`BookProof.ChapterCoherentFidelity.bornWeightC_eq_fidelity_normalized` (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) : bornWeightC q k j = fidel

Proved

BookProof.ChapterCoherentFidelity.bornWeightC_eq_fidelity_normalized

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentFidelity.

BookProof.ChapterCoherentFidelity.bornWeightC_eq_fidelity_normalized (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) : bornWeightC q k j = fidelityC q (k j) / ∑ l, fidelityC q (k l)

Formalization note: Lean 4 identifier BookProof.ChapterCoherentFidelity.bornWeightC_eq_fidelity_normalized.

Preamble

-- Generated from ChapterCoherentFidelity.lean — theorem BookProof.ChapterCoherentFidelity.bornWeightC_eq_fidelity_normalized
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterCoherentFidelity
import Definitions.Def_ChapterCoherentOverlapComplex
open BookProof.ChapterCoherentOverlapComplex
open BookProof.ChapterCoherentFidelity


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlapComplex BookProof.ChapterSoftmaxSharpness

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentFidelity.bornWeightC_eq_fidelity_normalized (q : EuclideanSpace ℂ (Fin n))
    (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) :
    bornWeightC q k j = fidelityC q (k j) / ∑ l, fidelityC q (k l) := by sorry

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