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


1. f : ℤ ⟶ ℤ
2. L : polynomial-constraints() List
3. (∃X∈negate-poly-constraints(L). satisfies-poly-constraints(f;X))
⇐⇒ (∀X∈L.(∃Z∈negate-poly-constraint(X). satisfies-poly-constraints(f;Z)))
⊢ (∀X∈L.¬satisfies-poly-constraints(f;X)) ⇐⇒ (∀X∈L.(∃Z∈negate-poly-constraint(X). satisfies-poly-constraints(f;Z)))
BY
{ ((RWO  "l_all_iff" 0 THENA Auto) THEN RWO  "satisfies-negate-poly-constraint" 0 THEN Auto) }

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Latex:

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Latex:

1.  f  :  \mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}
2.  L  :  polynomial-constraints()  List
3.  (\mexists{}X\mmember{}negate-poly-constraints(L).  satisfies-poly-constraints(f;X))
\mLeftarrow{}{}\mRightarrow{}  (\mforall{}X\mmember{}L.(\mexists{}Z\mmember{}negate-poly-constraint(X).  satisfies-poly-constraints(f;Z)))
\mvdash{}  (\mforall{}X\mmember{}L.\mneg{}satisfies-poly-constraints(f;X))
\mLeftarrow{}{}\mRightarrow{}  (\mforall{}X\mmember{}L.(\mexists{}Z\mmember{}negate-poly-constraint(X).  satisfies-poly-constraints(f;Z)))


By

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Latex:
((RWO    "l\_all\_iff"  0  THENA  Auto)  THEN  RWO    "satisfies-negate-poly-constraint"  0  THEN  Auto)

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