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Step * 4 of Lemma satisfies_int_formula_dnf


1. left : int_formula()
2. right : int_formula()
3. ∀f:ℤ ⟶ ℤ. (int_formula_prop(f;left) ⇐⇒ (∃X∈int_formula_dnf(left). satisfies-poly-constraints(f;X)))
4. ∀f:ℤ ⟶ ℤ. (int_formula_prop(f;right) ⇐⇒ (∃X∈int_formula_dnf(right). satisfies-poly-constraints(f;X)))
5. f : ℤ ⟶ ℤ
⊢ int_formula_prop(f;left) ∧ int_formula_prop(f;right)
⇐⇒ (∃X∈and-poly-constraints(int_formula_dnf(left);int_formula_dnf(right)). satisfies-poly-constraints(f;X))
BY
{ ((RWO "3 4" 0 THENA Auto) THEN RWO "satisfies-and-poly-constraints" 0 THEN Auto) }

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Latex:

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Latex:

1.  left  :  int\_formula()
2.  right  :  int\_formula()
3.  \mforall{}f:\mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}
          (int\_formula\_prop(f;left)  \mLeftarrow{}{}\mRightarrow{}  (\mexists{}X\mmember{}int\_formula\_dnf(left).  satisfies-poly-constraints(f;X)))
4.  \mforall{}f:\mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}
          (int\_formula\_prop(f;right)  \mLeftarrow{}{}\mRightarrow{}  (\mexists{}X\mmember{}int\_formula\_dnf(right).  satisfies-poly-constraints(f;X)))
5.  f  :  \mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}
\mvdash{}  int\_formula\_prop(f;left)  \mwedge{}  int\_formula\_prop(f;right)
\mLeftarrow{}{}\mRightarrow{}  (\mexists{}X\mmember{}and-poly-constraints(int\_formula\_dnf(left);int\_formula\_dnf(right)).  ...)


By

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Latex:
((RWO  "3  4"  0  THENA  Auto)  THEN  RWO  "satisfies-and-poly-constraints"  0  THEN  Auto)

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