`BookProof.ChapterAttentionCollision.collisionProb_uniform` (hm : 0 < m) : collisionProb (fun _ : Fin m => (1 : ℝ) / m) = (m : ℝ)⁻¹

Proved

BookProof.ChapterAttentionCollision.collisionProb_uniform

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionCollision.

BookProof.ChapterAttentionCollision.collisionProb_uniform (hm : 0 < m) : collisionProb (fun _ : Fin m => (1 : ℝ) / m) = (m : ℝ)⁻¹

Formalization note: Lean 4 identifier BookProof.ChapterAttentionCollision.collisionProb_uniform.

Preamble

-- Generated from ChapterAttentionCollision.lean — theorem BookProof.ChapterAttentionCollision.collisionProb_uniform
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionCollision
open BookProof.ChapterAttentionCollision


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionCollision.collisionProb_uniform (hm : 0 < m) :
    collisionProb (fun _ : Fin m => (1 : ℝ) / m) = (m : ℝ)⁻¹ := by sorry

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