Prove2Me

`BookProof.ChapterAttentionRetrieval.exp_le_denom` (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : Real.exp (beta * s j) ≤ ∑ l, Real.exp (beta * s l)

Proved
BookProof.ChapterAttentionRetrieval.exp_le_denom

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionRetrieval.

BookProof.ChapterAttentionRetrieval.exp_le_denom (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : Real.exp (beta * s j) ≤ ∑ l, Real.exp (beta * s l)

Formalization note: Lean 4 identifier BookProof.ChapterAttentionRetrieval.exp_le_denom.

Preamble
-- Generated from ChapterAttentionRetrieval.lean — theorem BookProof.ChapterAttentionRetrieval.exp_le_denom
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionRetrieval
open BookProof.ChapterAttentionRetrieval


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m n : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
Formal statement
theorem BookProof.ChapterAttentionRetrieval.exp_le_denom (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) :
    Real.exp (beta * s j) ≤ ∑ l, Real.exp (beta * s l) := by sorry

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