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Step * of Lemma W-ext

∀[A:Type]. ∀[B:A ⟶ Type].  W(A;a.B[a]) ≡ a:A × (B[a] ⟶ W(A;a.B[a]))
BY
{ (Auto
   THEN (InstLemma `param-W-ext` [⌜Unit⌝;⌜λ2p.A⌝;⌜λ2p a.B[a]⌝;⌜so_lambda(p,a,b.⋅)⌝]⋅ THENA Auto)
   THEN (With ⌜⋅⌝ (D (-1))⋅ THENA Auto)
   THEN Reduce (-1)
   THEN Fold `W` (-1)
   THEN Trivial) }

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Latex:

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


By

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

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