`BookProof.ChapterAttentionStreaming.one_sub_newWeight_eq` (beta sn : ℝ) (s : Fin m → ℝ) : 1 - newWeight beta sn s = (∑ l, Real.exp (beta * s l)) / ((∑ l, Real.exp (beta * s l)) +

Proved

BookProof.ChapterAttentionStreaming.one_sub_newWeight_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionStreaming.

BookProof.ChapterAttentionStreaming.one_sub_newWeight_eq (beta sn : ℝ) (s : Fin m → ℝ) : 1 - newWeight beta sn s = (∑ l, Real.exp (beta * s l)) / ((∑ l, Real.exp (beta * s l)) + Real.exp (beta * sn))

Formalization note: Lean 4 identifier BookProof.ChapterAttentionStreaming.one_sub_newWeight_eq.

Preamble

-- Generated from ChapterAttentionStreaming.lean — theorem BookProof.ChapterAttentionStreaming.one_sub_newWeight_eq
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionStreaming
open BookProof.ChapterAttentionStreaming


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

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

Formal statement

theorem BookProof.ChapterAttentionStreaming.one_sub_newWeight_eq (beta sn : ℝ) (s : Fin m → ℝ) :
    1 - newWeight beta sn s
      = (∑ l, Real.exp (beta * s l))
          / ((∑ l, Real.exp (beta * s l)) + Real.exp (beta * sn)) := by sorry

View graph