Prove2Me

`BookProof.ChapterEntropyTemperature.heatCapacity_nonneg` (beta : ℝ) (s : Fin m → ℝ) : 0 ≤ heatCapacity beta s

Proved
BookProof.ChapterEntropyTemperature.heatCapacity_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEntropyTemperature.

BookProof.ChapterEntropyTemperature.heatCapacity_nonneg (beta : ℝ) (s : Fin m → ℝ) : 0 ≤ heatCapacity beta s

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

Preamble
-- Generated from ChapterEntropyTemperature.lean — theorem BookProof.ChapterEntropyTemperature.heatCapacity_nonneg
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.heatCapacity_nonneg (beta : ℝ) (s : Fin m → ℝ) : 0 ≤ heatCapacity beta s := by sorry

View graph