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Step * 4 of Lemma bag-filter_wf

.....antecedent..... 
1. T : Type
2. p : T ⟶ 𝔹
3. as : T List
4. bs : T List
5. permutation(T;as;bs)
⊢ permutation({x:T| ↑p[x]} ;filter(λx.p[x];as);filter(λx.p[x];bs))
BY
{ (InstLemma `permutation-filter` [⌜T⌝;⌜as⌝;⌜bs⌝;⌜λ2x.p[x]⌝]⋅ THEN Auto) }

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Latex:

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Latex:
.....antecedent..... 
1.  T  :  Type
2.  p  :  T  {}\mrightarrow{}  \mBbbB{}
3.  as  :  T  List
4.  bs  :  T  List
5.  permutation(T;as;bs)
\mvdash{}  permutation(\{x:T|  \muparrow{}p[x]\}  ;filter(\mlambda{}x.p[x];as);filter(\mlambda{}x.p[x];bs))


By

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Latex:
(InstLemma  `permutation-filter`  [\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}as\mkleeneclose{};\mkleeneopen{}bs\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.p[x]\mkleeneclose{}]\mcdot{}  THEN  Auto)

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