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`BookProof.ChapterSinusoidalPosition.peInner_shift` (w : Fin n → ℝ) (p q t : ℝ) : peInner w (p + t) (q + t) = peInner w p q

Proved
BookProof.ChapterSinusoidalPosition.peInner_shift

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSinusoidalPosition.

BookProof.ChapterSinusoidalPosition.peInner_shift (w : Fin n → ℝ) (p q t : ℝ) : peInner w (p + t) (q + t) = peInner w p q

Formalization note: Lean 4 identifier BookProof.ChapterSinusoidalPosition.peInner_shift.

Preamble
-- Generated from ChapterSinusoidalPosition.lean — theorem BookProof.ChapterSinusoidalPosition.peInner_shift
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterSinusoidalPosition
open BookProof.ChapterSinusoidalPosition


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {n : ℕ}
Formal statement
theorem BookProof.ChapterSinusoidalPosition.peInner_shift (w : Fin n → ℝ) (p q t : ℝ) :
    peInner w (p + t) (q + t) = peInner w p q := by sorry

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