case class ExistsIntroRule(subProof: NDProof, A: Formula, term: Expr, v: Var) extends UnaryNDProof with CommonRule with Product with Serializable

An NDProof ending with an existential quantifier introduction:

       (π)
     Γ :- A[x\t]
    ------------∃:i
     Γ :- ∃x.A

subProof

The proof π.

A

The formula A.

term

The term t.

v

The variable x.

Source
nd.scala
Type Hierarchy
Ordering
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  2. By Inheritance
Inherited
  1. ExistsIntroRule
  2. Serializable
  3. CommonRule
  4. ContextRule
  5. UnaryNDProof
  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. Protected

Instance Constructors

  1. new ExistsIntroRule(subProof: NDProof, A: Formula, term: Expr, v: Var)

    subProof

    The proof π.

    A

    The formula A.

    term

    The term t.

    v

    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 ExistsIntroRule toany2stringadd[ExistsIntroRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (ExistsIntroRule, B)
    Implicit
    This member is added by an implicit conversion from ExistsIntroRule toArrowAssoc[ExistsIntroRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. val A: Formula
  7. def NDRuleCreationException(message: String): NDRuleCreationException
    Attributes
    protected
    Definition Classes
    NDProof
  8. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  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
    ExistsIntroRuleSequentProof
  11. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  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: (ExistsIntroRule) => Boolean, msg: => Any): ExistsIntroRule
    Implicit
    This member is added by an implicit conversion from ExistsIntroRule toEnsuring[ExistsIntroRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  18. def ensuring(cond: (ExistsIntroRule) => Boolean): ExistsIntroRule
    Implicit
    This member is added by an implicit conversion from ExistsIntroRule toEnsuring[ExistsIntroRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: Boolean, msg: => Any): ExistsIntroRule
    Implicit
    This member is added by an implicit conversion from ExistsIntroRule toEnsuring[ExistsIntroRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. def ensuring(cond: Boolean): ExistsIntroRule
    Implicit
    This member is added by an implicit conversion from ExistsIntroRule toEnsuring[ExistsIntroRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  22. def equals(that: Any): Boolean
    Definition Classes
    DagProof → Equals → AnyRef → Any
  23. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from ExistsIntroRule toStringFormat[ExistsIntroRule] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @inline()
  24. def formulasToBeDeleted: Seq[Seq[SequentIndex]]
    Attributes
    protected
    Definition Classes
    ContextRule
  25. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  26. def getSequentConnector: SequentConnector

    The object connecting the lower and upper sequents.auxFormulas.

    The object connecting the lower and upper sequents.auxFormulas.

    Definition Classes
    UnaryNDProof
  27. val hashCode: Int
    Definition Classes
    DagProof
  28. def immediateSubProofs: Seq[NDProof]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryNDProofDagProof
  29. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  30. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  31. val mainFormula: Formula
  32. def mainFormulaSequent: Sequent[Formula]
    Definition Classes
    ExistsIntroRuleContextRule
  33. def mainFormulas: Seq[Formula]

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  34. 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
  35. def name: String

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    ExistsIntroRuleDagProof
  36. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  37. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  38. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  39. 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
  40. def premise: Sequent[Formula]

    The upper sequent of the rule.

    The upper sequent of the rule.

    Definition Classes
    UnaryNDProof
  41. def premises: Seq[Sequent[Formula]]

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  42. def productElementNames: Iterator[String]
    Definition Classes
    Product
  43. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  44. val subProof: NDProof

    The immediate subproof of the rule.

    The immediate subproof of the rule.

    Definition Classes
    ExistsIntroRuleUnaryNDProof
  45. 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
  46. def subProofs: Set[NDProof]

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

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

    Definition Classes
    DagProof
  47. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  48. val term: Expr
  49. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  50. 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
  51. val v: Var
  52. 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
  53. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  54. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  55. 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): (ExistsIntroRule, B)
    Implicit
    This member is added by an implicit conversion from ExistsIntroRule toArrowAssoc[ExistsIntroRule] 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 UnaryNDProof

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 fromExistsIntroRule to any2stringadd[ExistsIntroRule]

Inherited by implicit conversion StringFormat fromExistsIntroRule to StringFormat[ExistsIntroRule]

Inherited by implicit conversion Ensuring fromExistsIntroRule to Ensuring[ExistsIntroRule]

Inherited by implicit conversion ArrowAssoc fromExistsIntroRule to ArrowAssoc[ExistsIntroRule]

Ungrouped