`BookProof.ChapterCoherentFidelity.fidelityC_ofReal` (q k : EuclideanSpace ℝ (Fin n)) : fidelityC (ofRealVec q) (ofRealVec k) = Real.exp (-‖q - k‖ ^ 2)

Proved

BookProof.ChapterCoherentFidelity.fidelityC_ofReal

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentFidelity.

BookProof.ChapterCoherentFidelity.fidelityC_ofReal (q k : EuclideanSpace ℝ (Fin n)) : fidelityC (ofRealVec q) (ofRealVec k) = Real.exp (-‖q - k‖ ^ 2)

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

Preamble

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


open scoped BigOperators

noncomputable section


open BookProof.ChapterCoherentOverlapComplex BookProof.ChapterSoftmaxSharpness

variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentFidelity.fidelityC_ofReal (q k : EuclideanSpace ℝ (Fin n)) :
    fidelityC (ofRealVec q) (ofRealVec k) = Real.exp (-‖q - k‖ ^ 2) := by sorry

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