case class ExistsElimRule(leftSubProof: NDProof, rightSubProof: NDProof, aux: SequentIndex, eigenVariable: Var) extends BinaryNDProof with CommonRule with Eigenvariable with Product with Serializable

An NDProof ending with an existential quantifier elimination:

        (π1)         (π2)
    Γ :- ∃x.A   Π, A[x\α] :- B
   ----------------------------∃:e
       Γ, Π :- B
This rule is only applicable if the eigenvariable condition is satisfied: α must not occur freely in Π, and B

leftSubProof

The proof π1.

rightSubProof

The proof π2.

aux

The index of A[x\α].

eigenVariable

The variable α.

Source
nd.scala
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. ExistsElimRule
  2. Serializable
  3. Serializable
  4. Eigenvariable
  5. CommonRule
  6. ContextRule
  7. BinaryNDProof
  8. NDProof
  9. SequentProof
  10. DagProof
  11. Product
  12. Equals
  13. AnyRef
  14. Any
Implicitly
  1. by any2stringadd
  2. by StringFormat
  3. by Ensuring
  4. by ArrowAssoc
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Visibility
  1. Public
  2. All

Instance Constructors

  1. new ExistsElimRule(leftSubProof: NDProof, rightSubProof: NDProof, aux: SequentIndex, eigenVariable: Var)

    leftSubProof

    The proof π1.

    rightSubProof

    The proof π2.

    aux

    The index of A[x\α].

    eigenVariable

    The variable α.

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 ExistsElimRule to any2stringadd[ExistsElimRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ExistsElimRule, B)
    Implicit
    This member is added by an implicit conversion from ExistsElimRule to ArrowAssoc[ExistsElimRule] 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 aux: SequentIndex
  9. val auxFormula: Formula
  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
    ExistsElimRuleSequentProof
  12. val auxShouldBe: Formula
  13. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  14. lazy val conclusion: Sequent[Formula]

    The conclusion of the rule.

    The conclusion of the rule.

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

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

    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see 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. val eigenVariable: Var
    Definition Classes
    ExistsElimRuleEigenvariable
  19. final def endSequent: Sequent[Formula]

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    NDProof
  20. def ensuring(cond: (ExistsElimRule) ⇒ Boolean, msg: ⇒ Any): ExistsElimRule
    Implicit
    This member is added by an implicit conversion from ExistsElimRule to Ensuring[ExistsElimRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: (ExistsElimRule) ⇒ Boolean): ExistsElimRule
    Implicit
    This member is added by an implicit conversion from ExistsElimRule to Ensuring[ExistsElimRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: Boolean, msg: ⇒ Any): ExistsElimRule
    Implicit
    This member is added by an implicit conversion from ExistsElimRule to Ensuring[ExistsElimRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. def ensuring(cond: Boolean): ExistsElimRule
    Implicit
    This member is added by an implicit conversion from ExistsElimRule to Ensuring[ExistsElimRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  24. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  25. def equals(that: Any): Boolean
    Definition Classes
    DagProof → Equals → AnyRef → Any
  26. val existentialFormula: Formula
  27. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  28. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from ExistsElimRule to StringFormat[ExistsElimRule] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  29. def formulasToBeDeleted: Seq[Seq[SequentIndex]]
    Attributes
    protected
    Definition Classes
    ContextRule
  30. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  31. def getLeftSequentConnector: SequentConnector

    The object connecting the lower and left upper sequents.

    The object connecting the lower and left upper sequents.

    Definition Classes
    BinaryNDProof
  32. def getRightSequentConnector: SequentConnector

    The object connecting the lower and right upper sequents.

    The object connecting the lower and right upper sequents.

    Definition Classes
    BinaryNDProof
  33. val hashCode: Int
    Definition Classes
    DagProof
  34. def immediateSubProofs: Seq[NDProof]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    BinaryNDProofDagProof
  35. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  36. val leftContext: Sequent[Formula]
  37. def leftPremise: Sequent[Formula]

    The left upper sequent of the rule.

    The left upper sequent of the rule.

    Definition Classes
    BinaryNDProof
  38. val leftSubProof: NDProof

    The immediate left subproof of the rule.

    The immediate left subproof of the rule.

    Definition Classes
    ExistsElimRuleBinaryNDProof
  39. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  40. val mainFormula: Formula
  41. def mainFormulaSequent: Sequent[Formula]
    Definition Classes
    ExistsElimRuleContextRule
  42. def mainFormulas: Seq[Formula]

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  43. 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
  44. def name: String

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    ExistsElimRuleDagProof
  45. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  46. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  47. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  48. def occConnectors: Seq[SequentConnector]

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

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

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

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  50. val quantifiedVariable: Var
  51. val rightContext: Sequent[Formula]
  52. def rightPremise: Sequent[Formula]

    The right upper sequent of the rule.

    The right upper sequent of the rule.

    Definition Classes
    BinaryNDProof
  53. val rightSubProof: NDProof

    The immediate right subproof of the rule.

    The immediate right subproof of the rule.

    Definition Classes
    ExistsElimRuleBinaryNDProof
  54. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  55. val subFormula: Formula
  56. 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
  57. def subProofs: Set[NDProof]

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

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

    Definition Classes
    DagProof
  58. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  59. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  60. def treeLike: TreeLikeOps[NDProof]

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

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

    Definition Classes
    DagProof
  61. 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
  62. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  63. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  64. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  65. def [B](y: B): (ExistsElimRule, B)
    Implicit
    This member is added by an implicit conversion from ExistsElimRule to ArrowAssoc[ExistsElimRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Serializable

Inherited from Serializable

Inherited from Eigenvariable

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 from ExistsElimRule to any2stringadd[ExistsElimRule]

Inherited by implicit conversion StringFormat from ExistsElimRule to StringFormat[ExistsElimRule]

Inherited by implicit conversion Ensuring from ExistsElimRule to Ensuring[ExistsElimRule]

Inherited by implicit conversion ArrowAssoc from ExistsElimRule to ArrowAssoc[ExistsElimRule]

Ungrouped