c

gapt.proofs.nd

ExcludedMiddleRule

case class ExcludedMiddleRule(leftSubProof: NDProof, aux1: SequentIndex, rightSubProof: NDProof, aux2: SequentIndex) extends BinaryNDProof with CommonRule with Product with Serializable

An NDProof ending with excluded middle:

      (π1)       (π2)
   Γ, A :- B   Π, ¬A :- B
 -------------------------EM
         Γ, Π :- B

leftSubProof

The proof π1.

aux1

The index of A.

rightSubProof

The proof π2.

aux2

The index of ¬A.

Source
nd.scala
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. ExcludedMiddleRule
  2. Serializable
  3. CommonRule
  4. ContextRule
  5. BinaryNDProof
  6. NDProof
  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
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. Protected

Instance Constructors

  1. new ExcludedMiddleRule(leftSubProof: NDProof, aux1: SequentIndex, rightSubProof: NDProof, aux2: SequentIndex)

    leftSubProof

    The proof π1.

    aux1

    The index of A.

    rightSubProof

    The proof π2.

    aux2

    The index of ¬A.

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 ExcludedMiddleRule toany2stringadd[ExcludedMiddleRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ExcludedMiddleRule, B)
    Implicit
    This member is added by an implicit conversion from ExcludedMiddleRule toArrowAssoc[ExcludedMiddleRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def NDRuleCreationException(message: String): NDRuleCreationException
    Attributes
    protected
    Definition Classes
    NDProof
  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
    ExcludedMiddleRuleSequentProof
  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 dagLike: DagLikeOps[NDProof]

    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
  16. 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
  17. final def endSequent: Sequent[Formula]

    The end-sequent of the rule.

    The end-sequent of the rule.

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

    The object connecting the lower and left upper sequents.

    The object connecting the lower and left upper sequents.

    Definition Classes
    BinaryNDProof
  29. def getRightSequentConnector: SequentConnector

    The object connecting the lower and right upper sequents.

    The object connecting the lower and right upper sequents.

    Definition Classes
    BinaryNDProof
  30. val hashCode: Int
    Definition Classes
    DagProof
  31. def immediateSubProofs: Seq[NDProof]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    BinaryNDProofDagProof
  32. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  33. val leftB: Formula
  34. def leftPremise: Sequent[Formula]

    The left upper sequent of the rule.

    The left upper sequent of the rule.

    Definition Classes
    BinaryNDProof
  35. val leftSubProof: NDProof

    The immediate left subproof of the rule.

    The immediate left subproof of the rule.

    Definition Classes
    ExcludedMiddleRuleBinaryNDProof
  36. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  37. val mainFormula: Formula
  38. def mainFormulaSequent: Sequent[Formula]
    Definition Classes
    ExcludedMiddleRuleContextRule
  39. def mainFormulas: Seq[Formula]

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  40. 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
  41. def name: String

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    ExcludedMiddleRuleDagProof
  42. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  43. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  44. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  45. 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
  46. def premises: Seq[Sequent[Formula]]

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  47. def productElementNames: Iterator[String]
    Definition Classes
    Product
  48. val rightB: Formula
  49. def rightPremise: Sequent[Formula]

    The right upper sequent of the rule.

    The right upper sequent of the rule.

    Definition Classes
    BinaryNDProof
  50. val rightSubProof: NDProof

    The immediate right subproof of the rule.

    The immediate right subproof of the rule.

    Definition Classes
    ExcludedMiddleRuleBinaryNDProof
  51. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  52. def subProofAt(pos: List[Int]): NDProof

    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
  53. def subProofs: Set[NDProof]

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

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

    Definition Classes
    DagProof
  54. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  55. final def target: Formula

    The unique formula in the succedent of the end-sequent.

    The unique formula in the succedent of the end-sequent.

    Definition Classes
    NDProof
  56. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  57. def treeLike: TreeLikeOps[NDProof]

    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
  58. def validateIndices(premise: HOLSequent, antecedentIndices: 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.

    Attributes
    protected
    Definition Classes
    NDProof
  59. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  60. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  61. 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 ExcludedMiddleRule toStringFormat[ExcludedMiddleRule] 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): (ExcludedMiddleRule, B)
    Implicit
    This member is added by an implicit conversion from ExcludedMiddleRule toArrowAssoc[ExcludedMiddleRule] 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, NDProof]

Inherited from BinaryNDProof

Inherited from NDProof

Inherited from SequentProof[Formula, NDProof]

Inherited from DagProof[NDProof]

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromExcludedMiddleRule to any2stringadd[ExcludedMiddleRule]

Inherited by implicit conversion StringFormat fromExcludedMiddleRule to StringFormat[ExcludedMiddleRule]

Inherited by implicit conversion Ensuring fromExcludedMiddleRule to Ensuring[ExcludedMiddleRule]

Inherited by implicit conversion ArrowAssoc fromExcludedMiddleRule to ArrowAssoc[ExcludedMiddleRule]

Ungrouped