`BookProof.ChapterSoftmaxSharpness.tendsto_exp_mul_neg` (c : ℝ) (hc : c < 0) : Tendsto (fun b : ℝ => Real.exp (b * c)) atTop (𝓝 0)

Proved

BookProof.ChapterSoftmaxSharpness.tendsto_exp_mul_neg

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxSharpness.

BookProof.ChapterSoftmaxSharpness.tendsto_exp_mul_neg (c : ℝ) (hc : c < 0) : Tendsto (fun b : ℝ => Real.exp (b * c)) atTop (𝓝 0)

Formalization note: Lean 4 identifier BookProof.ChapterSoftmaxSharpness.tendsto_exp_mul_neg.

Preamble

-- Generated from ChapterSoftmaxSharpness.lean — theorem BookProof.ChapterSoftmaxSharpness.tendsto_exp_mul_neg
import Definitions.Def_ChapterSoftmaxBorn
import Mathlib
import Definitions.Def_ChapterSoftmaxSharpness
open BookProof.ChapterSoftmaxSharpness


open scoped BigOperators

noncomputable section


open Filter Topology BookProof.ChapterSoftmaxBorn

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxSharpness.tendsto_exp_mul_neg (c : ℝ) (hc : c < 0) :
    Tendsto (fun b : ℝ => Real.exp (b * c)) atTop (𝓝 0) := by sorry

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