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Step * of Lemma singleton-contr_wf

No Annotations
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[a:{X ⊢ _:A}].  (singleton-contr(X;A;a) ∈ {X ⊢ _:Contractible(Singleton(a))})
BY
{ (ProveWfLemma
   THEN (Assert singleton-contraction(X.Singleton(a);q.2)
                ∈ {X.Singleton(a) ⊢ _:(Path_Singleton((a)p) singleton-center(X.Singleton(a);(a)p) q)} BY
               Auto)
   THEN InferEqualTypeUp
   THEN Auto) }

1
.....subterm..... T:t
2:n
1. X : CubicalSet{j}
2. A : {X ⊢ _}
3. a : {X ⊢ _:A}
4. singleton-contraction(X.Singleton(a);q.2)
   ∈ {X.Singleton(a) ⊢ _:(Path_Singleton((a)p) singleton-center(X.Singleton(a);(a)p) q)}
⊢ (X.Singleton(a) ⊢ Path_Singleton((a)p) singleton-center(X.Singleton(a);(a)p) q)
= (X.Singleton(a) ⊢ Path_(Singleton(a))p (singleton-center(X;a))p q)
∈ cubical-type{[j' | i']:l}(X.Singleton(a))

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Latex:

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Latex:
No  Annotations
\mforall{}[X:j\mvdash{}].  \mforall{}[A:\{X  \mvdash{}  \_\}].  \mforall{}[a:\{X  \mvdash{}  \_:A\}].
    (singleton-contr(X;A;a)  \mmember{}  \{X  \mvdash{}  \_:Contractible(Singleton(a))\})


By

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Latex:
(ProveWfLemma
  THEN  (Assert  singleton-contraction(X.Singleton(a);q.2)
                            \mmember{}  \{X.Singleton(a)  \mvdash{}  \_:(Path\_Singleton((a)p)  singleton-center(X.Singleton(a);(a)p)
                                                                                    q)\}  BY
                          Auto)
  THEN  InferEqualTypeUp
  THEN  Auto)

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