Object

at.logic.gapt.proofs.lk

ImpRightRule

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object ImpRightRule

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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 UnaryLKProof with AuxiliaryFormulas with PrincipalFormulas

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    Takes two formulas term1 & term2 from the antecedent and
    succedent of s1, respectively, and introduces the implication
    A -> B into the succedent of s1.
    
    The rule:
         (rest of s1)
     sL, term1 |- term2, sR
    -------------------------(ImpRight)
     sL |- term1 -> term3, sR
    

    Takes two formulas term1 & term2 from the antecedent and
    succedent of s1, respectively, and introduces the implication
    A -> B into the succedent of s1.
    
    The rule:
         (rest of s1)
     sL, term1 |- term2, sR
    -------------------------(ImpRight)
     sL |- term1 -> term3, sR
    

    s1

    The proof with term1 in the antecedent and term2 in the succedent of its bottommost sequent.

    term1

    The formula in the antecedent of s1.

    term2

    The formula in the succedent of s1.

    returns

    An LK proof with the new inference.

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

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    Takes two formulas A & B (marked by term1oc in the antecedent
    and term2oc in the succedent of s1) and introduces the implication
    A -> B into the succedent of s1. This function merely returns
    the resulting sequent, not a proof
    
    The rule:
       (rest of s1)
      sL, A |- B, sR
    -------------------(ImpRight)
     sL |- A -> B, sR
    

    Takes two formulas A & B (marked by term1oc in the antecedent
    and term2oc in the succedent of s1) and introduces the implication
    A -> B into the succedent of s1. This function merely returns
    the resulting sequent, not a proof
    
    The rule:
       (rest of s1)
      sL, A |- B, sR
    -------------------(ImpRight)
     sL |- A -> B, sR
    

    s1

    The sequent with A in its antecedent and B in its succedent.

    term1oc

    The occurrence of A.

    term2oc

    The occurrence of B.

    returns

    The sequent (sL |- A -> B, sR).

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

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    Takes two formulas A & B (marked by term1oc in the antecedent
    and term2oc in the succedent of s1) and introduces the implication
    A -> B into the succedent of s1.
    
    The rule:
       (rest of s1)
      sL, A |- B, sR
    -------------------(ImpRight)
     sL |- A -> B, sR
    

    Takes two formulas A & B (marked by term1oc in the antecedent
    and term2oc in the succedent of s1) and introduces the implication
    A -> B into the succedent of s1.
    
    The rule:
       (rest of s1)
      sL, A |- B, sR
    -------------------(ImpRight)
     sL |- A -> B, sR
    

    s1

    The proof with A in the antecedent and B in the succedent of its bottommost sequent.

    term1oc

    The occurrence of A.

    term2oc

    The occurrence of B.

    returns

    An LK proof 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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  12. final def getClass(): Class[_]

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  13. def hashCode(): Int

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

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

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