Step
*
of Lemma
cc-adjoin-cube-restriction
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[J,K,g,v,u:Top].  (g((v;u)) ~ (g(v);(u v g)))
BY
{ (Auto
   THEN RepeatFor 2 (DVar `A')
   THEN RepUR ``cubical-type-ap-morph cc-adjoin-cube cube-context-adjoin`` 0
   THEN RepUR ``cubical-type-ap-morph cube-set-restriction`` 0
   THEN Auto) }
Latex:
Latex:
\mforall{}[X:CubicalSet].  \mforall{}[A:\{X  \mvdash{}  \_\}].  \mforall{}[J,K,g,v,u:Top].    (g((v;u))  \msim{}  (g(v);(u  v  g)))
By
Latex:
(Auto
  THEN  RepeatFor  2  (DVar  `A')
  THEN  RepUR  ``cubical-type-ap-morph  cc-adjoin-cube  cube-context-adjoin``  0
  THEN  RepUR  ``cubical-type-ap-morph  cube-set-restriction``  0
  THEN  Auto)
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