Class/Object

at.logic.gapt.proofs.lk

EqualityLeftRule

Related Docs: object EqualityLeftRule | package lk

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case class EqualityLeftRule(subProof: LKProof, eq: SequentIndex, aux: SequentIndex, replacementContext: Abs) extends EqualityRule with Product with Serializable

An LKProof ending with a left equality rule. There are two possible cases according to which direction the rule is applied in:

           (π)                            (π)
   A[s], s = t, Γ :- Δ            A[t], s = t, Γ :- Δ
  ---------------------eq:l      ---------------------eq:l
   A[t], s = t, Γ :- Δ            A[s], s = t, Γ :- Δ

In either case, the rule only replaces term occurrences at parallel positions. These positions are given by the positions argument.

subProof

The subproof π.

eq

The index of s = t.

aux

The index of the formula in which the replacement is to be performed.

replacementContext

A term λx.A[x] that designates the positions to be replaced.

Source
lk.scala
Linear Supertypes
Type Hierarchy
Ordering
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  2. By Inheritance
Inherited
  1. EqualityLeftRule
  2. Serializable
  3. Serializable
  4. EqualityRule
  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 EqualityLeftRule(subProof: LKProof, eq: SequentIndex, aux: SequentIndex, replacementContext: Abs)

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    subProof

    The subproof π.

    eq

    The index of s = t.

    aux

    The index of the formula in which the replacement is to be performed.

    replacementContext

    A term λx.A[x] that designates the positions to be replaced.

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

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    Implicit information
    This member is added by an implicit conversion from EqualityLeftRule to ArrowAssoc[EqualityLeftRule] 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 the formula in which the replacement is to be performed.

    The index of the formula in which the replacement is to be performed.

    Definition Classes
    EqualityLeftRuleEqualityRule
  9. val auxFormula: HOLFormula

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    Definition Classes
    EqualityRule
  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 auxInConclusion: SequentIndex

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    Definition Classes
    EqualityRule
  12. 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
    EqualityRuleSequentProof
  13. val by: LambdaExpression

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    Definition Classes
    EqualityRule
  14. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  15. lazy val conclusion: Sequent[HOLFormula]

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    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  16. def contexts: Seq[Sequent[HOLFormula]]

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    Attributes
    protected
    Definition Classes
    ContextRule
  17. 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
  18. 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
  19. final def endSequent: Sequent[HOLFormula]

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    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  20. def ensuring(cond: (EqualityLeftRule) ⇒ Boolean, msg: ⇒ Any): EqualityLeftRule

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

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

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

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

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    Definition Classes
    AnyRef
  25. val eq: SequentIndex

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    The index of s = t.

    The index of s = t.

    Definition Classes
    EqualityLeftRuleEqualityRule
  26. def eqInConclusion: SequentIndex

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    Definition Classes
    EqualityLeftRuleEqualityRule
  27. def equals(that: Any): Boolean

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    Definition Classes
    DagProof → Equals → AnyRef → Any
  28. def equation: HOLFormula

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    Definition Classes
    EqualityRule
  29. def finalize(): Unit

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

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

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    Definition Classes
    EqualityRuleContextRule
  32. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any
  33. 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
  34. val hashCode: Int

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

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    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

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

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    Definition Classes
    Any
  37. val leftToRight: Boolean

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    Definition Classes
    EqualityRule
  38. def longName: String

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    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  39. def mainFormula: HOLFormula

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    Definition Classes
    EqualityRule
  40. def mainFormulaSequent: Sequent[HOLFormula]

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    Definition Classes
    EqualityLeftRuleContextRule
  41. 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
  42. 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
  43. def name: String

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    The name of this rule (in symbols).

    The name of this rule (in symbols).

    Definition Classes
    EqualityLeftRuleDagProof
  44. final def ne(arg0: AnyRef): Boolean

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

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

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    Definition Classes
    AnyRef
  47. 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
  48. def premise: Sequent[HOLFormula]

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    The upper sequent of the rule.

    The upper sequent of the rule.

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

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    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  50. val replacementContext: Abs

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    A term λx.A[x] that designates the positions to be replaced.

    A term λx.A[x] that designates the positions to be replaced.

    Definition Classes
    EqualityLeftRuleEqualityRule
  51. def stepString(subProofLabels: Map[Any, String]): String

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    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  52. val subProof: LKProof

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    The subproof π.

    The subproof π.

    Definition Classes
    EqualityLeftRuleEqualityRuleUnaryLKProof
  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. val what: LambdaExpression

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    Definition Classes
    EqualityRule
  62. def [B](y: B): (EqualityLeftRule, B)

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

Inherited from Serializable

Inherited from Serializable

Inherited from EqualityRule

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 EqualityLeftRule to any2stringadd[EqualityLeftRule]

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

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

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

Ungrouped