`BookProof.ChapterAttentionCollision.collisionProb_le_one` {p : Fin m → ℝ} (hp0 : ∀ j, 0 ≤ p j) (hp1 : ∀ j, p j ≤ 1) (hsum : ∑ j, p j = 1) : collisionProb p ≤ 1

Proved

BookProof.ChapterAttentionCollision.collisionProb_le_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionCollision.

BookProof.ChapterAttentionCollision.collisionProb_le_one {p : Fin m → ℝ} (hp0 : ∀ j, 0 ≤ p j) (hp1 : ∀ j, p j ≤ 1) (hsum : ∑ j, p j = 1) : collisionProb p ≤ 1

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

Preamble

-- Generated from ChapterAttentionCollision.lean — theorem BookProof.ChapterAttentionCollision.collisionProb_le_one
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_le_one {p : Fin m → ℝ} (hp0 : ∀ j, 0 ≤ p j) (hp1 : ∀ j, p j ≤ 1)
    (hsum : ∑ j, p j = 1) : collisionProb p ≤ 1 := by sorry

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