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))} )`

Latex:

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

By

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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