`BookProof.ChapterCoherentFidelity.fidelityC_lt_iff_dist_lt` (q k k' : EuclideanSpace ℂ (Fin n)) : fidelityC q k < fidelityC q k' ↔ ‖q - k'‖ < ‖q - k‖

Proved

BookProof.ChapterCoherentFidelity.fidelityC_lt_iff_dist_lt

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentFidelity.

BookProof.ChapterCoherentFidelity.fidelityC_lt_iff_dist_lt (q k k' : EuclideanSpace ℂ (Fin n)) : fidelityC q k < fidelityC q k' ↔ ‖q - k'‖ < ‖q - k‖

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

Preamble

-- Generated from ChapterCoherentFidelity.lean — theorem BookProof.ChapterCoherentFidelity.fidelityC_lt_iff_dist_lt
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_lt_iff_dist_lt (q k k' : EuclideanSpace ℂ (Fin n)) :
    fidelityC q k < fidelityC q k' ↔ ‖q - k'‖ < ‖q - k‖ := by sorry

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