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Step * of Lemma discrete-presheaf-term-is-constant

No Annotations
∀[C:SmallCategory]. ∀[T:Type]. ∀[I:cat-ob(C)]. ∀[t:{Yoneda(I) ⊢ _:discr(T)}].
  (t = discr(t(cat-id(C) I)) ∈ {Yoneda(I) ⊢ _:discr(T)})
BY
{ (Auto
   THEN (InstLemma `discrete-presheaf-term-is-map` [⌜parm{i}⌝;⌜parm{i}⌝;⌜C⌝;⌜T⌝;⌜Yoneda(I)⌝]⋅ THENA Auto)
   THEN (InstLemma `ps-discrete-map-is-constant` [⌜parm{i}⌝;⌜parm{i}⌝;⌜C⌝;⌜T⌝;⌜I⌝;⌜t⌝]⋅ THENA Auto)
   THEN Fold `presheaf-term-at` (-1)
   THEN Fold `discrete-presheaf-term` (-1)
   THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}[C:SmallCategory].  \mforall{}[T:Type].  \mforall{}[I:cat-ob(C)].  \mforall{}[t:\{Yoneda(I)  \mvdash{}  \_:discr(T)\}].
    (t  =  discr(t(cat-id(C)  I)))


By

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Latex:
(Auto
  THEN  (InstLemma  `discrete-presheaf-term-is-map`  [\mkleeneopen{}parm\{i\}\mkleeneclose{};\mkleeneopen{}parm\{i\}\mkleeneclose{};\mkleeneopen{}C\mkleeneclose{};\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}Yoneda(I)\mkleeneclose{}]\mcdot{}
              THENA  Auto
              )
  THEN  (InstLemma  `ps-discrete-map-is-constant`  [\mkleeneopen{}parm\{i\}\mkleeneclose{};\mkleeneopen{}parm\{i\}\mkleeneclose{};\mkleeneopen{}C\mkleeneclose{};\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}t\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  Fold  `presheaf-term-at`  (-1)
  THEN  Fold  `discrete-presheaf-term`  (-1)
  THEN  Auto)

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