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Step * of Lemma Kan_id_filler_wf1

∀X:CubicalSet. ∀A:{X ⊢ _(Kan)}. ∀a,b:{X ⊢ _:Kan-type(A)}.
  (Kan_id_filler(X;A;a;b) ∈ I:(Cname List)
   ⟶ alpha:X(I)
   ⟶ J:(nameset(I) List)
   ⟶ x:nameset(I)
   ⟶ i:ℕ2
   ⟶ A-open-box(X;(Id_Kan-type(A) a b);I;alpha;J;x;i)
   ⟶ I-path(X;Kan-type(A);a;b;I;alpha))
BY
{ Auto }

1
1. X : CubicalSet
2. A : {X ⊢ _(Kan)}
3. a : {X ⊢ _:Kan-type(A)}
4. b : {X ⊢ _:Kan-type(A)}
⊢ Kan_id_filler(X;A;a;b) ∈ I:(Cname List)
  ⟶ alpha:X(I)
  ⟶ J:(nameset(I) List)
  ⟶ x:nameset(I)
  ⟶ i:ℕ2
  ⟶ A-open-box(X;(Id_Kan-type(A) a b);I;alpha;J;x;i)
  ⟶ I-path(X;Kan-type(A);a;b;I;alpha)

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Latex:

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Latex:
\mforall{}X:CubicalSet.  \mforall{}A:\{X  \mvdash{}  \_(Kan)\}.  \mforall{}a,b:\{X  \mvdash{}  \_:Kan-type(A)\}.
    (Kan\_id\_filler(X;A;a;b)  \mmember{}  I:(Cname  List)
      {}\mrightarrow{}  alpha:X(I)
      {}\mrightarrow{}  J:(nameset(I)  List)
      {}\mrightarrow{}  x:nameset(I)
      {}\mrightarrow{}  i:\mBbbN{}2
      {}\mrightarrow{}  A-open-box(X;(Id\_Kan-type(A)  a  b);I;alpha;J;x;i)
      {}\mrightarrow{}  I-path(X;Kan-type(A);a;b;I;alpha))


By

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Latex:
Auto

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