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at.logic.gapt.proofs.lk

AndLeft2Rule

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object AndLeft2Rule

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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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    Replaces a formula term2 with the conjunction
    term1 ∧ term2 in the antecedent of a sequent.
    If term1 occurs more than once, only one occurrence is replaced.
    
    The rule:
        (rest of s1)
      sL, term2 |- sR
    ----------------------- (AndLeft2)
    sL, term1 ∧ term2 |- sR
    

    Replaces a formula term2 with the conjunction
    term1 ∧ term2 in the antecedent of a sequent.
    If term1 occurs more than once, only one occurrence is replaced.
    
    The rule:
        (rest of s1)
      sL, term2 |- sR
    ----------------------- (AndLeft2)
    sL, term1 ∧ term2 |- sR
    

    s1

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

    term1

    The new term to add.

    term2

    The term to be replaced by the new conjunct.

    returns

    An LK Proof ending with the new inference.

  5. def apply(s1: OccSequent, term1: HOLFormula, term2oc: FormulaOccurrence): Sequent[FormulaOccurrence]

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    Replaces a formula F (marked by term2oc) with the conjunction term1 ∧ F in the antecedent of a sequent.

    Replaces a formula F (marked by term2oc) with the conjunction term1 ∧ F in the antecedent of a sequent. This function merely returns a sequent, not a proof.

    s1

    The sequent (sL, F |- sR).

    term1

    The new term to add.

    term2oc

    The occurrence of F in the antecedent of s1

    returns

    The sequent (sL, F ∧ term2 |- sR).

  6. def apply(s1: LKProof, term1: HOLFormula, term2oc: FormulaOccurrence): UnaryTree[OccSequent] with UnaryLKProof with AuxiliaryFormulas with PrincipalFormulas { def rule: at.logic.gapt.proofs.lk.AndLeft2RuleType.type }

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    Replaces a formula F (marked by term2oc) with the conjunction
    term1 ∧ F in the antecedent of a sequent.
    
    The rule:
        (rest of s1)
        sL, F |- sR
    ------------------- (AndLeft2)
    sL, term1 ∧ F |- sR
    

    Replaces a formula F (marked by term2oc) with the conjunction
    term1 ∧ F in the antecedent of a sequent.
    
    The rule:
        (rest of s1)
        sL, F |- sR
    ------------------- (AndLeft2)
    sL, term1 ∧ F |- sR
    

    s1

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

    term1

    The new term to add.

    term2oc

    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 right subformula.

    Returns the right subformula.

    main

    A formula of the form l And r

    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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