`BookProof.ChapterSoftmaxSharpness.ampBorn_nonneg` (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (j : Fin m) : 0 ≤ ampBorn q k j

Proved

BookProof.ChapterSoftmaxSharpness.ampBorn_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSoftmaxSharpness.

BookProof.ChapterSoftmaxSharpness.ampBorn_nonneg (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (j : Fin m) : 0 ≤ ampBorn q k j

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

Preamble

-- Generated from ChapterSoftmaxSharpness.lean — theorem BookProof.ChapterSoftmaxSharpness.ampBorn_nonneg
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_nonneg (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n))
    (j : Fin m) : 0 ≤ ampBorn q k j := by sorry

View graph