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Step * 1 2 1 1 of Lemma satisfies-negate-poly-constraints


1. f : ℤ ⟶ ℤ
2. u : polynomial-constraints()
⊢ ∀v1:polynomial-constraints() List
    ((∃X∈v1. satisfies-poly-constraints(f;X))
    ⇐⇒ (∃Z∈v1. satisfies-poly-constraints(f;Z))
        ∧ (∀X∈[].(∃Z∈negate-poly-constraint(X). satisfies-poly-constraints(f;Z))))
BY
{ (RWO "l_all_nil_iff" 0 THEN Auto) }

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Latex:

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Latex:

1.  f  :  \mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}
2.  u  :  polynomial-constraints()
\mvdash{}  \mforall{}v1:polynomial-constraints()  List
        ((\mexists{}X\mmember{}v1.  satisfies-poly-constraints(f;X))
        \mLeftarrow{}{}\mRightarrow{}  (\mexists{}Z\mmember{}v1.  satisfies-poly-constraints(f;Z))
                \mwedge{}  (\mforall{}X\mmember{}[].(\mexists{}Z\mmember{}negate-poly-constraint(X).  satisfies-poly-constraints(f;Z))))


By

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Latex:
(RWO  "l\_all\_nil\_iff"  0  THEN  Auto)

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