`BookProof.ChapterCoherentOverlapComplex.bornWeightC_phase_invariant` (q : EuclideanSpace ℂ (Fin n)) (k k' : Fin m → EuclideanSpace ℂ (Fin n)) (hnorm : ∀ l, ‖k' l‖ = ‖k l‖) (hre :

Proved

BookProof.ChapterCoherentOverlapComplex.bornWeightC_phase_invariant

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOverlapComplex.

BookProof.ChapterCoherentOverlapComplex.bornWeightC_phase_invariant (q : EuclideanSpace ℂ (Fin n)) (k k' : Fin m → EuclideanSpace ℂ (Fin n)) (hnorm : ∀ l, ‖k' l‖ = ‖k l‖) (hre : ∀ l, (inner ℂ q (k' l) : ℂ).re = (inner ℂ q (k l) : ℂ).re) (j : Fin m) : bornWeightC q k' j = bornWeightC q k j

Formalization note: Lean 4 identifier BookProof.ChapterCoherentOverlapComplex.bornWeightC_phase_invariant.

Preamble

-- Generated from ChapterCoherentOverlapComplex.lean — theorem BookProof.ChapterCoherentOverlapComplex.bornWeightC_phase_invariant
import Mathlib
import Definitions.Def_ChapterCoherentOverlapComplex
open BookProof.ChapterCoherentOverlapComplex


open scoped BigOperators

noncomputable section


variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentOverlapComplex.bornWeightC_phase_invariant (q : EuclideanSpace ℂ (Fin n))
    (k k' : Fin m → EuclideanSpace ℂ (Fin n)) (hnorm : ∀ l, ‖k' l‖ = ‖k l‖)
    (hre : ∀ l, (inner ℂ q (k' l) : ℂ).re = (inner ℂ q (k l) : ℂ).re) (j : Fin m) :
    bornWeightC q k' j = bornWeightC q k j := by sorry

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