`BookProof.ChapterAttentionMixture.mixture_nonneg` {w : Fin H → ℝ} {p : Fin H → Fin m → ℝ} (hw : ∀ h, 0 ≤ w h) (hp : ∀ h j, 0 ≤ p h j) (j : Fin m) : 0 ≤ mixture w p j

Proved

BookProof.ChapterAttentionMixture.mixture_nonneg

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMixture.

BookProof.ChapterAttentionMixture.mixture_nonneg {w : Fin H → ℝ} {p : Fin H → Fin m → ℝ} (hw : ∀ h, 0 ≤ w h) (hp : ∀ h j, 0 ≤ p h j) (j : Fin m) : 0 ≤ mixture w p j

Formalization note: Lean 4 identifier BookProof.ChapterAttentionMixture.mixture_nonneg.

Preamble

-- Generated from ChapterAttentionMixture.lean — theorem BookProof.ChapterAttentionMixture.mixture_nonneg
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionMixture
open BookProof.ChapterAttentionMixture


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m H : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]

Formal statement

theorem BookProof.ChapterAttentionMixture.mixture_nonneg {w : Fin H → ℝ} {p : Fin H → Fin m → ℝ} (hw : ∀ h, 0 ≤ w h)
    (hp : ∀ h j, 0 ≤ p h j) (j : Fin m) : 0 ≤ mixture w p j := by sorry

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