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Step * of Lemma fill-type-up-1

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∀[Gamma:j⊢]. ∀[A:{Gamma.𝕀 ⊢ _}]. ∀[cA:Gamma.𝕀 ⊢ CompOp(A)]. ∀[u:{Gamma ⊢ _:(A)[0(𝕀)]}].
  ((app(fill-type-up(Gamma;A;cA); (u)p))[1(𝕀)] = app(transport-fun(Gamma;A;cA); u) ∈ {Gamma ⊢ _:(A)[1(𝕀)]})
BY
{ (RepeatFor 3 (Intro) THEN (Assert Gamma.𝕀 ⊢ ((A)[0(𝕀)])p BY Auto) THEN Intro) }

1
1. Gamma : CubicalSet{j}
2. A : {Gamma.𝕀 ⊢ _}
3. cA : Gamma.𝕀 ⊢ CompOp(A)
4. Gamma.𝕀 ⊢ ((A)[0(𝕀)])p
5. u : {Gamma ⊢ _:(A)[0(𝕀)]}
⊢ (app(fill-type-up(Gamma;A;cA); (u)p))[1(𝕀)] = app(transport-fun(Gamma;A;cA); u) ∈ {Gamma ⊢ _:(A)[1(𝕀)]}

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Latex:

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Latex:
No  Annotations
\mforall{}[Gamma:j\mvdash{}].  \mforall{}[A:\{Gamma.\mBbbI{}  \mvdash{}  \_\}].  \mforall{}[cA:Gamma.\mBbbI{}  \mvdash{}  CompOp(A)].  \mforall{}[u:\{Gamma  \mvdash{}  \_:(A)[0(\mBbbI{})]\}].
    ((app(fill-type-up(Gamma;A;cA);  (u)p))[1(\mBbbI{})]  =  app(transport-fun(Gamma;A;cA);  u))


By

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Latex:
(RepeatFor  3  (Intro)  THEN  (Assert  Gamma.\mBbbI{}  \mvdash{}  ((A)[0(\mBbbI{})])p  BY  Auto)  THEN  Intro)

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