`BookProof.ChapterRotaryPosition.bornWeightC_rotaryEncode_shift` (omega : Fin n → ℝ) (a c : ℝ) (pos : Fin m → ℝ) (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n

Proved

BookProof.ChapterRotaryPosition.bornWeightC_rotaryEncode_shift

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterRotaryPosition.

BookProof.ChapterRotaryPosition.bornWeightC_rotaryEncode_shift (omega : Fin n → ℝ) (a c : ℝ) (pos : Fin m → ℝ) (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) : bornWeightC (rotaryEncode omega (a + c) q) (fun l => rotaryEncode omega (pos l + c) (k l)) j = bornWeightC (rotaryEncode omega a q) (fun l => rotaryEncode omega (pos l) (k l)) j

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

Preamble

-- Generated from ChapterRotaryPosition.lean — theorem BookProof.ChapterRotaryPosition.bornWeightC_rotaryEncode_shift
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.bornWeightC_rotaryEncode_shift (omega : Fin n → ℝ) (a c : ℝ)
    (pos : Fin m → ℝ) (q : EuclideanSpace ℂ (Fin n))
    (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) :
    bornWeightC (rotaryEncode omega (a + c) q)
        (fun l => rotaryEncode omega (pos l + c) (k l)) j
      = bornWeightC (rotaryEncode omega a q) (fun l => rotaryEncode omega (pos l) (k l)) j := by sorry

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