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Step * 2 1 1 1 of Lemma satisfies-gcd-reduce-ineq-constraints


1. n : ℕ+
2. xs : {L:ℤ List| ||L|| = n ∈ ℤ} 
3. 0 < ||xs|| ∧ (hd(xs) = 1 ∈ ℤ)
⊢ ∀sat:{L:ℤ List| ||L|| = n ∈ ℤ}  List
    ((↑isl(gcd-reduce-ineq-constraints(sat;[])))
    ⇒ (∀as∈outl(gcd-reduce-ineq-constraints(sat;[])).xs ⋅ as ≥0)
    ⇒ (∀as∈[].xs ⋅ as ≥0))
BY
{ TACTIC:Auto }

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Latex:

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Latex:

1.  n  :  \mBbbN{}\msupplus{}
2.  xs  :  \{L:\mBbbZ{}  List|  ||L||  =  n\} 
3.  0  <  ||xs||  \mwedge{}  (hd(xs)  =  1)
\mvdash{}  \mforall{}sat:\{L:\mBbbZ{}  List|  ||L||  =  n\}    List
        ((\muparrow{}isl(gcd-reduce-ineq-constraints(sat;[])))
        {}\mRightarrow{}  (\mforall{}as\mmember{}outl(gcd-reduce-ineq-constraints(sat;[])).xs  \mcdot{}  as  \mgeq{}0)
        {}\mRightarrow{}  (\mforall{}as\mmember{}[].xs  \mcdot{}  as  \mgeq{}0))


By

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Latex:
TACTIC:Auto

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