cube-family(alpha;L;(f  o  g))  \msim{}  cu-cube-family(f(alpha);L;g))


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  RepUR  ``cu-cube-family  cube-set-restriction  cubical-universe``  0\mcdot{}
  THEN  RepUR  ``csm-Kan-cubical-type  csm-ap-type  unit-cube-map  csm-ap``  0
  THEN  Auto)

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