case class ExistsLeftRule(subProof: LKProof, aux: SequentIndex, eigenVariable: Var, quantifiedVariable: Var) extends UnaryLKProof with CommonRule with Eigenvariable with Product with Serializable

An LKProof ending with an existential quantifier on the left:

          (π)
     A[x\α], Γ :- Δ
    ---------------∀:r
      ∃x.A Γ :- Δ
This rule is only applicable if the eigenvariable condition is satisfied: α must not occur freely in Γ :- Δ.

subProof

The proof π.

aux

The index of A[x\α].

eigenVariable

The variable α.

quantifiedVariable

The variable x.

Source
ExistsLeftRule.scala
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. ExistsLeftRule
  2. Serializable
  3. Eigenvariable
  4. CommonRule
  5. ContextRule
  6. UnaryLKProof
  7. LKProof
  8. SequentProof
  9. DagProof
  10. Product
  11. Equals
  12. AnyRef
  13. 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 ExistsLeftRule(subProof: LKProof, aux: SequentIndex, eigenVariable: Var, quantifiedVariable: Var)

    subProof

    The proof π.

    aux

    The index of A[x\α].

    eigenVariable

    The variable α.

    quantifiedVariable

    The variable x.

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 ExistsLeftRule toany2stringadd[ExistsLeftRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ExistsLeftRule, B)
    Implicit
    This member is added by an implicit conversion from ExistsLeftRule toArrowAssoc[ExistsLeftRule] 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 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
    ExistsLeftRuleSequentProof
  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. val context: Sequent[Formula]
  15. def contexts: Seq[Sequent[Formula]]
    Attributes
    protected
    Definition Classes
    ContextRule
  16. def dagLike: DagLikeOps[LKProof]

    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
    ExistsLeftRuleEigenvariable
  19. final def endSequent: HOLSequent

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  20. def ensuring(cond: (ExistsLeftRule) => Boolean, msg: => Any): ExistsLeftRule
    Implicit
    This member is added by an implicit conversion from ExistsLeftRule toEnsuring[ExistsLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: (ExistsLeftRule) => Boolean): ExistsLeftRule
    Implicit
    This member is added by an implicit conversion from ExistsLeftRule toEnsuring[ExistsLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: Boolean, msg: => Any): ExistsLeftRule
    Implicit
    This member is added by an implicit conversion from ExistsLeftRule toEnsuring[ExistsLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. def ensuring(cond: Boolean): ExistsLeftRule
    Implicit
    This member is added by an implicit conversion from ExistsLeftRule toEnsuring[ExistsLeftRule] 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. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from ExistsLeftRule toStringFormat[ExistsLeftRule] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  27. def formulasToBeDeleted: Seq[Seq[SequentIndex]]
    Attributes
    protected
    Definition Classes
    ContextRule
  28. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  29. def getSequentConnector: SequentConnector

    The object connecting the lower and upper sequents.auxFormulas

    The object connecting the lower and upper sequents.auxFormulas

    Definition Classes
    UnaryLKProof
  30. val hashCode: Int
    Definition Classes
    DagProof
  31. def immediateSubProofs: Seq[LKProof]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryLKProofDagProof
  32. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  33. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  34. val mainFormula: Formula
  35. def mainFormulaSequent: HOLSequent
    Definition Classes
    ExistsLeftRuleContextRule
  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
    ExistsLeftRuleDagProof
  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 premise: HOLSequent

    The upper sequent of the rule.

    The upper sequent of the rule.

    Definition Classes
    UnaryLKProof
  44. def premises: Seq[Sequent[Formula]]

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  45. def productElementNames: Iterator[String]
    Definition Classes
    Product
  46. val quantifiedVariable: Var
  47. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  48. val subFormula: Formula
  49. val subProof: LKProof

    The immediate subproof of the rule.

    The immediate subproof of the rule.

    Definition Classes
    ExistsLeftRuleUnaryLKProof
  50. 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
  51. def subProofs: Set[LKProof]

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

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

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

    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
  55. 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
  56. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  57. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  58. 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
    Deprecated

    (Since version ) see corresponding Javadoc for more information.

  2. def [B](y: B): (ExistsLeftRule, B)
    Implicit
    This member is added by an implicit conversion from ExistsLeftRule toArrowAssoc[ExistsLeftRule] 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 Eigenvariable

Inherited from CommonRule

Inherited from ContextRule[Formula, LKProof]

Inherited from UnaryLKProof

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 fromExistsLeftRule to any2stringadd[ExistsLeftRule]

Inherited by implicit conversion StringFormat fromExistsLeftRule to StringFormat[ExistsLeftRule]

Inherited by implicit conversion Ensuring fromExistsLeftRule to Ensuring[ExistsLeftRule]

Inherited by implicit conversion ArrowAssoc fromExistsLeftRule to ArrowAssoc[ExistsLeftRule]

Ungrouped