case class ExistsElimRule(leftSubProof: NDProof, rightSubProof: NDProof, aux: SequentIndex, eigenVariable: Var) extends BinaryNDProof with CommonRule with Eigenvariable with Product with Serializable
An NDProof ending with an existential quantifier elimination:
(π1) (π2)
Γ :- ∃x.A Π, A[x\α] :- B
----------------------------∃:e
Γ, Π :- B
This rule is only applicable if the eigenvariable condition is satisfied: α must not occur freely in Π, and B
- leftSubProof
The proof π1.
- rightSubProof
The proof π2.
- aux
The index of A[x\α].
- eigenVariable
The variable α.
- Source
- nd.scala
- Alphabetic
- By Inheritance
- ExistsElimRule
- Serializable
- Eigenvariable
- CommonRule
- ContextRule
- BinaryNDProof
- NDProof
- SequentProof
- DagProof
- Product
- Equals
- AnyRef
- Any
- by any2stringadd
- by StringFormat
- by Ensuring
- by ArrowAssoc
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- Public
- Protected
Instance Constructors
- new ExistsElimRule(leftSubProof: NDProof, rightSubProof: NDProof, aux: SequentIndex, eigenVariable: Var)
- leftSubProof
The proof π1.
- rightSubProof
The proof π2.
- aux
The index of A[x\α].
- eigenVariable
The variable α.
Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- def +(other: String): String
- Implicit
- This member is added by an implicit conversion from ExistsElimRule toany2stringadd[ExistsElimRule] performed by method any2stringadd in scala.Predef.
- Definition Classes
- any2stringadd
- def ->[B](y: B): (ExistsElimRule, B)
- Implicit
- This member is added by an implicit conversion from ExistsElimRule toArrowAssoc[ExistsElimRule] performed by method ArrowAssoc in scala.Predef.
- Definition Classes
- ArrowAssoc
- Annotations
- @inline()
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def NDRuleCreationException(message: String): NDRuleCreationException
- Attributes
- protected
- Definition Classes
- NDProof
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- val aux: SequentIndex
- val auxFormula: Formula
- 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
- 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
- ExistsElimRule → SequentProof
- val auxShouldBe: Formula
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
- lazy val conclusion: Sequent[Formula]
The conclusion of the rule.
The conclusion of the rule.
- Definition Classes
- ContextRule → SequentProof
- def contexts: Seq[Sequent[Formula]]
- Attributes
- protected
- Definition Classes
- ContextRule
- 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
- 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
- val eigenVariable: Var
- Definition Classes
- ExistsElimRule → Eigenvariable
- final def endSequent: Sequent[Formula]
The end-sequent of the rule.
The end-sequent of the rule.
- Definition Classes
- NDProof
- def ensuring(cond: (ExistsElimRule) => Boolean, msg: => Any): ExistsElimRule
- Implicit
- This member is added by an implicit conversion from ExistsElimRule toEnsuring[ExistsElimRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- def ensuring(cond: (ExistsElimRule) => Boolean): ExistsElimRule
- Implicit
- This member is added by an implicit conversion from ExistsElimRule toEnsuring[ExistsElimRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- def ensuring(cond: Boolean, msg: => Any): ExistsElimRule
- Implicit
- This member is added by an implicit conversion from ExistsElimRule toEnsuring[ExistsElimRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- def ensuring(cond: Boolean): ExistsElimRule
- Implicit
- This member is added by an implicit conversion from ExistsElimRule toEnsuring[ExistsElimRule] performed by method Ensuring in scala.Predef.
- Definition Classes
- Ensuring
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(that: Any): Boolean
- Definition Classes
- DagProof → Equals → AnyRef → Any
- val existentialFormula: Formula
- def formulasToBeDeleted: Seq[Seq[SequentIndex]]
- Attributes
- protected
- Definition Classes
- ContextRule
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native() @IntrinsicCandidate()
- def getLeftSequentConnector: SequentConnector
The object connecting the lower and left upper sequents.
The object connecting the lower and left upper sequents.
- Definition Classes
- BinaryNDProof
- def getRightSequentConnector: SequentConnector
The object connecting the lower and right upper sequents.
The object connecting the lower and right upper sequents.
- Definition Classes
- BinaryNDProof
- val hashCode: Int
- Definition Classes
- DagProof
- def immediateSubProofs: Seq[NDProof]
The immediate subproofs of this rule.
The immediate subproofs of this rule.
- Definition Classes
- BinaryNDProof → DagProof
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- val leftContext: Sequent[Formula]
- def leftPremise: Sequent[Formula]
The left upper sequent of the rule.
The left upper sequent of the rule.
- Definition Classes
- BinaryNDProof
- val leftSubProof: NDProof
The immediate left subproof of the rule.
The immediate left subproof of the rule.
- Definition Classes
- ExistsElimRule → BinaryNDProof
- def longName: String
The name of this rule (in words).
The name of this rule (in words).
- Definition Classes
- DagProof
- val mainFormula: Formula
- def mainFormulaSequent: Sequent[Formula]
- Definition Classes
- ExistsElimRule → ContextRule
- def mainFormulas: Seq[Formula]
The list of main formulas of the rule.
The list of main formulas of the rule.
- Definition Classes
- SequentProof
- 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
- ContextRule → SequentProof
- def name: String
The name of this rule (in symbols).
The name of this rule (in symbols).
- Definition Classes
- ExistsElimRule → DagProof
- final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @IntrinsicCandidate()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @IntrinsicCandidate()
- 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
- ContextRule → SequentProof
- def premises: Seq[Sequent[Formula]]
The upper sequents of the rule.
The upper sequents of the rule.
- Definition Classes
- SequentProof
- def productElementNames: Iterator[String]
- Definition Classes
- Product
- val quantifiedVariable: Var
- val rightContext: Sequent[Formula]
- def rightPremise: Sequent[Formula]
The right upper sequent of the rule.
The right upper sequent of the rule.
- Definition Classes
- BinaryNDProof
- val rightSubProof: NDProof
The immediate right subproof of the rule.
The immediate right subproof of the rule.
- Definition Classes
- ExistsElimRule → BinaryNDProof
- def stepString(subProofLabels: Map[Any, String]): String
- Attributes
- protected
- Definition Classes
- SequentProof → DagProof
- val subFormula: Formula
- 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
- def subProofs: Set[NDProof]
Set of all (transitive) sub-proofs including this.
Set of all (transitive) sub-proofs including this.
- Definition Classes
- DagProof
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- 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
- def toString(): String
- Definition Classes
- DagProof → AnyRef → Any
- 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
- 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
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
Deprecated Value Members
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable]) @Deprecated
- Deprecated
- def formatted(fmtstr: String): String
- Implicit
- This member is added by an implicit conversion from ExistsElimRule toStringFormat[ExistsElimRule] performed by method StringFormat in scala.Predef.
- Definition Classes
- StringFormat
- Annotations
- @deprecated @inline()
- Deprecated
(Since version 2.12.16) Use
formatString.format(value)instead ofvalue.formatted(formatString), or use thef""string interpolator. In Java 15 and later,formattedresolves to the new method in String which has reversed parameters.
- def →[B](y: B): (ExistsElimRule, B)
- Implicit
- This member is added by an implicit conversion from ExistsElimRule toArrowAssoc[ExistsElimRule] 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.
This is the API documentation for GAPT.
The main package is gapt.