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Step * of Lemma universe-type_wf

No Annotations
∀[X:j⊢]. ∀[t:{X ⊢ _:c𝕌}]. ∀[I:fset(ℕ)]. ∀[a:X(I)].  formal-cube(I) ⊢ universe-type(t;I;a)
BY
{ (Intros
   THEN Unfold `universe-type` 0
   THEN Unhide
   THEN (Assert X ⊢' c𝕌 BY
               Auto)
   THEN (GenConclTerm ⌜t(a)⌝⋅ THENA Auto)
   THEN RWO "cubical-universe-at" (-2)
   THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}[X:j\mvdash{}].  \mforall{}[t:\{X  \mvdash{}  \_:c\mBbbU{}\}].  \mforall{}[I:fset(\mBbbN{})].  \mforall{}[a:X(I)].    formal-cube(I)  \mvdash{}  universe-type(t;I;a)


By

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Latex:
(Intros
  THEN  Unfold  `universe-type`  0
  THEN  Unhide
  THEN  (Assert  X  \mvdash{}'  c\mBbbU{}  BY
                          Auto)
  THEN  (GenConclTerm  \mkleeneopen{}t(a)\mkleeneclose{}\mcdot{}  THENA  Auto)
  THEN  RWO  "cubical-universe-at"  (-2)
  THEN  Auto)

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