Finite-nine escaped Form b exclusion at v1

Proved

Erdos9796FiniteNine.form_b_v1

by mysticflounder · Sep 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

discrete-geometryerdos-97finite-nineproof-transfer

At the first distinguished triangle vertex, an escaping four-point distance class cannot contain one point in the second cap interior together with the second triangle vertex in the third cap.

Preamble

/-
Copyright (c) 2026 Adam McKenna. All rights reserved.
Released under GPL-3.0-or-later as described in the file LICENSE.
Authors: Adam McKenna
-/

import Definitions.Def_Erdos9796FiniteNine_N8Interface

/-! Statement-only transfer node for the escaped Form b exclusion at `v₁`.

SKETCH — NOT PROMOTABLE. The source project already proves this result; the proof
solution will be transferred separately after this public theorem node exists.
-/

open scoped EuclideanGeometry

Formal statement

theorem Erdos9796FiniteNine.form_b_v1 {A : Finset ℝ²}
    (S : Batch3N9.Problem97.FiniteEndpointShell A) :
    S.N4dExcludesFormB_v1 := by sorry

Source

https://github.com/mysticflounder/erdos-97-96-formalization/tree/6e3e2a849c67f518d75fd45a09a201a6c8f4cd8f/lean/Erdos9796Proof/P97

View graph