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gapt/gapt/gapt.examples/gapt.examples.prime/furstenberg

furstenberg

gapt.examples.prime.furstenberg
case class furstenberg(k: Int) extends PrimeDefinitions

Furstenberg's topological proof of the infinitude of primes.

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

Attributes

Source
furstenberg.scala
Graph
Supertypes
trait Serializable
trait Product
trait Equals
class TacticsProof
class Object
trait Matchable
class Any
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Known subtypes
object furstenberg3

Members list

Value members

Concrete methods

def RQ(n: Int): LKProof

Attributes

Source
furstenberg.scala
def lambda(n: Int): LKProof

Attributes

Source
furstenberg.scala
def psi2Right(n: Int): LKProof

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Source
furstenberg.scala
def varrho2(n: Int): LKProof

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

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

Attributes

Source
furstenberg.scala

Inherited methods

def main(args: Array[String]): Unit

Attributes

Inherited from:
TacticsProof
Source
TacticsProof.scala
def productElementNames: Iterator[String]

An iterator over the names of all the elements of this product.

An iterator over the names of all the elements of this product.

Attributes

Inherited from:
Product
Source
Product.scala
def productIterator: Iterator[Any]

An iterator over all the elements of this product.

An iterator over all the elements of this product.

Attributes

Returns

in the default implementation, an Iterator[Any]

Inherited from:
Product
Source
Product.scala

Concrete fields

val FQ: LKProof

Attributes

Source
furstenberg.scala
val FR: LKProof

Attributes

Source
furstenberg.scala
val Pi_1: LKProof

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Source
furstenberg.scala
val compCompProof: LKProof

Attributes

Source
furstenberg.scala
val deMorgan1: LKProof

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Source
furstenberg.scala
val infiniteSubset: LKProof

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Source
furstenberg.scala
val intersectionOpen: LKProof

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Source
furstenberg.scala
val openClosedProof: LKProof

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Source
furstenberg.scala
val pgt0: LKProof

Attributes

Source
furstenberg.scala
val phi2: LKProof

Attributes

Source
furstenberg.scala
val progClosed: LKProof

Attributes

Source
furstenberg.scala
val proof: LKProof

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Source
furstenberg.scala
val psi1: LKProof

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Source
furstenberg.scala
val psi1Left: LKProof

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Source
furstenberg.scala
val psi1Right: LKProof

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Source
furstenberg.scala
val psi2: LKProof

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Source
furstenberg.scala
val singletonFinite: LKProof

Attributes

Source
furstenberg.scala
val unionClosed: LKProof

Attributes

Source
furstenberg.scala

Implicits

Inherited implicits

implicit def ctx: ImmutableContext

Attributes

Inherited from:
TacticsProof0
Source
TacticsProof.scala
implicit def spliceNum(i: Int): Splice[Expr]

Attributes

Inherited from:
PrimeDefinitions
Source
PrimeDefinitions.scala
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