Step * 7 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. : ℤ ⟶ ℤ
⊢ ¬int_formula_prop(f;form) ⇐⇒ (∃X∈negate-poly-constraints(int_formula_dnf(form)). satisfies-poly-constraints(f;X))
BY
((RWO "2" THENA Auto) THEN GenConclTerms Auto [⌜int_formula_dnf(form)⌝]⋅}

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. : ℤ ⟶ ℤ
4. 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))


Latex:


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{}
\mvdash{}  \mneg{}int\_formula\_prop(f;form)
\mLeftarrow{}{}\mRightarrow{}  (\mexists{}X\mmember{}negate-poly-constraints(int\_formula\_dnf(form)).  satisfies-poly-constraints(f;X))


By


Latex:
((RWO  "2"  0  THENA  Auto)  THEN  GenConclTerms  Auto  [\mkleeneopen{}int\_formula\_dnf(form)\mkleeneclose{}]\mcdot{})




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