Step
*
of Lemma
bag-mapfilter-fast-eq2
∀[A,B:Type]. ∀[bs:bag(A)]. ∀[P:A ⟶ 𝔹]. ∀[f:{x:A| ↑P[x]}  ⟶ B].
  (bag-mapfilter(f;P;bs) = bag-mapfilter-fast(f;P;bs) ∈ bag(B))
BY
{ Auto }
Latex:
Latex:
\mforall{}[A,B:Type].  \mforall{}[bs:bag(A)].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[f:\{x:A|  \muparrow{}P[x]\}    {}\mrightarrow{}  B].
    (bag-mapfilter(f;P;bs)  =  bag-mapfilter-fast(f;P;bs))
By
Latex:
Auto
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