`BookProof.ChapterRotaryPosition.inner_rotaryEncode` (omega : Fin n → ℝ) (a b : ℝ) (q k : EuclideanSpace ℂ (Fin n)) : (inner ℂ (rotaryEncode omega a q) (rotaryEncode omega b k) : ℂ

Proved

BookProof.ChapterRotaryPosition.inner_rotaryEncode

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterRotaryPosition.

BookProof.ChapterRotaryPosition.inner_rotaryEncode (omega : Fin n → ℝ) (a b : ℝ) (q k : EuclideanSpace ℂ (Fin n)) : (inner ℂ (rotaryEncode omega a q) (rotaryEncode omega b k) : ℂ) = inner ℂ q (rotaryEncode omega (b - a) k)

Formalization note: Lean 4 identifier BookProof.ChapterRotaryPosition.inner_rotaryEncode.

Preamble

-- Generated from ChapterRotaryPosition.lean — theorem BookProof.ChapterRotaryPosition.inner_rotaryEncode
import Definitions.Def_ChapterCoherentOverlapComplex
import Mathlib
import Definitions.Def_ChapterRotaryPosition
open BookProof.ChapterRotaryPosition


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlapComplex

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterRotaryPosition.inner_rotaryEncode (omega : Fin n → ℝ) (a b : ℝ) (q k : EuclideanSpace ℂ (Fin n)) :
    (inner ℂ (rotaryEncode omega a q) (rotaryEncode omega b k) : ℂ)
      = inner ℂ q (rotaryEncode omega (b - a) k) := by sorry

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