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Step * of Lemma flip-permutes-permutations-list2

∀n:ℕ. ∀i,j:ℕn.  permutation({p:ℕn ⟶ ℕn| Inj(ℕn;ℕn;p)} ;permutations-list(n);map(λf.((i, j) o f);permutations-list(n)))
BY
{ (Auto THEN BLemma `permutation-of-permutations-list` THEN Auto) }

1
1. n : ℕ
2. i : ℕn
3. j : ℕn
⊢ Bij({p:ℕn ⟶ ℕn| Inj(ℕn;ℕn;p)} ;{p:ℕn ⟶ ℕn| Inj(ℕn;ℕn;p)} ;λf.((i, j) o f))

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Latex:

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Latex:
\mforall{}n:\mBbbN{}.  \mforall{}i,j:\mBbbN{}n.
    permutation(\{p:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n|  Inj(\mBbbN{}n;\mBbbN{}n;p)\}  ;permutations-list(n);
                            map(\mlambda{}f.((i,  j)  o  f);permutations-list(n)))


By

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Latex:
(Auto  THEN  BLemma  `permutation-of-permutations-list`  THEN  Auto)

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