`BookProof.ChapterAttentionCollision.inv_card_le_collisionProb` {p : Fin m → ℝ} (hsum : ∑ j, p j = 1) : (m : ℝ)⁻¹ ≤ collisionProb p

Proved

BookProof.ChapterAttentionCollision.inv_card_le_collisionProb

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionCollision.

BookProof.ChapterAttentionCollision.inv_card_le_collisionProb {p : Fin m → ℝ} (hsum : ∑ j, p j = 1) : (m : ℝ)⁻¹ ≤ collisionProb p

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

Preamble

-- Generated from ChapterAttentionCollision.lean — theorem BookProof.ChapterAttentionCollision.inv_card_le_collisionProb
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.inv_card_le_collisionProb {p : Fin m → ℝ} (hsum : ∑ j, p j = 1) :
    (m : ℝ)⁻¹ ≤ collisionProb p := by sorry

View graph