`BookProof.ChapterEntropyTemperature.attentionEntropy_antitoneOn` (s : Fin m → ℝ) (i : Fin m) : AntitoneOn (fun b : ℝ => attentionEntropy b s) (Set.Ici (0 : ℝ))

Proved

BookProof.ChapterEntropyTemperature.attentionEntropy_antitoneOn

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEntropyTemperature.

BookProof.ChapterEntropyTemperature.attentionEntropy_antitoneOn (s : Fin m → ℝ) (i : Fin m) : AntitoneOn (fun b : ℝ => attentionEntropy b s) (Set.Ici (0 : ℝ))

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

Preamble

-- Generated from ChapterEntropyTemperature.lean — theorem BookProof.ChapterEntropyTemperature.attentionEntropy_antitoneOn
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_antitoneOn (s : Fin m → ℝ) (i : Fin m) :
    AntitoneOn (fun b : ℝ => attentionEntropy b s) (Set.Ici (0 : ℝ)) := by sorry

View graph