`BookProof.ChapterAttentionMarkov.attentionMatrix_pos` (beta : ℝ) (S : Fin m → Fin m → ℝ) (i j : Fin m) : 0 < attentionMatrix beta S i j

Proved

BookProof.ChapterAttentionMarkov.attentionMatrix_pos

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionMarkov.

BookProof.ChapterAttentionMarkov.attentionMatrix_pos (beta : ℝ) (S : Fin m → Fin m → ℝ) (i j : Fin m) : 0 < attentionMatrix beta S i j

Formalization note: Lean 4 identifier BookProof.ChapterAttentionMarkov.attentionMatrix_pos.

Preamble

-- Generated from ChapterAttentionMarkov.lean — theorem BookProof.ChapterAttentionMarkov.attentionMatrix_pos
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionMarkov
open BookProof.ChapterAttentionMarkov


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionMarkov.attentionMatrix_pos (beta : ℝ) (S : Fin m → Fin m → ℝ) (i j : Fin m) :
    0 < attentionMatrix beta S i j := by sorry

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