RationalDistanceProblem.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 1 contain sorry, 0 declared as axioms

Rational distance problem

References:

Wikipedia
mathoverflow/418260 asked by user Yuan Yang
D19 in Unsolved Problems in Number Theory by Richard K. Guy

Imports (1)

FormalConjecturesUtil

def RationalDistanceProblem.UnitSquareCorners line 37 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fin, OfNat.ofNat, Nat, EuclideanSpace, Real
Proof uses: Matrix.vecCons, WithLp.toLp, ENNReal, Matrix.vecEmpty
11 instances, coercions and auxiliary constants left out.
theorem RationalDistanceProblem.rational_distance_problem Does there exist a point in the plane at rational distance from all four vertices of the unit square? sorry line 44 source
Source documentation
Does there exist a point in the plane at rational distance from all four vertices of the unit square?

depends on sorry what this means
Statement uses: Iff, True, Exists, EuclideanSpace, Real, Fin, OfNat.ofNat, Nat, Not, Irrational, Dist.dist, ENNReal, RationalDistanceProblem.UnitSquareCorners
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
20 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem rational_distance_problem :
    answer(sorry) ↔ ∃ P : ℝ² , ∀ i, ¬ Irrational (dist P (UnitSquareCorners i)) := by
…
```
Mentions: RationalDistanceProblem.UnitSquareCorners