Class/Object

at.logic.gapt.proofs.lk

AndLeftRule

Related Docs: object AndLeftRule | package lk

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case class AndLeftRule(subProof: LKProof, aux1: SequentIndex, aux2: SequentIndex) extends UnaryLKProof with CommonRule with Product with Serializable

An LKProof ending with a conjunction on the left:

        (π)
    A, B, Γ :- Δ
   --------------
   A ∧ B, Γ :- Δ

subProof

The subproof π.

aux1

The index of A.

aux2

The index of B.

Source
lk.scala
Linear Supertypes
Type Hierarchy
Ordering
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  2. By Inheritance
Inherited
  1. AndLeftRule
  2. Serializable
  3. Serializable
  4. CommonRule
  5. ContextRule
  6. UnaryLKProof
  7. LKProof
  8. SequentProof
  9. DagProof
  10. Product
  11. Equals
  12. AnyRef
  13. 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 AndLeftRule(subProof: LKProof, aux1: SequentIndex, aux2: SequentIndex)

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    subProof

    The subproof π.

    aux1

    The index of A.

    aux2

    The index of B.

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

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    Implicit information
    This member is added by an implicit conversion from AndLeftRule to ArrowAssoc[AndLeftRule] 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 aux1: SequentIndex

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    The index of A.

  9. val aux2: SequentIndex

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    The index of B.

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

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    Attributes
    protected
    Definition Classes
    ContextRule
  15. 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
  16. 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
  17. final def endSequent: Sequent[HOLFormula]

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    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  18. def ensuring(cond: (AndLeftRule) ⇒ Boolean, msg: ⇒ Any): AndLeftRule

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

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

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

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

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

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

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

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

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

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    Definition Classes
    AnyRef → Any
  28. 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
  29. val hashCode: Int

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

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    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

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

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    Definition Classes
    Any
  32. val leftConjunct: HOLFormula

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  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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  35. def mainFormulaSequent: Sequent[HOLFormula]

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    Definition Classes
    AndLeftRuleContextRule
  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
    AndLeftRuleDagProof
  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 rightConjunct: HOLFormula

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

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    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  47. val subProof: LKProof

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    The subproof π.

    The subproof π.

    Definition Classes
    AndLeftRuleUnaryLKProof
  48. 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
  49. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef
  50. def toString(): String

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    Definition Classes
    DagProof → AnyRef → Any
  51. 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
  52. 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
  53. final def wait(): Unit

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

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

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

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

Inherited from Serializable

Inherited from Serializable

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 AndLeftRule to any2stringadd[AndLeftRule]

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

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

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

Ungrouped