`BookProof.ChapterCoherentGeometry.bornWeight_le_iff_dist_le` (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (i j : Fin m) : bornWeight q k i ≤ bornWeight q

Proved

BookProof.ChapterCoherentGeometry.bornWeight_le_iff_dist_le

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentGeometry.

BookProof.ChapterCoherentGeometry.bornWeight_le_iff_dist_le (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (i j : Fin m) : bornWeight q k i ≤ bornWeight q k j ↔ ‖q - k j‖ ≤ ‖q - k i‖

Formalization note: Lean 4 identifier BookProof.ChapterCoherentGeometry.bornWeight_le_iff_dist_le.

Preamble

-- Generated from ChapterCoherentGeometry.lean — theorem BookProof.ChapterCoherentGeometry.bornWeight_le_iff_dist_le
import Mathlib
import Definitions.Def_ChapterCoherentGeometry
import Definitions.Def_ChapterCoherentOverlap
import Definitions.Def_ChapterSoftmaxBorn
open BookProof.ChapterCoherentOverlap
open BookProof.ChapterSoftmaxBorn
open BookProof.ChapterCoherentGeometry


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlap BookProof.ChapterSoftmaxBorn

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentGeometry.bornWeight_le_iff_dist_le (q : EuclideanSpace ℝ (Fin n))
    (k : Fin m → EuclideanSpace ℝ (Fin n)) (i j : Fin m) :
    bornWeight q k i ≤ bornWeight q k j ↔ ‖q - k j‖ ≤ ‖q - k i‖ := by sorry

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