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Step * of Lemma coW-ext

∀[A:Type]. ∀[B:A ⟶ Type].  coW(A;a.B[a]) ≡ a:A × (B[a] ⟶ coW(A;a.B[a]))
BY
{ ((UnivCD THENA Auto)
   THEN (InstLemma `param-co-W-ext` [⌜Unit⌝;⌜λ2x.A⌝;⌜λ2x a.B[a]⌝;⌜so_lambda(p,a,b.⋅)⌝]⋅ THENA Auto)
   THEN (D -1 With ⌜⋅⌝  THENA Auto)
   THEN Reduce -1
   THEN Fold `coW` (-1)
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].    coW(A;a.B[a])  \mequiv{}  a:A  \mtimes{}  (B[a]  {}\mrightarrow{}  coW(A;a.B[a]))


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  (InstLemma  `param-co-W-ext`  [\mkleeneopen{}Unit\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.A\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x  a.B[a]\mkleeneclose{};\mkleeneopen{}so\_lambda(p,a,b.\mcdot{})\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (D  -1  With  \mkleeneopen{}\mcdot{}\mkleeneclose{}    THENA  Auto)
  THEN  Reduce  -1
  THEN  Fold  `coW`  (-1)
  THEN  Auto)

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