Object

at.logic.gapt.proofs.lk

ExistsRightRule

Related Doc: package lk

Permalink

object ExistsRightRule extends WeakRuleHelper

Linear Supertypes
Ordering
  1. Alphabetic
  2. By inheritance
Inherited
  1. ExistsRightRule
  2. WeakRuleHelper
  3. QuantifierRuleHelper
  4. AnyRef
  5. Any
  1. Hide All
  2. Show all
Visibility
  1. Public
  2. All

Value Members

  1. final def !=(arg0: Any): Boolean

    Permalink
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int

    Permalink
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean

    Permalink
    Definition Classes
    AnyRef → Any
  4. def apply(s1: OccSequent, term1oc: FormulaOccurrence, main: HOLFormula, term: LambdaExpression): Sequent[FormulaOccurrence]

    Permalink

    Constructs a proof ending with an ExistsRight rule.
    
    The rule:
      (rest of s1)
     sL |- sR, A[term/x]
    -------------------- (ForallLeft)
    sL |- sR, Exists x.A
    

    Constructs a proof ending with an ExistsRight rule.
    
    The rule:
      (rest of s1)
     sL |- sR, A[term/x]
    -------------------- (ForallLeft)
    sL |- sR, Exists x.A
    

    s1

    The top proof with (sL, A[term/x] |- sR) as the bottommost sequent.

    term1oc

    The occurrence of the formula A[term/x], in which a term is to be all-quantified.

    main

    The resulting (Exists x.A), with some (not necessarily all) instances of term replaced by a newly introduced variable.

    term

    The term to be existentially quantified & whose substitution into the main formula yields the auxiliary formula.

    returns

    An LK Proof ending with the new inference.

  5. def apply(s1: LKProof, term1oc: FormulaOccurrence, main: HOLFormula, term: LambdaExpression): LKProof

    Permalink

    Constructs a proof ending with an ExistsRight rule.
    
    The rule:
      (rest of s1)
     sL |- sR, A[term/x]
    -------------------- (ExistsRight)
    sL |- sR, Exists x.A
    

    Constructs a proof ending with an ExistsRight rule.
    
    The rule:
      (rest of s1)
     sL |- sR, A[term/x]
    -------------------- (ExistsRight)
    sL |- sR, Exists x.A
    

    s1

    The top proof with (sL, A[term/x] |- sR) as the bottommost sequent.

    term1oc

    The occurrence of the formula A[term/x], in which a term is to be existentially quantified.

    main

    The resulting (Exists x.A), with some (not necessarily all) instances of term replaced by a newly introduced variable.

    term

    The term to be existentially quantified & whose substitution into the main formula yields the auxiliary formula.

    returns

    An LK Proof ending with the new inference.

  6. def apply(s1: LKProof, aux: HOLFormula, main: HOLFormula, term: LambdaExpression): LKProof

    Permalink

    Constructs a proof ending with an ExistsRight rule.
    
    The rule:
      (rest of s1)
     sL |- sR, A[term/x]
    -------------------- (ExistsRight)
    sL |- sR, Exists x.A
    

    Constructs a proof ending with an ExistsRight rule.
    
    The rule:
      (rest of s1)
     sL |- sR, A[term/x]
    -------------------- (ExistsRight)
    sL |- sR, Exists x.A
    

    s1

    The top proof with (sL, A[term/x] |- sR) as the bottommost sequent.

    aux

    The formula A[term/x], in which a term is to be existentially quantified.

    main

    The resulting (Exists x.A), with some (not necessarily all) instances of term replaced by a newly introduced variable.

    term

    The term to be existentially quantified & whose substitution into the main formula yields the auxiliary formula.

    returns

    An LK Proof ending with the new inference.

  7. final def asInstanceOf[T0]: T0

    Permalink
    Definition Classes
    Any
  8. def clone(): AnyRef

    Permalink
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  9. def computeAux(main: HOLFormula, term: LambdaExpression): (Var, HOLFormula)

    Permalink
    Definition Classes
    WeakRuleHelper
  10. final def eq(arg0: AnyRef): Boolean

    Permalink
    Definition Classes
    AnyRef
  11. def equals(arg0: Any): Boolean

    Permalink
    Definition Classes
    AnyRef → Any
  12. def finalize(): Unit

    Permalink
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  13. final def getClass(): Class[_]

    Permalink
    Definition Classes
    AnyRef → Any
  14. def hashCode(): Int

    Permalink
    Definition Classes
    AnyRef → Any
  15. final def isInstanceOf[T0]: Boolean

    Permalink
    Definition Classes
    Any
  16. final def ne(arg0: AnyRef): Boolean

    Permalink
    Definition Classes
    AnyRef
  17. final def notify(): Unit

    Permalink
    Definition Classes
    AnyRef
  18. final def notifyAll(): Unit

    Permalink
    Definition Classes
    AnyRef
  19. final def synchronized[T0](arg0: ⇒ T0): T0

    Permalink
    Definition Classes
    AnyRef
  20. def toString(): String

    Permalink
    Definition Classes
    AnyRef → Any
  21. def unapply(proof: LKProof): Option[(LKProof, OccSequent, FormulaOccurrence, FormulaOccurrence, LambdaExpression)]

    Permalink
  22. final def wait(): Unit

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

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

    Permalink
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from WeakRuleHelper

Inherited from QuantifierRuleHelper

Inherited from AnyRef

Inherited from Any

Ungrouped