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Step * 2 1 of Lemma permute-to-front-permutation


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

1
1. [T] : Type
2. L : T List
3. idxs : ℕ List
4. v : ℕ||L|| List
5. (filter(λi.int-list-member(i;idxs);upto(||L||)) @ filter(λi.(¬bint-list-member(i;idxs));upto(||L||)))
= v
∈ (ℕ||L|| List)
⊢ Inj(ℕ||L||;ℕ||L||;λi.v[i])

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Latex:

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Latex:

1.  [T]  :  Type
2.  L  :  T  List
3.  idxs  :  \mBbbN{}  List
\mvdash{}  Inj(\mBbbN{}||L||;\mBbbN{}||L||;\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])


By

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Latex:
xxx(GenConclAtAddrType  \mBbbN{}||L||  List  [3;1;2]\mcdot{}  THENA  Auto)xxx

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