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Step * of Lemma bag-combine-assoc

∀[f,g:Top]. ∀[bs:bag(Top)].  (⋃y∈⋃x∈bs.f[x].g[y] ~ ⋃x∈bs.⋃y∈f[x].g[y])
BY
{ ((UnivCD THENA Auto)
   THEN RepUR ``bag-combine bag-union bag-map`` 0
   THEN (RWO "concat-map-assoc" 0 THENA Auto)
   THEN Reduce 0
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[f,g:Top].  \mforall{}[bs:bag(Top)].    (\mcup{}y\mmember{}\mcup{}x\mmember{}bs.f[x].g[y]  \msim{}  \mcup{}x\mmember{}bs.\mcup{}y\mmember{}f[x].g[y])


By

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Latex:
((UnivCD  THENA  Auto)
  THEN  RepUR  ``bag-combine  bag-union  bag-map``  0
  THEN  (RWO  "concat-map-assoc"  0  THENA  Auto)
  THEN  Reduce  0
  THEN  Auto)

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