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Step * of Lemma sum-as-bag-accum

∀[n:ℕ]. ∀[f:ℕn ⟶ ℤ].  (Σ(f[x] | x < n) ~ bag-accum(x,y.x + y;0;[x∈bag-map(λx.f[x];upto(n))|¬b(x =z 0)]))
BY
{ (Auto THEN (RWO "sum-as-accum-filter" 0 THENA Auto) THEN RepUR ``bag-accum bag-map bag-filter`` 0 THEN Auto) }

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Latex:

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Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[f:\mBbbN{}n  {}\mrightarrow{}  \mBbbZ{}].
    (\mSigma{}(f[x]  |  x  <  n)  \msim{}  bag-accum(x,y.x  +  y;0;[x\mmember{}bag-map(\mlambda{}x.f[x];upto(n))|\mneg{}\msubb{}(x  =\msubz{}  0)]))


By

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Latex:
(Auto
  THEN  (RWO  "sum-as-accum-filter"  0  THENA  Auto)
  THEN  RepUR  ``bag-accum  bag-map  bag-filter``  0
  THEN  Auto)

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