`BookProof.ChapterCoherentFidelity.fidelityC_translation_invariant` (q k v : EuclideanSpace ℂ (Fin n)) : fidelityC (q + v) (k + v) = fidelityC q k

Proved

BookProof.ChapterCoherentFidelity.fidelityC_translation_invariant

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentFidelity.

BookProof.ChapterCoherentFidelity.fidelityC_translation_invariant (q k v : EuclideanSpace ℂ (Fin n)) : fidelityC (q + v) (k + v) = fidelityC q k

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

Preamble

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


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlapComplex BookProof.ChapterSoftmaxSharpness

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentFidelity.fidelityC_translation_invariant (q k v : EuclideanSpace ℂ (Fin n)) :
    fidelityC (q + v) (k + v) = fidelityC q k := by sorry

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