Object

at.logic.gapt.proofs.lkOld

ContractionRightRule

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object ContractionRightRule

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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    Eliminates a duplicate occurrence of a formula term1
    from the succedent of a sequent. The two occurrences are automatically
    chosen; if term1 occurs less than twice, an exception is thrown.
    If term1 occurs more than twice, multiple applications of this
    function are needed to remove all duplicate occurrences.
    
    The rule:
     (rest of s1)
    sL |- sR, term1, term1
    ----------------------- (ContractionRight)
    sL |- sR, term1
    

    Eliminates a duplicate occurrence of a formula term1
    from the succedent of a sequent. The two occurrences are automatically
    chosen; if term1 occurs less than twice, an exception is thrown.
    If term1 occurs more than twice, multiple applications of this
    function are needed to remove all duplicate occurrences.
    
    The rule:
     (rest of s1)
    sL |- sR, term1, term1
    ----------------------- (ContractionRight)
    sL |- sR, term1
    

    s1

    The top proof with (sL |- sR, term1, term1) as the bottommost sequent.

    term1

    The formula whose duplicate occurrence is to be removed.

    returns

    An LK Proof ending with the new inference.

  5. def apply(s1: OccSequent, term1oc: FormulaOccurrence, term2oc: FormulaOccurrence): Sequent[FormulaOccurrence]

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    Eliminates a duplicate occurrence of a formula F (marked by term1oc and term2oc) from the succecedent of a sequent.

    Eliminates a duplicate occurrence of a formula F (marked by term1oc and term2oc) from the succecedent of a sequent. This method merely returns the changed sequent, not a proof.

    s1

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

    term1oc

    The first occurrence of F

    term2oc

    The second occurrence of F

    returns

    The sequent (sL |- sR, F).

  6. def apply(s1: LKProof, term1oc: FormulaOccurrence, term2oc: FormulaOccurrence): UnaryTree[OccSequent] with base.UnaryLKProof with AuxiliaryFormulas with PrincipalFormulas { def rule: at.logic.gapt.proofs.lkOld.ContractionRightRuleType.type }

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    Eliminates a duplicate occurrence of a formula F
    (marked by term1oc and term2oc) from the succedent of a sequent.
    
    The rule:
     (rest of s1)
    sL |- sR, F, F
    --------------- (ContractionRight)
    sL |- sR, F
    

    Eliminates a duplicate occurrence of a formula F
    (marked by term1oc and term2oc) from the succedent of a sequent.
    
    The rule:
     (rest of s1)
    sL |- sR, F, F
    --------------- (ContractionRight)
    sL |- sR, F
    

    s1

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

    term1oc

    The first occurrence of F

    term2oc

    The second occurrence of F

    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. final def eq(arg0: AnyRef): Boolean

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  10. def equals(arg0: Any): Boolean

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  11. def finalize(): Unit

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  14. final def isInstanceOf[T0]: Boolean

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

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  16. final def notify(): Unit

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  17. final def notifyAll(): Unit

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

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  19. def toString(): String

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

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  21. final def wait(): Unit

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

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