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


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

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Latex:

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Latex:

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


By

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Latex:
TACTIC:(RepUR  ``gcd-reduce-ineq-constraints  accumulate\_abort``  0  THEN  Auto)

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