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Step * of Lemma bag-mapfilter-wf2

∀[T,A:Type]. ∀[bs:bag(T)]. ∀[p:{b:T| b ↓∈ bs}  ⟶ 𝔹]. ∀[f:{x:{b:T| b ↓∈ bs} | ↑p[x]}  ⟶ A].
  (bag-mapfilter(f;p;bs) ∈ bag(A))
BY
{ ((UnivCD THENA Auto)
   THEN (InstLemma `bag-mapfilter_wf` [⌜{b:T| b ↓∈ bs} ⌝]⋅ THENA Auto)
   THEN BHyp (-1) 
   THEN Try (Complete (Auto))
   THEN BLemma `bag-subtype`
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T,A:Type].  \mforall{}[bs:bag(T)].  \mforall{}[p:\{b:T|  b  \mdownarrow{}\mmember{}  bs\}    {}\mrightarrow{}  \mBbbB{}].  \mforall{}[f:\{x:\{b:T|  b  \mdownarrow{}\mmember{}  bs\}  |  \muparrow{}p[x]\}    {}\mrightarrow{}  A].
    (bag-mapfilter(f;p;bs)  \mmember{}  bag(A))


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  (InstLemma  `bag-mapfilter\_wf`  [\mkleeneopen{}\{b:T|  b  \mdownarrow{}\mmember{}  bs\}  \mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  BHyp  (-1) 
  THEN  Try  (Complete  (Auto))
  THEN  BLemma  `bag-subtype`
  THEN  Auto)

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