betaRules top-level property

List<(Set<(LogicAtom, bool)>, (LogicAtom, bool))> betaRules

Implementation

final betaRules = [
  // Rules implying LogicAtom('composite') = true
  (
    {
      (LogicAtom('even'), true),
      (LogicAtom('positive'), true),
      (LogicAtom('prime'), false)
    },
    (LogicAtom('composite'), true)
  ),

  // Rules implying LogicAtom('even') = false
  (
    {
      (LogicAtom('composite'), false),
      (LogicAtom('positive'), true),
      (LogicAtom('prime'), false)
    },
    (LogicAtom('even'), false)
  ),

  // Rules implying LogicAtom('even') = true
  (
    {(LogicAtom('integer'), true), (LogicAtom('odd'), false)},
    (LogicAtom('even'), true)
  ),

  // Rules implying LogicAtom('extendedNegative') = true
  (
    {
      (LogicAtom('extendedPositive'), false),
      (LogicAtom('extendedReal'), true),
      (LogicAtom('zero'), false)
    },
    (LogicAtom('extendedNegative'), true)
  ),
  (
    {
      (LogicAtom('extendedNonPositive'), true),
      (LogicAtom('extendedNonzero'), true)
    },
    (LogicAtom('extendedNegative'), true)
  ),

  // Rules implying LogicAtom('extendedNonNegative') = true
  (
    {(LogicAtom('extendedNegative'), false), (LogicAtom('extendedReal'), true)},
    (LogicAtom('extendedNonNegative'), true)
  ),

  // Rules implying LogicAtom('extendedNonPositive') = true
  (
    {(LogicAtom('extendedPositive'), false), (LogicAtom('extendedReal'), true)},
    (LogicAtom('extendedNonPositive'), true)
  ),

  // Rules implying LogicAtom('extendedNonzero') = true
  (
    {(LogicAtom('extendedReal'), true), (LogicAtom('zero'), false)},
    (LogicAtom('extendedNonzero'), true)
  ),

  // Rules implying LogicAtom('extendedPositive') = true
  (
    {
      (LogicAtom('extendedNegative'), false),
      (LogicAtom('extendedReal'), true),
      (LogicAtom('zero'), false)
    },
    (LogicAtom('extendedPositive'), true)
  ),
  (
    {
      (LogicAtom('extendedNonNegative'), true),
      (LogicAtom('extendedNonzero'), true)
    },
    (LogicAtom('extendedPositive'), true)
  ),

  // Rules implying LogicAtom('extendedReal') = false
  (
    {(LogicAtom('infinite'), false), (LogicAtom('real'), false)},
    (LogicAtom('extendedReal'), false)
  ),
  (
    {
      (LogicAtom('extendedNegative'), false),
      (LogicAtom('extendedPositive'), false),
      (LogicAtom('zero'), false)
    },
    (LogicAtom('extendedReal'), false)
  ),

  // Rules implying LogicAtom('infinite') = true
  (
    {(LogicAtom('extendedReal'), true), (LogicAtom('real'), false)},
    (LogicAtom('infinite'), true)
  ),

  // Rules implying LogicAtom('irrational') = true
  (
    {(LogicAtom('rational'), false), (LogicAtom('real'), true)},
    (LogicAtom('irrational'), true)
  ),

  // Rules implying LogicAtom('negative') = true
  (
    {
      (LogicAtom('positive'), false),
      (LogicAtom('real'), true),
      (LogicAtom('zero'), false)
    },
    (LogicAtom('negative'), true)
  ),
  (
    {(LogicAtom('nonPositive'), true), (LogicAtom('nonzero'), true)},
    (LogicAtom('negative'), true)
  ),
  (
    {(LogicAtom('extendedNegative'), true), (LogicAtom('finite'), true)},
    (LogicAtom('negative'), true)
  ),

