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Step * 1 of Lemma permute-to-front-permutation

.....wf..... 
1. T : Type
2. L : T List
3. idxs : ℕ List
⊢ λi.filter(λi.int-list-member(i;idxs);upto(||L||)) @ filter(λi.(¬bint-list-member(i;idxs));upto(||L||))[i] ∈ ℕ||L||
  ⟶ ℕ||L||
BY
{ Auto }

1
1. T : Type
2. L : T List
3. idxs : ℕ List
4. i : ℕ||L||
⊢ i < ||filter(λi.int-list-member(i;idxs);upto(||L||))|| + ||filter(λi.(¬bint-list-member(i;idxs));upto(||L||))||

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Latex:

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Latex:
.....wf..... 
1.  T  :  Type
2.  L  :  T  List
3.  idxs  :  \mBbbN{}  List
\mvdash{}  \mlambda{}i.filter(\mlambda{}i.int-list-member(i;idxs);upto(||L||))
          @  filter(\mlambda{}i.(\mneg{}\msubb{}int-list-member(i;idxs));upto(||L||))[i]  \mmember{}  \mBbbN{}||L||  {}\mrightarrow{}  \mBbbN{}||L||


By

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Latex:
Auto

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