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Step * 2 of Lemma add-polynom_wf


1. n : {1...}
2. ∀n:ℕn. ∀[p,q:polynom(n)].  (add-polynom(n;tt;p;q) ∈ polynom(n))
⊢ ∀[p,q:{p:polynom(n - 1) List| polyform-lead-nonzero(n;p)} ].
    (add-polynom(n;tt;p;q) ∈ {p:polynom(n - 1) List| polyform-lead-nonzero(n;p)} )
BY
{ (D -1 With ⌜n - 1⌝  THENA Auto) }

1
1. n : {1...}
2. ∀[p,q:polynom(n - 1)].  (add-polynom(n - 1;tt;p;q) ∈ polynom(n - 1))
⊢ ∀[p,q:{p:polynom(n - 1) List| polyform-lead-nonzero(n;p)} ].
    (add-polynom(n;tt;p;q) ∈ {p:polynom(n - 1) List| polyform-lead-nonzero(n;p)} )

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Latex:

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Latex:

1.  n  :  \{1...\}
2.  \mforall{}n:\mBbbN{}n.  \mforall{}[p,q:polynom(n)].    (add-polynom(n;tt;p;q)  \mmember{}  polynom(n))
\mvdash{}  \mforall{}[p,q:\{p:polynom(n  -  1)  List|  polyform-lead-nonzero(n;p)\}  ].
        (add-polynom(n;tt;p;q)  \mmember{}  \{p:polynom(n  -  1)  List|  polyform-lead-nonzero(n;p)\}  )


By

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Latex:
(D  -1  With  \mkleeneopen{}n  -  1\mkleeneclose{}    THENA  Auto)

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