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Step * 2 1 2 1 1 of Lemma permutation-sign-compose


1. n : ℕ
⊢ ∀h:{p:ℕn ⟶ ℕn| Inj(ℕn;ℕn;p)} . ∀i,j:ℕn.
    permutation-sign(n;h o (i, j)) = (-permutation-sign(n;h)) ∈ ℤ supposing ¬(i = j ∈ ℤ)
BY
{ ((InstLemma `permutation-sign-flip` [⌜n⌝]⋅ THENA Auto) THEN RepeatFor 3 (ParallelLast') THEN Auto) }

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Latex:

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Latex:

1.  n  :  \mBbbN{}
\mvdash{}  \mforall{}h:\{p:\mBbbN{}n  {}\mrightarrow{}  \mBbbN{}n|  Inj(\mBbbN{}n;\mBbbN{}n;p)\}  .  \mforall{}i,j:\mBbbN{}n.
        permutation-sign(n;h  o  (i,  j))  =  (-permutation-sign(n;h))  supposing  \mneg{}(i  =  j)


By

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Latex:
((InstLemma  `permutation-sign-flip`  [\mkleeneopen{}n\mkleeneclose{}]\mcdot{}  THENA  Auto)  THEN  RepeatFor  3  (ParallelLast')  THEN  Auto)

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