`BookProof.ChapterRotaryPosition.coherentOverlapC_rotaryEncode` (omega : Fin n → ℝ) (a b : ℝ) (q k : EuclideanSpace ℂ (Fin n)) : coherentOverlapC (rotaryEncode omega a q) (rotaryEn

Proved

BookProof.ChapterRotaryPosition.coherentOverlapC_rotaryEncode

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterRotaryPosition.

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

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

Preamble

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


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlapComplex

variable {n m : ℕ}

Formal statement

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

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