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at.logic.gapt.proofs.lk

DefinitionLeftRule

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object DefinitionLeftRule

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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, aux: HOLFormula, main: HOLFormula): UnaryTree[OccSequent] with UnaryLKProof with AuxiliaryFormulas with PrincipalFormulas

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    Constructs a proof ending with a DefinitionLeft rule.
    In it, a term aux is replaced by formula main,
    i.e. aux is defined as main.
    
    This rule does not check for contradictory definitions elsewhere in s1, and thus
    the burden of correct usage is on the programmer!
    Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof.
    
    The rule:
     (rest of s1)
     sL, aux |- sR
    ---------------- (DefinitionLeft)
    sL, main |- sR
    

    Constructs a proof ending with a DefinitionLeft rule.
    In it, a term aux is replaced by formula main,
    i.e. aux is defined as main.
    
    This rule does not check for contradictory definitions elsewhere in s1, and thus
    the burden of correct usage is on the programmer!
    Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof.
    
    The rule:
     (rest of s1)
     sL, aux |- sR
    ---------------- (DefinitionLeft)
    sL, main |- sR
    

    s1

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

    aux

    The term to be replaced by its definition.

    main

    The formula with which aux is to be replaced.

    returns

    An LK Proof ending with the new inference.

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

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    Replaces a term by its definition.
    In the returned sequent, a term A (marked by term1oc) is replaced by formula main,
    i.e. A is defined as main.
    
    This rule does not check for contradictory definitions elsewhere in s1, and thus
    the burden of correct usage is on the programmer!
    Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof.
    
    The rule:
      (rest of s1)
      sL, A |- sR
    --------------- (DefinitionLeft)
    sL, main |- sR
    

    Replaces a term by its definition.
    In the returned sequent, a term A (marked by term1oc) is replaced by formula main,
    i.e. A is defined as main.
    
    This rule does not check for contradictory definitions elsewhere in s1, and thus
    the burden of correct usage is on the programmer!
    Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof.
    
    The rule:
      (rest of s1)
      sL, A |- sR
    --------------- (DefinitionLeft)
    sL, main |- sR
    

    s1

    Sequent (sL, A |- sR).

    term1oc

    The occurrence of A in s1.

    main

    The formula with which A is to be replaced.

    returns

    The sequent (sL, main |- sR).

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

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    Constructs a proof ending with a DefinitionLeft rule.
    In it, a term A (marked by term1oc) is replaced by formula main,
    i.e. A is defined as main.
    
    This rule does not check for contradictory definitions elsewhere in s1, and thus
    the burden of correct usage is on the programmer!
    Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof.
    
    The rule:
      (rest of s1)
      sL, A |- sR
    --------------- (DefinitionLeft)
    sL, main |- sR
    

    Constructs a proof ending with a DefinitionLeft rule.
    In it, a term A (marked by term1oc) is replaced by formula main,
    i.e. A is defined as main.
    
    This rule does not check for contradictory definitions elsewhere in s1, and thus
    the burden of correct usage is on the programmer!
    Being a nonstandard rule, this is also incompatible with methods like LKToExpansionProof.
    
    The rule:
      (rest of s1)
      sL, A |- sR
    --------------- (DefinitionLeft)
    sL, main |- sR
    

    s1

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

    term1oc

    The occurrence of A in s1.

    main

    The formula with which A is to be replaced.

    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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  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)]

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  21. final def wait(): Unit

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

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