`BookProof.ChapterCoherentOverlapComplex.softmaxDenomC_pos` (beta : ℝ) (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) : 0 < ∑ l, Real.exp (beta *

Proved

BookProof.ChapterCoherentOverlapComplex.softmaxDenomC_pos

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOverlapComplex.

BookProof.ChapterCoherentOverlapComplex.softmaxDenomC_pos (beta : ℝ) (q : EuclideanSpace ℂ (Fin n)) (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) : 0 < ∑ l, Real.exp (beta * (inner ℂ q (k l) : ℂ).re)

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

Preamble

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


open scoped BigOperators

noncomputable section


variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentOverlapComplex.softmaxDenomC_pos (beta : ℝ) (q : EuclideanSpace ℂ (Fin n))
    (k : Fin m → EuclideanSpace ℂ (Fin n)) (j : Fin m) :
    0 < ∑ l, Real.exp (beta * (inner ℂ q (k l) : ℂ).re) := by sorry

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