---

Step * 2 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])
∧ ((L o λi.filter(λi.int-list-member(i;idxs);upto(||L||)) @ filter(λi.(¬bint-list-member(i;idxs));upto(||L||))[i])
  = (L o λi.filter(λi.int-list-member(i;idxs);upto(||L||)) @ filter(λi.(¬bint-list-member(i;idxs));upto(||L||))[i])
  ∈ (T List))
BY
{ Auto }

1
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])

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

---

Latex:

---

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])
\mwedge{}  ((L  o  \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])
    =  (L  o  \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

---

Latex:
Auto

---

Home Index