Class/Object

at.logic.gapt.proofs.lk

ExistsLeftRule

Related Docs: object ExistsLeftRule | package lk

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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
lk.scala
Linear Supertypes
Type Hierarchy
Ordering
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  2. By Inheritance
Inherited
  1. ExistsLeftRule
  2. Serializable
  3. Serializable
  4. Eigenvariable
  5. CommonRule
  6. ContextRule
  7. UnaryLKProof
  8. LKProof
  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 ExistsLeftRule(subProof: LKProof, aux: SequentIndex, eigenVariable: Var, quantifiedVariable: Var)

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    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

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    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any
  3. def +(other: String): String

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    Implicit information
    This member is added by an implicit conversion from ExistsLeftRule to any2stringadd[ExistsLeftRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ExistsLeftRule, B)

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    Implicit information
    This member is added by an implicit conversion from ExistsLeftRule to ArrowAssoc[ExistsLeftRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any
  6. def LKRuleCreationException(message: String): LKRuleCreationException

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    Definition Classes
    LKProof
  7. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  8. val aux: SequentIndex

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    The index of A[x\α].

  9. val auxFormula: HOLFormula

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  10. def auxFormulas: Seq[Seq[HOLFormula]]

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    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]]

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    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

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  13. lazy val conclusion: Sequent[HOLFormula]

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    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  14. val context: Sequent[HOLFormula]

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  15. def contexts: Seq[Sequent[HOLFormula]]

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    Attributes
    protected
    Definition Classes
    ContextRule
  16. def dagLike: DagLikeOps[LKProof]

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    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

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    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

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    The variable α.

    The variable α.

    Definition Classes
    ExistsLeftRuleEigenvariable
  19. final def endSequent: Sequent[HOLFormula]

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    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  20. def ensuring(cond: (ExistsLeftRule) ⇒ Boolean, msg: ⇒ Any): ExistsLeftRule

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    Implicit information
    This member is added by an implicit conversion from ExistsLeftRule to Ensuring[ExistsLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: (ExistsLeftRule) ⇒ Boolean): ExistsLeftRule

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    Implicit information
    This member is added by an implicit conversion from ExistsLeftRule to Ensuring[ExistsLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: Boolean, msg: ⇒ Any): ExistsLeftRule

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    Implicit information
    This member is added by an implicit conversion from ExistsLeftRule to Ensuring[ExistsLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. def ensuring(cond: Boolean): ExistsLeftRule

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    Implicit information
    This member is added by an implicit conversion from ExistsLeftRule to Ensuring[ExistsLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  24. final def eq(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  25. def equals(that: Any): Boolean

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    Definition Classes
    DagProof → Equals → AnyRef → Any
  26. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  27. def formatted(fmtstr: String): String

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    Implicit information
    This member is added by an implicit conversion from ExistsLeftRule to StringFormat[ExistsLeftRule] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  28. def formulasToBeDeleted: Seq[Seq[SequentIndex]]

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    Attributes
    protected
    Definition Classes
    ContextRule
  29. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any
  30. def getOccConnector: OccConnector[HOLFormula]

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    The object connecting the lower and upper sequents.auxFormulas

    The object connecting the lower and upper sequents.auxFormulas

    Definition Classes
    UnaryLKProof
  31. val hashCode: Int

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    Definition Classes
    DagProof → AnyRef → Any
  32. def immediateSubProofs: Seq[LKProof]

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    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryLKProofDagProof
  33. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  34. def longName: String

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    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  35. val mainFormula: HOLFormula

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  36. def mainFormulaSequent: Sequent[HOLFormula]

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    Definition Classes
    ExistsLeftRuleContextRule
  37. def mainFormulas: Seq[HOLFormula]

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    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  38. def mainIndices: Seq[SequentIndex]

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    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
  39. def name: String

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    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    ExistsLeftRuleDagProof
  40. final def ne(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef
  41. final def notify(): Unit

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    Definition Classes
    AnyRef
  42. final def notifyAll(): Unit

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    Definition Classes
    AnyRef
  43. def occConnectors: Seq[OccConnector[HOLFormula]]

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

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

    Definition Classes
    ContextRuleSequentProof
  44. def premise: Sequent[HOLFormula]

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    The upper sequent of the rule.

    The upper sequent of the rule.

    Definition Classes
    UnaryLKProof
  45. def premises: Seq[Sequent[HOLFormula]]

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    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  46. val quantifiedVariable: Var

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    The variable x.

  47. def stepString(subProofLabels: Map[Any, String]): String

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    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  48. val subFormula: HOLFormula

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  49. val subProof: LKProof

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    The proof π.

    The proof π.

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

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

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

    Definition Classes
    DagProof
  51. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  52. def toString(): String

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    Definition Classes
    DagProof → AnyRef → Any
  53. def treeLike: TreeLikeOps[LKProof]

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    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
  54. def validateIndices(premise: HOLSequent, antecedentIndices: Seq[SequentIndex], succedentIndices: Seq[SequentIndex]): Unit

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    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
  55. final def wait(): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  56. final def wait(arg0: Long, arg1: Int): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  57. final def wait(arg0: Long): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  58. def [B](y: B): (ExistsLeftRule, B)

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    Implicit information
    This member is added by an implicit conversion from ExistsLeftRule to ArrowAssoc[ExistsLeftRule] 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[HOLFormula, LKProof]

Inherited from UnaryLKProof

Inherited from LKProof

Inherited from SequentProof[HOLFormula, LKProof]

Inherited from DagProof[LKProof]

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd from ExistsLeftRule to any2stringadd[ExistsLeftRule]

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

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

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

Ungrouped