`BookProof.ChapterCoherentOverlapComplex.innerC_eq_sum` (q k : EuclideanSpace ℂ (Fin n)) : inner ℂ q k = ∑ i, (starRingEnd ℂ) (q i) * k i

Proved

BookProof.ChapterCoherentOverlapComplex.innerC_eq_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOverlapComplex.

BookProof.ChapterCoherentOverlapComplex.innerC_eq_sum (q k : EuclideanSpace ℂ (Fin n)) : inner ℂ q k = ∑ i, (starRingEnd ℂ) (q i) * k i

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

Preamble

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


open scoped BigOperators

noncomputable section


variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentOverlapComplex.innerC_eq_sum (q k : EuclideanSpace ℂ (Fin n)) :
    inner ℂ q k = ∑ i, (starRingEnd ℂ) (q i) * k i := by sorry

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