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Step * of Lemma bag-filter-combine2

∀[T,U:Type]. ∀[P:T ⟶ 𝔹]. ∀[f:U ⟶ bag(T)]. ∀[b:bag(U)].  ([x∈⋃z∈b.f[z]|P[x]] = ⋃z∈b.[x∈f[z]|P[x]] ∈ bag({x:T| ↑P[x]} ))
BY
{ ((UnivCD THENA Auto)
   THEN Unfold `bag-combine` 0
   THEN (RWO "bag-filter-union" 0 THENA Auto)
   THEN (RWO "bag-map-map" 0 THENA Auto)
   THEN RepUR ``compose`` 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T,U:Type].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[f:U  {}\mrightarrow{}  bag(T)].  \mforall{}[b:bag(U)].    ([x\mmember{}\mcup{}z\mmember{}b.f[z]|P[x]]  =  \mcup{}z\mmember{}b.[x\mmember{}f[z]|P[x]])


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  Unfold  `bag-combine`  0
  THEN  (RWO  "bag-filter-union"  0  THENA  Auto)
  THEN  (RWO  "bag-map-map"  0  THENA  Auto)
  THEN  RepUR  ``compose``  0
  THEN  Auto)

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