gapt-examples
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gapt-examples/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

Graph
Supertypes
trait Serializable
trait Product
trait Equals
class TacticsProof
class TacticsProof0
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
def lambda(n: Int): LKProof
def psi2Right(n: Int): LKProof
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

Inherited methods

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

Attributes

Inherited from:
TacticsProof
def productElementNames: Iterator[String]

Attributes

Inherited from:
Product
def productIterator: Iterator[Any]

Attributes

Inherited from:
Product

Concrete fields

val FQ: LKProof
val FR: LKProof
val Pi_1: LKProof
val compCompProof: LKProof
val deMorgan1: LKProof
val infiniteSubset: LKProof
val intersectionOpen: LKProof
val openClosedProof: LKProof
val pgt0: LKProof
val phi2: LKProof
val progClosed: LKProof
val proof: LKProof
val psi1: LKProof
val psi1Left: LKProof
val psi1Right: LKProof
val psi2: LKProof
val singletonFinite: LKProof
val singletonNonempty: LKProof
val unionClosed: LKProof

Implicits

Inherited implicits

implicit def ctx: ImmutableContext

Attributes

Inherited from:
TacticsProof0
implicit def spliceNum(i: Int): Splice[Expr]

Attributes

Inherited from:
PrimeDefinitions
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