c

gapt.proofs.nd

OrIntro2Rule

case class OrIntro2Rule(subProof: NDProof, leftDisjunct: Formula) extends UnaryNDProof with CommonRule with Product with Serializable

An NDProof ending with introduction of a disjunction, with a new formula as the left disjunct:

      (π)
     Γ :- A
   ------------∨:i2
    Γ :- B ∨ A

subProof

The subproof π.

leftDisjunct

The formula B.

Source
nd.scala
Type Hierarchy
Ordering
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Inherited
  1. OrIntro2Rule
  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 OrIntro2Rule(subProof: NDProof, leftDisjunct: Formula)

    subProof

    The subproof π.

    leftDisjunct

    The formula B.

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 OrIntro2Rule toany2stringadd[OrIntro2Rule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (OrIntro2Rule, B)
    Implicit
    This member is added by an implicit conversion from OrIntro2Rule toArrowAssoc[OrIntro2Rule] 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. 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
  9. 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
    OrIntro2RuleSequentProof
  10. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  11. lazy val conclusion: Sequent[Formula]

    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  12. def contexts: Seq[Sequent[Formula]]
    Attributes
    protected
    Definition Classes
    ContextRule
  13. def dagLike: DagLikeOps[NDProof]

    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see gapt.proofs.DagProof.DagLikeOps for a list.

    Operations that view the sub-proofs as a DAG, which ignore duplicate sub-proofs, see gapt.proofs.DagProof.DagLikeOps for a list.

    Definition Classes
    DagProof
  14. 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
  15. final def endSequent: Sequent[Formula]

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    NDProof
  16. def ensuring(cond: (OrIntro2Rule) => Boolean, msg: => Any): OrIntro2Rule
    Implicit
    This member is added by an implicit conversion from OrIntro2Rule toEnsuring[OrIntro2Rule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. def ensuring(cond: (OrIntro2Rule) => Boolean): OrIntro2Rule
    Implicit
    This member is added by an implicit conversion from OrIntro2Rule toEnsuring[OrIntro2Rule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  18. def ensuring(cond: Boolean, msg: => Any): OrIntro2Rule
    Implicit
    This member is added by an implicit conversion from OrIntro2Rule toEnsuring[OrIntro2Rule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: Boolean): OrIntro2Rule
    Implicit
    This member is added by an implicit conversion from OrIntro2Rule toEnsuring[OrIntro2Rule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  21. def equals(that: Any): Boolean
    Definition Classes
    DagProof → Equals → AnyRef → Any
  22. def formulasToBeDeleted: Seq[Seq[SequentIndex]]
    Attributes
    protected
    Definition Classes
    ContextRule
  23. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  24. def getSequentConnector: SequentConnector

    The object connecting the lower and upper sequents.auxFormulas.

    The object connecting the lower and upper sequents.auxFormulas.

    Definition Classes
    UnaryNDProof
  25. val hashCode: Int
    Definition Classes
    DagProof
  26. def immediateSubProofs: Seq[NDProof]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryNDProofDagProof
  27. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  28. val leftDisjunct: Formula
  29. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  30. val mainFormula: Formula
  31. def mainFormulaSequent: Sequent[Formula]
    Definition Classes
    OrIntro2RuleContextRule
  32. def mainFormulas: Seq[Formula]

    The list of main formulas of the rule.

    The list of main formulas of the rule.

    Definition Classes
    SequentProof
  33. 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
  34. def name: String

    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    OrIntro2RuleDagProof
  35. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  36. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  37. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  38. 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
  39. def premise: Sequent[Formula]

    The upper sequent of the rule.

    The upper sequent of the rule.

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

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  41. def productElementNames: Iterator[String]
    Definition Classes
    Product
  42. val rightDisjunct: Formula
  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
    OrIntro2RuleUnaryNDProof
  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. final def target: Formula

    The unique formula in the succedent of the end-sequent.

    The unique formula in the succedent of the end-sequent.

    Definition Classes
    NDProof
  49. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  50. def treeLike: TreeLikeOps[NDProof]

    Operations that view the sub-proofs as a tree, see gapt.proofs.DagProof.TreeLikeOps for a list.

    Operations that view the sub-proofs as a tree, see gapt.proofs.DagProof.TreeLikeOps for a list.

    Definition Classes
    DagProof
  51. 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
  52. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  53. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  54. 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
  2. def formatted(fmtstr: String): String
    Implicit
    This member is added by an implicit conversion from OrIntro2Rule toStringFormat[OrIntro2Rule] performed by method StringFormat in scala.Predef.
    Definition Classes
    StringFormat
    Annotations
    @deprecated @inline()
    Deprecated

    (Since version 2.12.16) Use formatString.format(value) instead of value.formatted(formatString), or use the f"" string interpolator. In Java 15 and later, formatted resolves to the new method in String which has reversed parameters.

  3. def [B](y: B): (OrIntro2Rule, B)
    Implicit
    This member is added by an implicit conversion from OrIntro2Rule toArrowAssoc[OrIntro2Rule] 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 fromOrIntro2Rule to any2stringadd[OrIntro2Rule]

Inherited by implicit conversion StringFormat fromOrIntro2Rule to StringFormat[OrIntro2Rule]

Inherited by implicit conversion Ensuring fromOrIntro2Rule to Ensuring[OrIntro2Rule]

Inherited by implicit conversion ArrowAssoc fromOrIntro2Rule to ArrowAssoc[OrIntro2Rule]

Ungrouped