`BookProof.ChapterSoftmaxSharpness.ampBorn_smul_query` (c : ℝ) (hc : c ≠ 0) (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (j : Fin m) : ampBorn (c • q) k j

Proved

BookProof.ChapterSoftmaxSharpness.ampBorn_smul_query

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxSharpness.

BookProof.ChapterSoftmaxSharpness.ampBorn_smul_query (c : ℝ) (hc : c ≠ 0) (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (j : Fin m) : ampBorn (c • q) k j = ampBorn q k j

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

Preamble

-- Generated from ChapterSoftmaxSharpness.lean — theorem BookProof.ChapterSoftmaxSharpness.ampBorn_smul_query
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.ampBorn_smul_query (c : ℝ) (hc : c ≠ 0) (q : EuclideanSpace ℝ (Fin n))
    (k : Fin m → EuclideanSpace ℝ (Fin n)) (j : Fin m) :
    ampBorn (c • q) k j = ampBorn q k j := by sorry

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