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Step * of Lemma bag-filter-split

∀[T:Type]. ∀[p:T ⟶ 𝔹]. ∀[bs:bag(T)].  (([x∈bs|p[x]] + [x∈bs|¬bp[x]]) = bs ∈ bag(T))
BY
{ (Auto
   THEN BagToList (-1)
   THEN Auto
   THEN Try ((DoSubsume THEN Auto))
   THEN RepUR ``bag-append bag-filter`` 0
   THEN EqTypeCD
   THEN Auto
   THEN BLemma `permutation-split`
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[p:T  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[bs:bag(T)].    (([x\mmember{}bs|p[x]]  +  [x\mmember{}bs|\mneg{}\msubb{}p[x]])  =  bs)


By

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Latex:
(Auto
  THEN  BagToList  (-1)
  THEN  Auto
  THEN  Try  ((DoSubsume  THEN  Auto))
  THEN  RepUR  ``bag-append  bag-filter``  0
  THEN  EqTypeCD
  THEN  Auto
  THEN  BLemma  `permutation-split`
  THEN  Auto)

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