Prove2Me

`BookProof.ChapterEntropyTemperature.attentionEntropy_le_log_card` (s : Fin m → ℝ) (i : Fin m) {beta : ℝ} (hbeta : 0 ≤ beta) : attentionEntropy beta s ≤ Real.log m

Proved
BookProof.ChapterEntropyTemperature.attentionEntropy_le_log_card

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEntropyTemperature.

BookProof.ChapterEntropyTemperature.attentionEntropy_le_log_card (s : Fin m → ℝ) (i : Fin m) {beta : ℝ} (hbeta : 0 ≤ beta) : attentionEntropy beta s ≤ Real.log m

Formalization note: Lean 4 identifier BookProof.ChapterEntropyTemperature.attentionEntropy_le_log_card.

Preamble
-- Generated from ChapterEntropyTemperature.lean — theorem BookProof.ChapterEntropyTemperature.attentionEntropy_le_log_card
import Definitions.Def_ChapterAttentionEntropy
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterEntropyTemperature
open BookProof.ChapterEntropyTemperature


open scoped BigOperators

noncomputable section


open BookProof.ChapterAttentionEntropy BookProof.ChapterSoftmaxSharpness

variable {m : ℕ}
Formal statement
theorem BookProof.ChapterEntropyTemperature.attentionEntropy_le_log_card (s : Fin m → ℝ) (i : Fin m) {beta : ℝ}
    (hbeta : 0 ≤ beta) : attentionEntropy beta s ≤ Real.log m := by sorry

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