Step * 2 of Lemma bag-member-filter


1. Type
2. T ⟶ 𝔹
3. T
4. bs List
5. List
6. filter(λx.P[x];bs) ∈ bag(T)
7. (x ∈ L)
⊢ ↑P[x] ∈ ℙ
BY
(EqTypeHD (-2)⋅
   THEN Auto
   THEN InstLemma `member-permutation` [⌜T⌝;⌜L⌝;⌜filter(λx.P[x];bs)⌝]⋅
   THEN Auto
   THEN (FHyp (-1) [-2] THEN Auto THEN (RWO "member_filter" (-1) THENM Reduce (-1)) THEN Auto)⋅}


Latex:


Latex:

1.  T  :  Type
2.  P  :  T  {}\mrightarrow{}  \mBbbB{}
3.  x  :  T
4.  bs  :  T  List
5.  L  :  T  List
6.  L  =  filter(\mlambda{}x.P[x];bs)
7.  (x  \mmember{}  L)
\mvdash{}  \muparrow{}P[x]  \mmember{}  \mBbbP{}


By


Latex:
(EqTypeHD  (-2)\mcdot{}
  THEN  Auto
  THEN  InstLemma  `member-permutation`  [\mkleeneopen{}T\mkleeneclose{};\mkleeneopen{}L\mkleeneclose{};\mkleeneopen{}filter(\mlambda{}x.P[x];bs)\mkleeneclose{}]\mcdot{}
  THEN  Auto
  THEN  (FHyp  (-1)  [-2]  THEN  Auto  THEN  (RWO  "member\_filter"  (-1)  THENM  Reduce  (-1))  THEN  Auto)\mcdot{})




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