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

Proved

BookProof.ChapterRotaryPosition.inner_rotaryEncode_shift

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterRotaryPosition.

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

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

Preamble

-- Generated from ChapterRotaryPosition.lean — theorem BookProof.ChapterRotaryPosition.inner_rotaryEncode_shift
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_shift (omega : Fin n → ℝ) (a b c : ℝ)
    (q k : EuclideanSpace ℂ (Fin n)) :
    (inner ℂ (rotaryEncode omega (a + c) q) (rotaryEncode omega (b + c) k) : ℂ)
      = inner ℂ (rotaryEncode omega a q) (rotaryEncode omega b k) := by sorry

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