Object

at.logic.gapt.proofs.lkOld

OrRightRule

Related Doc: package lkOld

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object OrRightRule

Source
macroRules.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, term2: HOLFormula): UnaryTree[OccSequent] with base.UnaryLKProof with AuxiliaryFormulas with PrincipalFormulas

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    Replaces a formulas term1, term2 with the disjunction
    term1 ∨ term2 in the succedent of a sequent.
    
    The rule:
        (rest of s1)
    sL |- sR, term1, term2
    ---------------------- (OrRight)
    sL |- sR, term1 ∨ term2
    

    Replaces a formulas term1, term2 with the disjunction
    term1 ∨ term2 in the succedent of a sequent.
    
    The rule:
        (rest of s1)
    sL |- sR, term1, term2
    ---------------------- (OrRight)
    sL |- sR, term1 ∨ term2
    

    s1

    The top proof with (sL |- sR, term1, term2) as the bottommost sequent.

    term1

    The first formula to be replaced in the succedent of s1.

    term2

    The second formula to be replaced in the succedent of s2.

    returns

    An LK Proof ending with the new inference.

  5. 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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    Replaces a formulas A, B (marked by term1oc & term2oc) with the disjunction
    A ∨ B in the succedent of a sequent.
    
    The rule:
        (rest of s1)
      sL|- sR, A, B
    ------------------- (OrRight)
    sL |- sR, A ∨ B
    

    Replaces a formulas A, B (marked by term1oc & term2oc) with the disjunction
    A ∨ B in the succedent of a sequent.
    
    The rule:
        (rest of s1)
      sL|- sR, A, B
    ------------------- (OrRight)
    sL |- sR, A ∨ B
    

    s1

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

    term1oc

    The occurrence of A in the succedent of s1.

    term2oc

    The occurrence of B in the succedent of s2.

    returns

    An LK Proof ending with the new inference.

  6. final def asInstanceOf[T0]: T0

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  13. final def isInstanceOf[T0]: Boolean

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

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  15. final def notify(): Unit

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  19. final def wait(): Unit

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

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