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Step * 3 of Lemma Kan_sigma_filler_wf

.....wf..... 
1. X : CubicalSet
2. A : {X ⊢ _(Kan)}
3. B : {X.Kan-type(A) ⊢ _(Kan)}
4. filler : I:(Cname List)
⟶ alpha:X(I)
⟶ J:(nameset(I) List)
⟶ x:nameset(I)
⟶ i:ℕ2
⟶ A-open-box(X;Σ Kan-type(A) Kan-type(B);I;alpha;J;x;i)
⟶ Σ Kan-type(A) Kan-type(B)(alpha)
⊢ istype(Kan-A-filler(X;Σ Kan-type(A) Kan-type(B);filler))
BY
{ TACTIC:Auto }

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Latex:

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Latex:
.....wf..... 
1.  X  :  CubicalSet
2.  A  :  \{X  \mvdash{}  \_(Kan)\}
3.  B  :  \{X.Kan-type(A)  \mvdash{}  \_(Kan)\}
4.  filler  :  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;\mSigma{}  Kan-type(A)  Kan-type(B);I;alpha;J;x;i)
{}\mrightarrow{}  \mSigma{}  Kan-type(A)  Kan-type(B)(alpha)
\mvdash{}  istype(Kan-A-filler(X;\mSigma{}  Kan-type(A)  Kan-type(B);filler))


By

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Latex:
TACTIC:Auto

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