`BookProof.ChapterSoftmaxSharpness.tendsto_coherentBorn_smul_query` (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (r : ℝ) (hk : ∀ l, ‖k l‖ = r) (j : Fin m)

Proved

BookProof.ChapterSoftmaxSharpness.tendsto_coherentBorn_smul_query

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxSharpness.

BookProof.ChapterSoftmaxSharpness.tendsto_coherentBorn_smul_query (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (r : ℝ) (hk : ∀ l, ‖k l‖ = r) (j : Fin m) (hmax : ∀ l, l ≠ j → (inner ℝ q (k l) : ℝ) < inner ℝ q (k j)) : Tendsto (fun c : ℝ => bornWeight (c • q) k j) atTop (𝓝 1)

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

Preamble

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


open scoped BigOperators

noncomputable section


open Filter Topology BookProof.ChapterSoftmaxBorn

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterSoftmaxSharpness.tendsto_coherentBorn_smul_query (q : EuclideanSpace ℝ (Fin n))
    (k : Fin m → EuclideanSpace ℝ (Fin n)) (r : ℝ) (hk : ∀ l, ‖k l‖ = r) (j : Fin m)
    (hmax : ∀ l, l ≠ j → (inner ℝ q (k l) : ℝ) < inner ℝ q (k j)) :
    Tendsto (fun c : ℝ => bornWeight (c • q) k j) atTop (𝓝 1) := by sorry

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