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


1. f : ℤ ⟶ ℤ
2. u : polynomial-constraints()
3. v : polynomial-constraints() List
⊢ (∃X∈negate-poly-constraints([u / v]). satisfies-poly-constraints(f;X))
⇐⇒ (∀X∈[u / v].(∃Z∈negate-poly-constraint(X). satisfies-poly-constraints(f;Z)))
BY
{ ((RepUR ``negate-poly-constraints`` 0 THEN (RWO "l_all_cons" 0 THENA Auto))
   THEN (GenConclTerm ⌜negate-poly-constraint(u)⌝⋅ THENA Auto)
   THEN Thin (-1)
   THEN MoveToConcl (-1)) }

1
1. f : ℤ ⟶ ℤ
2. u : polynomial-constraints()
3. v : polynomial-constraints() List
⊢ ∀v1:polynomial-constraints() List
    ((∃X∈accumulate (with value sofar and list item X):
          and-poly-constraints(sofar;negate-poly-constraint(X))
         over list:
           v
         with starting value:
          v1). satisfies-poly-constraints(f;X))
    ⇐⇒ (∃Z∈v1. satisfies-poly-constraints(f;Z))
        ∧ (∀X∈v.(∃Z∈negate-poly-constraint(X). satisfies-poly-constraints(f;Z))))

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Latex:

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Latex:

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


By

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Latex:
((RepUR  ``negate-poly-constraints``  0  THEN  (RWO  "l\_all\_cons"  0  THENA  Auto))
  THEN  (GenConclTerm  \mkleeneopen{}negate-poly-constraint(u)\mkleeneclose{}\mcdot{}  THENA  Auto)
  THEN  Thin  (-1)
  THEN  MoveToConcl  (-1))

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