Packages

c

gapt.examples.prime

furstenberg

case class furstenberg(k: Int) extends TacticsProof with PrimeDefinitions with Product with Serializable

Furstenberg's topological proof of the infinitude of primes.

furstenberg(k) proves that there are more than k primes.

Source
furstenberg.scala
Known Subclasses
Type Hierarchy
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. furstenberg
  2. Serializable
  3. Product
  4. Equals
  5. PrimeDefinitions
  6. TacticsProof
  7. TacticsProof0
  8. AnyRef
  9. 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 furstenberg(k: Int)

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 furstenberg toany2stringadd[furstenberg] performed by method any2stringadd in scala.Predef.
    Definition Classes
    any2stringadd
  4. def ->[B](y: B): (furstenberg, B)
    Implicit
    This member is added by an implicit conversion from furstenberg toArrowAssoc[furstenberg] performed by method ArrowAssoc in scala.Predef.
    Definition Classes
    ArrowAssoc
    Annotations
    @inline()
  5. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  6. val FQ: LKProof
  7. val FR: LKProof
  8. val Pi_1: LKProof
  9. def RQ(n: Int): LKProof
  10. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  11. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native() @IntrinsicCandidate()
  12. val compCompProof: LKProof
  13. implicit def ctx: ImmutableContext
    Definition Classes
    TacticsProof0
  14. def ctx_=(newContext: ImmutableContext): Unit
    Attributes
    protected
    Definition Classes
    TacticsProof0
  15. val deMorgan1: LKProof
  16. def ensuring(cond: (furstenberg) => Boolean, msg: => Any): furstenberg
    Implicit
    This member is added by an implicit conversion from furstenberg toEnsuring[furstenberg] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  17. def ensuring(cond: (furstenberg) => Boolean): furstenberg
    Implicit
    This member is added by an implicit conversion from furstenberg toEnsuring[furstenberg] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  18. def ensuring(cond: Boolean, msg: => Any): furstenberg
    Implicit
    This member is added by an implicit conversion from furstenberg toEnsuring[furstenberg] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  19. def ensuring(cond: Boolean): furstenberg
    Implicit
    This member is added by an implicit conversion from furstenberg toEnsuring[furstenberg] performed by method Ensuring in scala.Predef.
    Definition Classes
    Ensuring
  20. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  21. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @IntrinsicCandidate()
  22. val infiniteSubset: LKProof
  23. val intersectionOpen: LKProof
  24. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  25. val k: Int
    Definition Classes
    furstenbergPrimeDefinitions
  26. def lambda(n: Int): LKProof
  27. def main(args: Array[String]): Unit
    Definition Classes
    TacticsProof
  28. val mutableContext: MutableContext
    Attributes
    protected
    Definition Classes
    TacticsProof0
  29. implicit def mutableCtxImplicit: MutableContext
    Attributes
    protected
    Definition Classes
    TacticsProof
  30. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  31. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  32. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @IntrinsicCandidate()
  33. val openClosedProof: LKProof
  34. val pgt0: LKProof
  35. val phi2: LKProof
  36. def productElementNames: Iterator[String]
    Definition Classes
    Product
  37. val progClosed: LKProof
  38. val proof: LKProof
  39. val psi1: LKProof
  40. val psi1Left: LKProof
  41. val psi1Right: LKProof
  42. val psi2: LKProof
  43. def psi2Right(n: Int): LKProof
  44. val singletonFinite: LKProof
  45. val singletonNonempty: LKProof
  46. implicit def spliceNum(i: Int): Splice[Expr]
    Definition Classes
    PrimeDefinitions
  47. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  48. val unionClosed: LKProof
  49. def varrho2(n: Int): LKProof

    Proof of x ∈ S[n] :- ∃y ( y ∈ P[n] ∧ x ∈ ν(0,y) )

  50. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  51. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()
  52. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])

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

Inherited from Equals

Inherited from PrimeDefinitions

Inherited from TacticsProof

Inherited from TacticsProof0

Inherited from AnyRef

Inherited from Any

Inherited by implicit conversion any2stringadd fromfurstenberg to any2stringadd[furstenberg]

Inherited by implicit conversion StringFormat fromfurstenberg to StringFormat[furstenberg]

Inherited by implicit conversion Ensuring fromfurstenberg to Ensuring[furstenberg]

Inherited by implicit conversion ArrowAssoc fromfurstenberg to ArrowAssoc[furstenberg]

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