`BookProof.ChapterAttentionPrior.priorSoftmax_eq_posterior` (w : Fin m → ℝ) (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : priorSoftmax w beta s j = posterior w (fun l (_ : Unit) => Real

Proved

BookProof.ChapterAttentionPrior.priorSoftmax_eq_posterior

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionPrior.

BookProof.ChapterAttentionPrior.priorSoftmax_eq_posterior (w : Fin m → ℝ) (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) : priorSoftmax w beta s j = posterior w (fun l (_ : Unit) => Real.exp (beta * s l)) () j

Formalization note: Lean 4 identifier BookProof.ChapterAttentionPrior.priorSoftmax_eq_posterior.

Preamble

-- Generated from ChapterAttentionPrior.lean — theorem BookProof.ChapterAttentionPrior.priorSoftmax_eq_posterior
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionPrior
import Definitions.Def_ChapterBayesInference
open BookProof.ChapterBayesInference
open BookProof.ChapterAttentionPrior


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionPrior.priorSoftmax_eq_posterior (w : Fin m → ℝ) (beta : ℝ) (s : Fin m → ℝ) (j : Fin m) :
    priorSoftmax w beta s j
      = posterior w (fun l (_ : Unit) => Real.exp (beta * s l)) () j := by sorry

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