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Step * 1 of Lemma minus-poly_wf


1. p : iMonomial() List
2. ∀i:ℕ||p||. ∀j:ℕi.  imonomial-less(p[j];p[i])
3. i : ℕ||map(λm.minus-monomial(m);p)||
4. j : ℕi
⊢ imonomial-less(map(λm.minus-monomial(m);p)[j];map(λm.minus-monomial(m);p)[i])
BY
{ ((RWO "select-map" 0 THENA Auto) THEN Reduce 0) }

1
1. p : iMonomial() List
2. ∀i:ℕ||p||. ∀j:ℕi.  imonomial-less(p[j];p[i])
3. i : ℕ||map(λm.minus-monomial(m);p)||
4. j : ℕi
⊢ imonomial-less(minus-monomial(p[j]);minus-monomial(p[i]))

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Latex:

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Latex:

1.  p  :  iMonomial()  List
2.  \mforall{}i:\mBbbN{}||p||.  \mforall{}j:\mBbbN{}i.    imonomial-less(p[j];p[i])
3.  i  :  \mBbbN{}||map(\mlambda{}m.minus-monomial(m);p)||
4.  j  :  \mBbbN{}i
\mvdash{}  imonomial-less(map(\mlambda{}m.minus-monomial(m);p)[j];map(\mlambda{}m.minus-monomial(m);p)[i])


By

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Latex:
((RWO  "select-map"  0  THENA  Auto)  THEN  Reduce  0)

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