  // Rules implying LogicAtom('nonInteger') = true
  (
    {(LogicAtom('extendedReal'), true), (LogicAtom('integer'), false)},
    (LogicAtom('nonInteger'), true)
  ),

  // Rules implying LogicAtom('nonNegative') = true
  (
    {(LogicAtom('negative'), false), (LogicAtom('real'), true)},
    (LogicAtom('nonNegative'), true)
  ),
  (
    {(LogicAtom('extendedNonNegative'), true), (LogicAtom('finite'), true)},
    (LogicAtom('nonNegative'), true)
  ),

  // Rules implying LogicAtom('nonPositive') = true
  (
    {(LogicAtom('positive'), false), (LogicAtom('real'), true)},
    (LogicAtom('nonPositive'), true)
  ),
  (
    {(LogicAtom('extendedNonPositive'), true), (LogicAtom('finite'), true)},
    (LogicAtom('nonPositive'), true)
  ),

  // Rules implying LogicAtom('nonzero') = true
  (
    {(LogicAtom('extendedNonzero'), true), (LogicAtom('finite'), true)},
    (LogicAtom('nonzero'), true)
  ),

  // Rules implying LogicAtom('odd') = true
  (
    {(LogicAtom('even'), false), (LogicAtom('integer'), true)},
    (LogicAtom('odd'), true)
  ),

  // Rules implying LogicAtom('positive') = false
  (
    {
      (LogicAtom('composite'), false),
      (LogicAtom('even'), true),
      (LogicAtom('prime'), false)
    },
    (LogicAtom('positive'), false)
  ),

  // Rules implying LogicAtom('positive') = true
  (
    {
      (LogicAtom('negative'), false),
      (LogicAtom('real'), true),
      (LogicAtom('zero'), false)
    },
    (LogicAtom('positive'), true)
  ),
  (
    {(LogicAtom('nonNegative'), true), (LogicAtom('nonzero'), true)},
    (LogicAtom('positive'), true)
  ),
  (
    {(LogicAtom('extendedPositive'), true), (LogicAtom('finite'), true)},
    (LogicAtom('positive'), true)
  ),

  // Rules implying LogicAtom('prime') = true
  (
    {
      (LogicAtom('composite'), false),
      (LogicAtom('even'), true),
      (LogicAtom('positive'), true)
    },
    (LogicAtom('prime'), true)
  ),

  // Rules implying LogicAtom('real') = false
  (
    {
      (LogicAtom('negative'), false),
      (LogicAtom('positive'), false),
      (LogicAtom('zero'), false)
    },
    (LogicAtom('real'), false)
  ),

  // Rules implying LogicAtom('real') = true
  (
    {(LogicAtom('extendedReal'), true), (LogicAtom('infinite'), false)},
    (LogicAtom('real'), true)
  ),
  (
    {(LogicAtom('extendedReal'), true), (LogicAtom('finite'), true)},
    (LogicAtom('real'), true)
  ),

  // Rules implying LogicAtom('transcendental') = true
  (
    {(LogicAtom('algebraic'), false), (LogicAtom('complex'), true)},
    (LogicAtom('transcendental'), true)
  ),

  // Rules implying LogicAtom('zero') = true
  (
    {
      (LogicAtom('extendedNegative'), false),
      (LogicAtom('extendedPositive'), false),
      (LogicAtom('extendedReal'), true)
    },
    (LogicAtom('zero'), true)
  ),
  (
    {
      (LogicAtom('negative'), false),
      (LogicAtom('positive'), false),
      (LogicAtom('real'), true)
    },
    (LogicAtom('zero'), true)
  ),
  (
    {
      (LogicAtom('extendedNonNegative'), true),
      (LogicAtom('extendedNonPositive'), true)
    },
    (LogicAtom('zero'), true)
  ),
  (
    {(LogicAtom('nonNegative'), true), (LogicAtom('nonPositive'), true)},
    (LogicAtom('zero'), true)
  ),
];