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Step * of Lemma bag-filter-map2

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∀[T,A:Type]. ∀[f:A ⟶ T]. ∀[p:T ⟶ 𝔹]. ∀[as:bag(A)].
  ([x∈bag-map(f;as)|p[x]] = bag-map(f;[x∈as|p[f x]]) ∈ bag({x:T| ↑p[x]} ))
BY
{ (Auto THEN (BagToList (-1) THENA Auto) THEN ExtWith [`a'] [⌜Top⌝]⋅ THEN Auto) }

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Latex:

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Latex:
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\mforall{}[T,A:Type].  \mforall{}[f:A  {}\mrightarrow{}  T].  \mforall{}[p:T  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[as:bag(A)].
    ([x\mmember{}bag-map(f;as)|p[x]]  =  bag-map(f;[x\mmember{}as|p[f  x]]))


By

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Latex:
(Auto  THEN  (BagToList  (-1)  THENA  Auto)  THEN  ExtWith  [`a']  [\mkleeneopen{}Top\mkleeneclose{}]\mcdot{}  THEN  Auto)

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