case class EqualityElimRule(leftSubProof: NDProof, rightSubProof: NDProof, formulaA: Formula, variablex: Var) extends BinaryNDProof with CommonRule with Product with Serializable

An NDProof ending with elimination of equality:

      (π1)         (π2)
   Γ :- s = t    Π :- A[x\s]
  ------------------------------eq:e
         Γ,Π :- A[x\t]

leftSubProof

The subproof π1.

rightSubProof

The subproof π2.

formulaA

The formula A.

variablex

The variable x.

Source
nd.scala
Type Hierarchy
Ordering
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  2. By Inheritance
Inherited
  1. EqualityElimRule
  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
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Visibility
  1. Public
  2. All

Instance Constructors

  1. new EqualityElimRule(leftSubProof: NDProof, rightSubProof: NDProof, formulaA: Formula, variablex: Var)

    leftSubProof

    The subproof π1.

    rightSubProof

    The subproof π2.

    formulaA

    The formula A.

    variablex

    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 EqualityElimRule toany2stringadd[EqualityElimRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (EqualityElimRule, B)
    Implicit
    This member is added by an implicit conversion from EqualityElimRule toArrowAssoc[EqualityElimRule] 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 auxFormula: Formula
  9. 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
  10. def auxIndices: Seq[Seq[Suc]]

    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
    EqualityElimRuleSequentProof
  11. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native()
  12. lazy val conclusion: Sequent[Formula]

    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  13. def contexts: Seq[Sequent[Formula]]
    Attributes
    protected
    Definition Classes
    ContextRule
  14. 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
  15. 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
  16. final def endSequent: Sequent[Formula]

    The end-sequent of the rule.

    The end-sequent of the rule.

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

    The object connecting the lower and left upper sequents.

    The object connecting the lower and left upper sequents.

    Definition Classes
    BinaryNDProof
  30. def getRightSequentConnector: SequentConnector

    The object connecting the lower and right upper sequents.

    The object connecting the lower and right upper sequents.

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

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    BinaryNDProofDagProof
  33. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  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
    EqualityElimRuleBinaryNDProof
  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
    EqualityElimRuleContextRule
  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
    EqualityElimRuleDagProof
  42. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  43. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  44. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  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. def rightPremise: Sequent[Formula]

    The right upper sequent of the rule.

    The right upper sequent of the rule.

    Definition Classes
    BinaryNDProof
  49. val rightSubProof: NDProof

    The immediate right subproof of the rule.

    The immediate right subproof of the rule.

    Definition Classes
    EqualityElimRuleBinaryNDProof
  50. val s: Expr
  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. val substitution1: Substitution
  55. val substitution2: Substitution
  56. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  57. val t: Expr
  58. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  59. 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
  60. 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
  61. val variablex: Var
  62. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  63. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  64. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()

Deprecated Value Members

  1. def [B](y: B): (EqualityElimRule, B)
    Implicit
    This member is added by an implicit conversion from EqualityElimRule toArrowAssoc[EqualityElimRule] 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 fromEqualityElimRule to any2stringadd[EqualityElimRule]

Inherited by implicit conversion StringFormat fromEqualityElimRule to StringFormat[EqualityElimRule]

Inherited by implicit conversion Ensuring fromEqualityElimRule to Ensuring[EqualityElimRule]

Inherited by implicit conversion ArrowAssoc fromEqualityElimRule to ArrowAssoc[EqualityElimRule]

Ungrouped