Class/Object

at.logic.gapt.proofs.lk

ExistsSkLeftRule

Related Docs: object ExistsSkLeftRule | package lk

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case class ExistsSkLeftRule(subProof: LKProof, aux: SequentIndex, mainFormula: HOLFormula, skolemTerm: LambdaExpression, skolemDef: LambdaExpression) extends UnaryLKProof with SkolemQuantifierRule with Product with Serializable

An LKProof ending with an existential quantifier on the left:

          (π)
     A[x\s(...)], Γ :- Δ
    --------------- ∃sk:l
      ∃x.A Γ :- Δ
This rule requires a Skolem function s(...)

subProof

The proof π.

aux

The index of A[x\s(...)].

mainFormula

The main formula A[x\s(...)]

skolemTerm

The Skolem term s(...)

skolemDef

The Skolem definition, see at.logic.gapt.expr.hol.SkolemFunctions

Source
lk.scala
Linear Supertypes
Type Hierarchy
Ordering
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  2. By Inheritance
Inherited
  1. ExistsSkLeftRule
  2. Serializable
  3. Serializable
  4. SkolemQuantifierRule
  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 ExistsSkLeftRule(subProof: LKProof, aux: SequentIndex, mainFormula: HOLFormula, skolemTerm: LambdaExpression, skolemDef: LambdaExpression)

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    subProof

    The proof π.

    aux

    The index of A[x\s(...)].

    mainFormula

    The main formula A[x\s(...)]

    skolemTerm

    The Skolem term s(...)

    skolemDef

    The Skolem definition, see at.logic.gapt.expr.hol.SkolemFunctions

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 ExistsSkLeftRule to any2stringadd[ExistsSkLeftRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ExistsSkLeftRule, B)

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    Implicit information
    This member is added by an implicit conversion from ExistsSkLeftRule to ArrowAssoc[ExistsSkLeftRule] 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\s(...)].

    The index of A[x\s(...)].

    Definition Classes
    ExistsSkLeftRuleSkolemQuantifierRule
  9. val auxFormula: HOLFormula

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    Definition Classes
    SkolemQuantifierRule
  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
    ExistsSkLeftRuleSequentProof
  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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    Definition Classes
    SkolemQuantifierRule
  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. final def endSequent: Sequent[HOLFormula]

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    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  19. def ensuring(cond: (ExistsSkLeftRule) ⇒ Boolean, msg: ⇒ Any): ExistsSkLeftRule

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

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

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

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

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

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

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

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

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

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    Definition Classes
    AnyRef → Any
  29. 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
  30. val hashCode: Int

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

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    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

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

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    Definition Classes
    Any
  33. def longName: String

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    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  34. val mainFormula: HOLFormula

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    The main formula A[x\s(...)]

    The main formula A[x\s(...)]

    Definition Classes
    ExistsSkLeftRuleSkolemQuantifierRule
  35. def mainFormulaSequent: Sequent[HOLFormula]

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    Definition Classes
    ExistsSkLeftRuleContextRule
  36. 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
  37. 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
  38. def name: String

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    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    ExistsSkLeftRuleDagProof
  39. final def ne(arg0: AnyRef): Boolean

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

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

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    Definition Classes
    AnyRef
  42. 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
  43. def premise: Sequent[HOLFormula]

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    The upper sequent of the rule.

    The upper sequent of the rule.

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

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    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  45. val quantifiedVariable: Var

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    Definition Classes
    ExistsSkLeftRuleSkolemQuantifierRule
  46. val skolemArgs: List[LambdaExpression]

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    Definition Classes
    SkolemQuantifierRule
  47. val skolemConst: Const

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    Definition Classes
    SkolemQuantifierRule
  48. val skolemDef: LambdaExpression

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    The Skolem definition, see at.logic.gapt.expr.hol.SkolemFunctions

    The Skolem definition, see at.logic.gapt.expr.hol.SkolemFunctions

    Definition Classes
    ExistsSkLeftRuleSkolemQuantifierRule
  49. val skolemTerm: LambdaExpression

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    The Skolem term s(...)

    The Skolem term s(...)

    Definition Classes
    ExistsSkLeftRuleSkolemQuantifierRule
  50. def stepString(subProofLabels: Map[Any, String]): String

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    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  51. val subFormula: HOLFormula

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    Definition Classes
    ExistsSkLeftRuleSkolemQuantifierRule
  52. val subProof: LKProof

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    The proof π.

    The proof π.

    Definition Classes
    ExistsSkLeftRuleUnaryLKProof
  53. 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
  54. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  55. def toString(): String

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    Definition Classes
    DagProof → AnyRef → Any
  56. 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
  57. 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
  58. final def wait(): Unit

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

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

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

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    Implicit information
    This member is added by an implicit conversion from ExistsSkLeftRule to ArrowAssoc[ExistsSkLeftRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc

Inherited from Serializable

Inherited from Serializable

Inherited from SkolemQuantifierRule

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 ExistsSkLeftRule to any2stringadd[ExistsSkLeftRule]

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

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

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

Ungrouped