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Step * of Lemma bag-filter-wf2

∀[T:Type]. ∀[bs:bag(T)]. ∀[p:{b:T| b ↓∈ bs}  ⟶ 𝔹].  ([x∈bs|p[x]] ∈ bag({x:{b:T| b ↓∈ bs} | ↑p[x]} ))
BY
{ ((UnivCD THENA Auto)
   THEN (InstLemma `bag-filter_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:Type].  \mforall{}[bs:bag(T)].  \mforall{}[p:\{b:T|  b  \mdownarrow{}\mmember{}  bs\}    {}\mrightarrow{}  \mBbbB{}].    ([x\mmember{}bs|p[x]]  \mmember{}  bag(\{x:\{b:T|  b  \mdownarrow{}\mmember{}  bs\}  |  \muparrow{}p[x]\}  )\000C)


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  (InstLemma  `bag-filter\_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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