case class CutRule(leftSubProof: LKProof, aux1: SequentIndex, rightSubProof: LKProof, aux2: SequentIndex) extends BinaryLKProof with CommonRule with Product with Serializable

An LKProof ending with a cut:

     (π1)         (π2)
   Γ :- Δ, A   A, Π :- Λ
  ------------------------
       Γ, Π :- Δ, Λ

leftSubProof

The proof π1.

aux1

The index of A in π1.

rightSubProof

The proof π2.

aux2

The index of A in π2.

Source
CutRule.scala
Type Hierarchy
Ordering
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  2. By Inheritance
Inherited
  1. CutRule
  2. Serializable
  3. CommonRule
  4. ContextRule
  5. BinaryLKProof
  6. LKProof
  7. SequentProof
  8. DagProof
  9. Product
  10. Equals
  11. AnyRef
  12. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new CutRule(leftSubProof: LKProof, aux1: SequentIndex, rightSubProof: LKProof, aux2: SequentIndex)

    leftSubProof

    The proof π1.

    aux1

    The index of A in π1.

    rightSubProof

    The proof π2.

    aux2

    The index of A in π2.

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. def +(other: String): String
    Implicit
    This member is added by an implicit conversion from CutRule toany2stringadd[CutRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (CutRule, B)
    Implicit
    This member is added by an implicit conversion from CutRule toArrowAssoc[CutRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def LKRuleCreationException(message: String): LKRuleCreationException
    Attributes
    protected
    Definition Classes
    LKProof
  7. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  8. val aux1: SequentIndex
  9. val aux2: SequentIndex
  10. def auxFormulas: Seq[Seq[Formula]]

    A list of lists containing the auxiliary formulas of the rule.

    A list of lists containing the auxiliary formulas of the rule. The first list constains the auxiliary formulas in the first premise and so on.

    Definition Classes
    SequentProof
  11. def auxIndices: Seq[Seq[SequentIndex]]

    A list of lists of SequentIndices denoting the auxiliary formula(s) of the rule.

    A list of lists of SequentIndices denoting the auxiliary formula(s) of the rule. The first list contains the auxiliary formulas in the first premise and so on.

    Definition Classes
    CutRuleSequentProof
  12. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  13. lazy val conclusion: Sequent[Formula]

    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  14. def contexts: Seq[Sequent[Formula]]
    Attributes
    protected
    Definition Classes
    ContextRule
  15. def cutFormula: Formula
  16. def dagLike: DagLikeOps[LKProof]

    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see gapt.proofs.DagProof.DagLikeOps for a list.

    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see gapt.proofs.DagProof.DagLikeOps for a list.

    Definition Classes
    DagProof
  17. def depth: Int

    Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.

    Depth of the proof, which is the maximum length of a path you can take via immediateSubProofs.

    Definition Classes
    DagProof
  18. final def endSequent: HOLSequent

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  19. def ensuring(cond: (CutRule) => Boolean, msg: => Any): CutRule
    Implicit
    This member is added by an implicit conversion from CutRule toEnsuring[CutRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: (CutRule) => Boolean): CutRule
    Implicit
    This member is added by an implicit conversion from CutRule toEnsuring[CutRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: Boolean, msg: => Any): CutRule
    Implicit
    This member is added by an implicit conversion from CutRule toEnsuring[CutRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: Boolean): CutRule
    Implicit
    This member is added by an implicit conversion from CutRule toEnsuring[CutRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  24. def equals(that: Any): Boolean
    Definition Classes
    DagProof → Equals → AnyRef → Any
  25. def formulasToBeDeleted: Seq[Seq[SequentIndex]]
    Attributes
    protected
    Definition Classes
    ContextRule
  26. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  27. def getLeftSequentConnector: SequentConnector

    The object connecting the lower and left upper sequents.

    The object connecting the lower and left upper sequents.

    Definition Classes
    BinaryLKProof
  28. def getRightSequentConnector: SequentConnector

    The object connecting the lower and right upper sequents.

    The object connecting the lower and right upper sequents.

    Definition Classes
    BinaryLKProof
  29. val hashCode: Int
    Definition Classes
    DagProof
  30. def immediateSubProofs: Seq[LKProof]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    BinaryLKProofDagProof
  31. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  32. def leftPremise: HOLSequent

    The left upper sequent of the rule.

