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Step * 7 1 of Lemma satisfies_int_formula_dnf


1. form : int_formula()
2. ∀f:ℤ ⟶ ℤ. (int_formula_prop(f;form) ⇐⇒ (∃X∈int_formula_dnf(form). satisfies-poly-constraints(f;X)))
3. f : ℤ ⟶ ℤ
4. v : polynomial-constraints() List
5. int_formula_dnf(form) = v ∈ (polynomial-constraints() List)
⊢ ¬(∃X∈v. satisfies-poly-constraints(f;X)) ⇐⇒ (∃X∈negate-poly-constraints(v). satisfies-poly-constraints(f;X))
BY
{ (RWO "not-l_exists" 0 THENA Auto) }

1
1. form : int_formula()
2. ∀f:ℤ ⟶ ℤ. (int_formula_prop(f;form) ⇐⇒ (∃X∈int_formula_dnf(form). satisfies-poly-constraints(f;X)))
3. f : ℤ ⟶ ℤ
4. v : polynomial-constraints() List
5. int_formula_dnf(form) = v ∈ (polynomial-constraints() List)
⊢ (∀X∈v.¬satisfies-poly-constraints(f;X)) ⇐⇒ (∃X∈negate-poly-constraints(v). satisfies-poly-constraints(f;X))

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Latex:

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Latex:

1.  form  :  int\_formula()
2.  \mforall{}f:\mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}
          (int\_formula\_prop(f;form)  \mLeftarrow{}{}\mRightarrow{}  (\mexists{}X\mmember{}int\_formula\_dnf(form).  satisfies-poly-constraints(f;X)))
3.  f  :  \mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}
4.  v  :  polynomial-constraints()  List
5.  int\_formula\_dnf(form)  =  v
\mvdash{}  \mneg{}(\mexists{}X\mmember{}v.  satisfies-poly-constraints(f;X))
\mLeftarrow{}{}\mRightarrow{}  (\mexists{}X\mmember{}negate-poly-constraints(v).  satisfies-poly-constraints(f;X))


By

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Latex:
(RWO  "not-l\_exists"  0  THENA  Auto)

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