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Step * 2 of Lemma presheaf-fun-eta


1. C : SmallCategory
2. X : ps_context{j:l}(C)
3. A : {X ⊢ _}
4. B : {X ⊢ _}
5. w : {X ⊢ _:(A ⟶ B)}
6. {X ⊢ _:(A ⟶ B)} = {X ⊢ _:ΠA (B)p} ∈ 𝕌{[i | j']}
⊢ (λapp((w)p; q)) = w ∈ {X ⊢ _:(A ⟶ B)}
BY
{ (InstLemma `presheaf-eta` [⌜C⌝;⌜X⌝;⌜A⌝;⌜(B)p⌝;⌜w⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  C  :  SmallCategory
2.  X  :  ps\_context\{j:l\}(C)
3.  A  :  \{X  \mvdash{}  \_\}
4.  B  :  \{X  \mvdash{}  \_\}
5.  w  :  \{X  \mvdash{}  \_:(A  {}\mrightarrow{}  B)\}
6.  \{X  \mvdash{}  \_:(A  {}\mrightarrow{}  B)\}  =  \{X  \mvdash{}  \_:\mPi{}A  (B)p\}
\mvdash{}  (\mlambda{}app((w)p;  q))  =  w


By

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Latex:
(InstLemma  `presheaf-eta`  [\mkleeneopen{}C\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}(B)p\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{}]\mcdot{}  THEN  Auto)

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