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

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
EqualityLeftRule.scala
Type Hierarchy
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Inherited
  1. EqualityLeftRule
  2. Serializable
  3. EqualityRule
  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. Protected

Instance Constructors

  1. new EqualityLeftRule(subProof: LKProof, eq: SequentIndex, aux: SequentIndex, replacementContext: Abs)

    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
    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 EqualityLeftRule toany2stringadd[EqualityLeftRule] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (EqualityLeftRule, B)
    Implicit
    This member is added by an implicit conversion from EqualityLeftRule toArrowAssoc[EqualityLeftRule] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. def LKRuleCreationException(message: String): LKRuleCreationException
    Attributes
    protected
    Definition Classes
    LKProof
  7. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  8. val aux: SequentIndex
    Definition Classes
    EqualityLeftRuleEqualityRule
  9. val auxFormula: Formula
    Definition Classes
    EqualityRule
  10. 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
  11. def auxInConclusion: SequentIndex
    Definition Classes
    EqualityRule
  12. def auxIndices: Seq[Seq[SequentIndex]]

    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: Expr
    Definition Classes
    EqualityRule
  14. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  15. lazy val conclusion: Sequent[Formula]

    The conclusion of the rule.

    The conclusion of the rule.

    Definition Classes
    ContextRuleSequentProof
  16. def contexts: Seq[Sequent[Formula]]
    Attributes
    protected
    Definition Classes
    ContextRule
  17. def dagLike: DagLikeOps[LKProof]

    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
  18. 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
  19. final def endSequent: HOLSequent

    The end-sequent of the rule.

    The end-sequent of the rule.

    Definition Classes
    LKProof
  20. def ensuring(cond: (EqualityLeftRule) => Boolean, msg: => Any): EqualityLeftRule
    Implicit
    This member is added by an implicit conversion from EqualityLeftRule toEnsuring[EqualityLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  21. def ensuring(cond: (EqualityLeftRule) => Boolean): EqualityLeftRule
    Implicit
    This member is added by an implicit conversion from EqualityLeftRule toEnsuring[EqualityLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  22. def ensuring(cond: Boolean, msg: => Any): EqualityLeftRule
    Implicit
    This member is added by an implicit conversion from EqualityLeftRule toEnsuring[EqualityLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  23. def ensuring(cond: Boolean): EqualityLeftRule
    Implicit
    This member is added by an implicit conversion from EqualityLeftRule toEnsuring[EqualityLeftRule] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  24. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  25. val eq: SequentIndex
    Definition Classes
    EqualityLeftRuleEqualityRule
  26. def eqInConclusion: SequentIndex
    Definition Classes
    EqualityRule
  27. def equals(that: Any): Boolean
    Definition Classes
    DagProof → Equals → AnyRef → Any
  28. def equation: Formula
    Definition Classes
    EqualityRule
  29. def formulasToBeDeleted: Seq[Seq[SequentIndex]]
    Definition Classes
    EqualityRuleContextRule
  30. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  31. def getSequentConnector: SequentConnector

    The object connecting the lower and upper sequents.auxFormulas

    The object connecting the lower and upper sequents.auxFormulas

    Definition Classes
    UnaryLKProof
  32. val hashCode: Int
    Definition Classes
    DagProof
  33. def immediateSubProofs: Seq[LKProof]

    The immediate subproofs of this rule.

    The immediate subproofs of this rule.

    Definition Classes
    UnaryLKProofDagProof
  34. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  35. val leftToRight: Boolean
    Definition Classes
    EqualityRule
  36. def longName: String

    The name of this rule (in words).

    The name of this rule (in words).

    Definition Classes
    DagProof
  37. def mainFormula: Formula
    Definition Classes
    EqualityRule
  38. def mainFormulaSequent: HOLSequent
    Definition Classes
    EqualityLeftRuleContextRule
  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
    EqualityLeftRuleDagProof
  42. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  43. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  44. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  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 premise: HOLSequent

    The upper sequent of the rule.

    The upper sequent of the rule.

    Definition Classes
    UnaryLKProof
  47. def premises: Seq[Sequent[Formula]]

    The upper sequents of the rule.

    The upper sequents of the rule.

    Definition Classes
    SequentProof
  48. def productElementNames: Iterator[String]
    Definition Classes
    Product
  49. val replacementContext: Abs
    Definition Classes
    EqualityLeftRuleEqualityRule
  50. def stepString(subProofLabels: Map[Any, String]): String
    Attributes
    protected
    Definition Classes
    SequentProofDagProof
  51. val subProof: LKProof

    The immediate subproof of the rule.

    The immediate subproof of the rule.

    Definition Classes
    EqualityLeftRuleEqualityRuleUnaryLKProof
  52. def subProofAt(pos: List[Int]): LKProof

    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[LKProof]

    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
    Definition Classes
    AnyRef
  55. def toString(): String
    Definition Classes
    DagProof → AnyRef → Any
  56. def treeLike: TreeLikeOps[LKProof]

    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
  57. final def validateIndices(premise: HOLSequent, antecedentIndices: Seq[SequentIndex], succedentIndices: 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.

    succedentIndices

    Indices that should be in the succedent.

    Attributes
    protected
    Definition Classes
    LKProof
  58. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  59. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  60. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  61. val what: Expr
    Definition Classes
    EqualityRule

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 EqualityLeftRule toStringFormat[EqualityLeftRule] 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): (EqualityLeftRule, B)
    Implicit
    This member is added by an implicit conversion from EqualityLeftRule toArrowAssoc[EqualityLeftRule] 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 EqualityRule

Inherited from CommonRule

Inherited from ContextRule[Formula, LKProof]

Inherited from UnaryLKProof

Inherited from LKProof

Inherited from SequentProof[Formula, LKProof]

Inherited from DagProof[LKProof]

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromEqualityLeftRule to any2stringadd[EqualityLeftRule]

Inherited by implicit conversion StringFormat fromEqualityLeftRule to StringFormat[EqualityLeftRule]

Inherited by implicit conversion Ensuring fromEqualityLeftRule to Ensuring[EqualityLeftRule]

Inherited by implicit conversion ArrowAssoc fromEqualityLeftRule to ArrowAssoc[EqualityLeftRule]

Ungrouped