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Step * of Lemma mul-polynom_wf

∀[n:ℕ]. ∀[p,q:polyform(n)].  (mul-polynom(n;p;q) ∈ polyform(n))
BY
{ (InductionOnNat THEN RecUnfold `mul-polynom` 0 THEN Reduce 0) }

1
1. n : ℤ
⊢ ∀[p,q:polyform(0)].  (p * q ∈ polyform(0))

2
1. n : ℤ
2. 0 < n
3. ∀[p,q:polyform(n - 1)].  (mul-polynom(n - 1;p;q) ∈ polyform(n - 1))
⊢ ∀[p,q:polyform(n)].
    (if n=0
        then p * q
        else eager-accum(z,a.add-polynom(n;tt;if null(z) then [] else z @ [polyconst(n - 1;0)] fi ;if poly-zero(n - 1;a)
             then []
             else map(λx.mul-polynom(n - 1;a;x);q)
             fi );polyconst(n;0);p) ∈ polyform(n))

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Latex:

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Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[p,q:polyform(n)].    (mul-polynom(n;p;q)  \mmember{}  polyform(n))


By

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Latex:
(InductionOnNat  THEN  RecUnfold  `mul-polynom`  0  THEN  Reduce  0)

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