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Step * of Lemma presheaf-sigma-equal

No Annotations
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[A:{X ⊢ _}]. ∀[B:{X.A ⊢ _}]. ∀[w,y:{X ⊢ _:Σ A B}].
  (w = y ∈ {X ⊢ _:Σ A B}) supposing ((w.2 = y.2 ∈ {X ⊢ _:(B)[w.1]}) and (w.1 = y.1 ∈ {X ⊢ _:A}))
BY
{ (Auto
   THEN (InstLemma `presheaf-pair-eta` [⌜C⌝;⌜X⌝;⌜A⌝;⌜B⌝;⌜w⌝]⋅ THENA Auto)
   THEN (InstLemma `presheaf-pair-eta` [⌜C⌝;⌜X⌝;⌜A⌝;⌜B⌝;⌜y⌝]⋅ THENA Auto)
   THEN (Assert ⌜presheaf-pair(w.1;w.2) = presheaf-pair(y.1;y.2) ∈ {X ⊢ _:Σ A B}⌝⋅ THENM Eq)
   THEN EqCDA
   THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}[C:SmallCategory].  \mforall{}[X:ps\_context\{j:l\}(C)].  \mforall{}[A:\{X  \mvdash{}  \_\}].  \mforall{}[B:\{X.A  \mvdash{}  \_\}].  \mforall{}[w,y:\{X  \mvdash{}  \_:\mSigma{}  A  B\}].
    (w  =  y)  supposing  ((w.2  =  y.2)  and  (w.1  =  y.1))


By

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Latex:
(Auto
  THEN  (InstLemma  `presheaf-pair-eta`  [\mkleeneopen{}C\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (InstLemma  `presheaf-pair-eta`  [\mkleeneopen{}C\mkleeneclose{};\mkleeneopen{}X\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}B\mkleeneclose{};\mkleeneopen{}y\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (Assert  \mkleeneopen{}presheaf-pair(w.1;w.2)  =  presheaf-pair(y.1;y.2)\mkleeneclose{}\mcdot{}  THENM  Eq)
  THEN  EqCDA
  THEN  Auto)

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