    The left upper sequent of the rule.

    Definition Classes
    BinaryLKProof
  33. val leftSubProof: LKProof

    The immediate left subproof of the rule.

    The immediate left subproof of the rule.

    Definition Classes
    CutRuleBinaryLKProof
  34. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  35. def mainFormulaSequent: HOLSequent
    Definition Classes
    CutRuleContextRule
  36. def mainFormulas: Seq[Formula]

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  37. def mainIndices: Vector[SequentIndex]

    A list of SequentIndices denoting the main formula(s) of the rule.

    A list of SequentIndices denoting the main formula(s) of the rule.

    Definition Classes
    ContextRuleSequentProof
  38. def name: String

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    CutRuleDagProof
  39. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  40. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  41. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  42. def occConnectors: IndexedSeq[SequentConnector]

    A list of occurrence connectors, one for each immediate subproof.

    A list of occurrence connectors, one for each immediate subproof.

    Definition Classes
    ContextRuleSequentProof
  43. def premises: Seq[Sequent[Formula]]

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  44. def productElementNames: Iterator[String]
    Definition Classes
    Product
  45. def rightPremise: HOLSequent

    The right upper sequent of the rule.

    The right upper sequent of the rule.

    Definition Classes
    BinaryLKProof
  46. val rightSubProof: LKProof

    The immediate right subproof of the rule.

    The immediate right subproof of the rule.

    Definition Classes
    CutRuleBinaryLKProof
  47. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  48. def subProofAt(pos: List[Int]): LKProof

    Returns the subproof at the given position: p.subProofAt(Nil) is p itself; p.subProofAt(i :: is) is the ith subproof of p.subProofAt(is).

    Returns the subproof at the given position: p.subProofAt(Nil) is p itself; p.subProofAt(i :: is) is the ith subproof of p.subProofAt(is).

    Definition Classes
    DagProof
  49. def subProofs: Set[LKProof]

    Set of all (transitive) sub-proofs including this.

    Set of all (transitive) sub-proofs including this.

    Definition Classes
    DagProof
  50. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  51. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  52. def treeLike: TreeLikeOps[LKProof]

    Operations that view the sub-proofs as a tree, see gapt.proofs.DagProof.TreeLikeOps for a list.

    Operations that view the sub-proofs as a tree, see gapt.proofs.DagProof.TreeLikeOps for a list.

    Definition Classes
    DagProof
  53. final def validateIndices(premise: HOLSequent, antecedentIndices: Seq[SequentIndex], succedentIndices: Seq[SequentIndex]): Unit

    Checks whether indices are in the right place and premise is defined at all of them.

    Checks whether indices are in the right place and premise is defined at all of them.

    premise

    The sequent to be checked.

    antecedentIndices

    Indices that should be in the antecedent.

    succedentIndices

    Indices that should be in the succedent.

    Attributes
    protected
    Definition Classes
    LKProof
  54. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  55. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  56. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable]) @Deprecated
    Deprecated
  2. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from CutRule toStringFormat[CutRule] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @deprecated @inline()
    Deprecated

    (Since version 2.12.16) Use formatString.format(value) instead of value.formatted(formatString), or use the f"" string interpolator. In Java 15 and later, formatted resolves to the new method in String which has reversed parameters.

  3. def [B](y: B): (CutRule, B)
    Implicit
    This member is added by an implicit conversion from CutRule toArrowAssoc[CutRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @deprecated
    Deprecated

    (Since version 2.13.0) Use -> instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.

Inherited from Serializable

Inherited from CommonRule

Inherited from ContextRule[Formula, LKProof]

Inherited from BinaryLKProof

Inherited from LKProof

Inherited from SequentProof[Formula, LKProof]

Inherited from DagProof[LKProof]

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromCutRule to any2stringadd[CutRule]

Inherited by implicit conversion StringFormat fromCutRule to StringFormat[CutRule]

Inherited by implicit conversion Ensuring fromCutRule to Ensuring[CutRule]

Inherited by implicit conversion ArrowAssoc fromCutRule to ArrowAssoc[CutRule]

Ungrouped