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updated to "formally solved" from open and included reference lean 1071 #3593

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updated to "formally solved" from open and included reference
aryanamol10 Mar 17, 2026
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Merge branch 'main' into mismatch1071
aryanamol10 Mar 17, 2026
55e6065
updated docstring to include credits and reference
aryanamol10 Mar 19, 2026
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Merge branch 'main' into mismatch1071
aryanamol10 Mar 19, 2026
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aryanamol10 Mar 20, 2026
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aryanamol10 Mar 20, 2026
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10 changes: 8 additions & 2 deletions FormalConjectures/ErdosProblems/1071.lean
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Expand Up @@ -49,8 +49,14 @@ theorem erdos_1071.parts.i :
(T : Set (ℝ² × ℝ²)).Pairwise SegmentsDisjoint) S := by
sorry

/-- Is there a region $R$ with a maximal set of disjoint unit line segments that is countably infinite? -/
@[category research open, AMS 52]
/-- Is there a region $R$ with a maximal set of disjoint unit line segments that is countably infinite?
Solved affirmatively by [Fo99], who gave an explicit construction.


This was formalized in Lean by Alexeev using Aristotle and ChatGPT.
-/
@[category research formally solved using lean4 at
"https://github.com/plby/lean-proofs/blob/main/src/v4.24.0/ErdosProblems/Erdos1071b.lean", AMS 52]
theorem erdos_1071.parts.ii :
answer(sorry) ↔ ∃ (R : Set ℝ²) (S : Set (ℝ² × ℝ²)),
S.Countable ∧ S.Infinite ∧
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