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at.logic.gapt.proofs.lk

WeakeningLeftRule

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object WeakeningLeftRule

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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: OccSequent, f: HOLFormula)(implicit factory: FOFactory): Sequent[FormulaOccurrence]

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    Introduces a formula into the antecedent of a sequent.

    Introduces a formula into the antecedent of a sequent. This method merely returns an extended sequent, not a proof.

    s1

    The sequent whose antecedent is to be weakened.

    f

    The formula to introduce into s1.

    returns

    The sequent s1, with the antecedent extended by f.

  5. def apply(s1: LKProof, f: HOLFormula)(implicit factory: FOFactory): UnaryTree[OccSequent] with UnaryLKProof with PrincipalFormulas { def rule: at.logic.gapt.proofs.lk.WeakeningLeftRuleType.type }

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    Introduces a formula into the left side of a sequent.
    
    The rule:
            (rest of s1)
     sL |- sR
    ------------ (WeakeningLeft)
    sL, f |- sR
    

    Introduces a formula into the left side of a sequent.
    
    The rule:
            (rest of s1)
     sL |- sR
    ------------ (WeakeningLeft)
    sL, f |- sR
    

    s1

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

    f

    The formula to introduce below s1.

    returns

    An LKProof ending with the new inference.

  6. final def asInstanceOf[T0]: T0

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

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