Object

at.logic.gapt.proofs.lkOld

NegRightRule

Related Doc: package lkOld

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object NegRightRule

Source
propositionalRules.scala
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  1. final def !=(arg0: Any): Boolean

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

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  4. def apply(s1: LKProof, term1: HOLFormula): UnaryTree[OccSequent] with base.UnaryLKProof with AuxiliaryFormulas with PrincipalFormulas

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  5. def apply(s1: OccSequent, term1oc: FormulaOccurrence): Sequent[FormulaOccurrence]

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    Replaces a formula F (marked by term1oc) in the antecedent of a sequent with its negation -F in the succedent of that sequent.

    Replaces a formula F (marked by term1oc) in the antecedent of a sequent with its negation -F in the succedent of that sequent. This function merely returns the resulting sequent, not a proof.

    s1

    The sequent (sL, F |- sR).

    term1oc

    The occurrence of F in the anteedent of s1.

    returns

    The sequent (sL |- -F, sR).

  6. def apply(s1: LKProof, term1oc: FormulaOccurrence): UnaryTree[OccSequent] with base.UnaryLKProof with AuxiliaryFormulas with PrincipalFormulas { def rule: at.logic.gapt.proofs.lkOld.NegRightRuleType.type }

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    Replaces a formula F (marked by term1oc) in the antecedent of
    a sequent  with its negation -F in the succedent of that sequent.
    
    The rule:
     (rest of s1)
     sL, F |- sR
    -------------- (NegLeft)
    sL |- -F, sR
    

    Replaces a formula F (marked by term1oc) in the antecedent of
    a sequent  with its negation -F in the succedent of that sequent.
    
    The rule:
     (rest of s1)
     sL, F |- sR
    -------------- (NegLeft)
    sL |- -F, sR
    

    s1

    The top proof with (sL, F |- sR) as the bottommost sequent.

    term1oc

    The occurrence of F in the antecedent of s1.

    returns

    An LK Proof ending with the new inference.

  7. final def asInstanceOf[T0]: T0

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  8. def clone(): AnyRef

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  9. def computeAux(main: HOLFormula): HOLFormula

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    Returns the subformula.

    Returns the subformula.

    main

    A formula of the Not l

    returns

    l.

  10. final def eq(arg0: AnyRef): Boolean

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  11. def equals(arg0: Any): Boolean

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  12. def finalize(): Unit

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  13. final def getClass(): Class[_]

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  14. def hashCode(): Int

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  15. final def isInstanceOf[T0]: Boolean

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  16. final def ne(arg0: AnyRef): Boolean

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  17. final def notify(): Unit

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  18. final def notifyAll(): Unit

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  19. final def synchronized[T0](arg0: ⇒ T0): T0

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  20. def toString(): String

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  21. def unapply(proof: LKProof): Option[(LKProof, OccSequent, FormulaOccurrence, FormulaOccurrence)]

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  22. final def wait(): Unit

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  23. final def wait(arg0: Long, arg1: Int): Unit

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  24. final def wait(arg0: Long): Unit

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