`BookProof.ChapterCoherentOverlapComplex.coherentBornC_eq_softmax_of_unit_keys` (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (hk : ∀ l, ‖k l‖ = 1) (j : Fin

Proved

BookProof.ChapterCoherentOverlapComplex.coherentBornC_eq_softmax_of_unit_keys

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOverlapComplex.

BookProof.ChapterCoherentOverlapComplex.coherentBornC_eq_softmax_of_unit_keys (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (hk : ∀ l, ‖k l‖ = 1) (j : Fin m) : bornWeightC q k j = softmaxC 2 q k j

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

Preamble

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


open scoped BigOperators

noncomputable section


variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentOverlapComplex.coherentBornC_eq_softmax_of_unit_keys (q : EuclideanSpace ℂ (Fin n))
    (k : Fin m → EuclideanSpace ℂ (Fin n)) (hk : ∀ l, ‖k l‖ = 1) (j : Fin m) :
    bornWeightC q k j = softmaxC 2 q k j := by sorry

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