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Step * of Lemma universe-comp-op_wf

No Annotations
∀[X:j⊢]. ∀[t:{X ⊢ _:c𝕌}].  (compOp(t) ∈ X ⊢ CompOp(decode(t)))
BY
{ (Intros⋅ THEN (MemTypeCD THENW (InstLemma `composition-uniformity_wf` [⌜X⌝;⌜decode(t)⌝;⌜comp⌝]⋅ THEN Auto))) }

1
1. X : CubicalSet{j}
2. t : {X ⊢ _:c𝕌}
⊢ compOp(t) ∈ I:fset(ℕ)
  ⟶ i:{i:ℕ| ¬i ∈ I} 
  ⟶ rho:X(I+i)
  ⟶ phi:𝔽(I)
  ⟶ u:{I+i,s(phi) ⊢ _:(decode(t))<rho> o iota}
  ⟶ cubical-path-0(X;decode(t);I;i;rho;phi;u)
  ⟶ cubical-path-1(X;decode(t);I;i;rho;phi;u)

2
.....set predicate..... 
1. X : CubicalSet{j}
2. t : {X ⊢ _:c𝕌}
⊢ composition-uniformity(X;decode(t);compOp(t))

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Latex:

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Latex:
No  Annotations
\mforall{}[X:j\mvdash{}].  \mforall{}[t:\{X  \mvdash{}  \_:c\mBbbU{}\}].    (compOp(t)  \mmember{}  X  \mvdash{}  CompOp(decode(t)))


By

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Latex:
(Intros\mcdot{}
  THEN  (MemTypeCD  THENW  (InstLemma  `composition-uniformity\_wf`  [\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}decode(t)\mkleeneclose{};\mkleeneopen{}comp\mkleeneclose{}]\mcdot{}  THEN  Auto))
  )

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