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Step * of Lemma full-omega_wf

∀[fmla:int_formula()]. (full-omega(fmla) ∈ {b:𝔹| b = ff ⇒ (¬satisfiable_int_formula(fmla))} )
BY
{ (Auto
   THEN Unfold `full-omega` 0
   THEN (InstLemma `satisfiable_int_formula_dnf` [⌜fmla⌝]⋅ THENA Auto)
   THEN MoveToConcl (-1)
   THEN (GenConclTerm ⌜int_formula_dnf(fmla)⌝⋅ THENA Auto)
   THEN (RWO "evalall-reduce" 0 THENA Auto)) }

1
1. fmla : int_formula()
2. v : polynomial-constraints() List
3. int_formula_dnf(fmla) = v ∈ (polynomial-constraints() List)
⊢ valueall-type(polynomial-constraints() List)

2
1. fmla : int_formula()
2. v : polynomial-constraints() List
3. int_formula_dnf(fmla) = v ∈ (polynomial-constraints() List)
⊢ (satisfiable_int_formula(fmla) ⇐⇒ (∃X∈v. satisfiable_polynomial_constraints(X)))
⇒ (eval dnf = v in
    eager-accum(sat,pc.sat
    ∨blet eqs,ineqs = pcs-to-integer-problem(pc) 
      in case omega(eqs;ineqs) of inl(x) => tt | inr(_) => ff;ff;dnf) ∈ {b:𝔹| 
                                                                         b = ff ⇒ (¬satisfiable_int_formula(fmla))} )

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Latex:

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Latex:
\mforall{}[fmla:int\_formula()].  (full-omega(fmla)  \mmember{}  \{b:\mBbbB{}|  b  =  ff  {}\mRightarrow{}  (\mneg{}satisfiable\_int\_formula(fmla))\}  )


By

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Latex:
(Auto
  THEN  Unfold  `full-omega`  0
  THEN  (InstLemma  `satisfiable\_int\_formula\_dnf`  [\mkleeneopen{}fmla\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  MoveToConcl  (-1)
  THEN  (GenConclTerm  \mkleeneopen{}int\_formula\_dnf(fmla)\mkleeneclose{}\mcdot{}  THENA  Auto)
  THEN  (RWO  "evalall-reduce"  0  THENA  Auto))

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