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Step * 2 2 of Lemma mul-ipoly-equiv


1. u : iMonomial()
2. v : iMonomial() List
3. q : iMonomial() List
4. ¬(q = [] ∈ (iMonomial() List))
⊢ ipolynomial-term(eager-accum(sofar,m.add-ipoly(sofar;mul-mono-poly(m;q));mul-mono-poly(u;q);v)) 
  ≡ ipolynomial-term([u / v]) (*) ipolynomial-term(q)
BY
{ Thin (-1) }

1
1. u : iMonomial()
2. v : iMonomial() List
3. q : iMonomial() List
⊢ ipolynomial-term(eager-accum(sofar,m.add-ipoly(sofar;mul-mono-poly(m;q));mul-mono-poly(u;q);v)) 
  ≡ ipolynomial-term([u / v]) (*) ipolynomial-term(q)

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Latex:

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Latex:

1.  u  :  iMonomial()
2.  v  :  iMonomial()  List
3.  q  :  iMonomial()  List
4.  \mneg{}(q  =  [])
\mvdash{}  ipolynomial-term(eager-accum(sofar,m.add-ipoly(sofar;mul-mono-poly(m;q));mul-mono-poly(u;q);v)) 
    \mequiv{}  ipolynomial-term([u  /  v])  (*)  ipolynomial-term(q)


By

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Latex:
Thin  (-1)

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