---

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


1. ineqs : iPolynomial() List
2. f : ℤ ⟶ ℤ
3. [] ∈ iPolynomial() List
⊢ ∀L:polynomial-constraints() List
    ((∃Z∈L. satisfies-poly-constraints(f;Z))
    ⇐⇒ (∃e∈[]. (0 ≤ int_term_value(f;ipolynomial-term(minus-poly(add-ipoly(e;const-poly(1))))))
        ∨ (0 ≤ int_term_value(f;ipolynomial-term(add-ipoly(e;const-poly(-1))))))
        ∨ (∃Z∈L. satisfies-poly-constraints(f;Z)))
BY
{ (RWO "l_exists_nil" 0 THEN Auto) }

---

Latex:

---

Latex:

1.  ineqs  :  iPolynomial()  List
2.  f  :  \mBbbZ{}  {}\mrightarrow{}  \mBbbZ{}
3.  []  \mmember{}  iPolynomial()  List
\mvdash{}  \mforall{}L:polynomial-constraints()  List
        ((\mexists{}Z\mmember{}L.  satisfies-poly-constraints(f;Z))
        \mLeftarrow{}{}\mRightarrow{}  (\mexists{}e\mmember{}[].  (0  \mleq{}  int\_term\_value(f;ipolynomial-term(minus-poly(add-ipoly(e;const-poly(1))))))
                \mvee{}  (0  \mleq{}  int\_term\_value(f;ipolynomial-term(add-ipoly(e;const-poly(-1))))))
                \mvee{}  (\mexists{}Z\mmember{}L.  satisfies-poly-constraints(f;Z)))


By

---

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

---

Home Index