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Step * of Lemma bag-mapfilter-append

∀[T:Type]. ∀[a:bag(T)]. ∀[b:bag(Top)]. ∀[f:Top]. ∀[P:T ⟶ 𝔹].
  (bag-mapfilter(f;P;a + b) ~ bag-mapfilter(f;P;a) + bag-mapfilter(f;P;b))
BY
{ (Auto
   THEN RepUR ``bag-mapfilter`` 0
   THEN (RWO "bag-filter-append" 0 THENA Auto)
   THEN RWO "bag-map-append" 0
   THEN Auto
   THEN DoSubsume
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[a:bag(T)].  \mforall{}[b:bag(Top)].  \mforall{}[f:Top].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbB{}].
    (bag-mapfilter(f;P;a  +  b)  \msim{}  bag-mapfilter(f;P;a)  +  bag-mapfilter(f;P;b))


By

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Latex:
(Auto
  THEN  RepUR  ``bag-mapfilter``  0
  THEN  (RWO  "bag-filter-append"  0  THENA  Auto)
  THEN  RWO  "bag-map-append"  0
  THEN  Auto
  THEN  DoSubsume
  THEN  Auto)

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