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Step * 1 2 of Lemma minus-poly-ringeq


1. r : Rng
2. p : iMonomial() List
3. ∀i:ℕ||p||. ∀j:ℕi.  imonomial-less(p[j];p[i])
⊢ ipolynomial-term(minus-poly(p)) ≡ "-"ipolynomial-term(p)
BY
{ xxx(ListInd 2 THEN Auto)xxx }

1
1. r : Rng
2. ∀i:ℕ||[]||. ∀j:ℕi.  imonomial-less([][j];[][i])
⊢ ipolynomial-term(minus-poly([])) ≡ "-"ipolynomial-term([])

2
1. r : Rng
2. u : iMonomial()
3. v : iMonomial() List
4. (∀i:ℕ||v||. ∀j:ℕi.  imonomial-less(v[j];v[i])) ⇒ ipolynomial-term(minus-poly(v)) ≡ "-"ipolynomial-term(v)
5. ∀i:ℕ||[u / v]||. ∀j:ℕi.  imonomial-less([u / v][j];[u / v][i])
⊢ ipolynomial-term(minus-poly([u / v])) ≡ "-"ipolynomial-term([u / v])

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Latex:

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Latex:

1.  r  :  Rng
2.  p  :  iMonomial()  List
3.  \mforall{}i:\mBbbN{}||p||.  \mforall{}j:\mBbbN{}i.    imonomial-less(p[j];p[i])
\mvdash{}  ipolynomial-term(minus-poly(p))  \mequiv{}  "-"ipolynomial-term(p)


By

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Latex:
xxx(ListInd  2  THEN  Auto)xxx

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