`BookProof.ChapterCoherentOverlapComplex.inner_ofRealVec` (q k : EuclideanSpace ℝ (Fin n)) : inner ℂ (ofRealVec q) (ofRealVec k) = ((inner ℝ q k : ℝ) : ℂ)

Proved

BookProof.ChapterCoherentOverlapComplex.inner_ofRealVec

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOverlapComplex.

BookProof.ChapterCoherentOverlapComplex.inner_ofRealVec (q k : EuclideanSpace ℝ (Fin n)) : inner ℂ (ofRealVec q) (ofRealVec k) = ((inner ℝ q k : ℝ) : ℂ)

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

Preamble

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


open scoped BigOperators

noncomputable section


variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentOverlapComplex.inner_ofRealVec (q k : EuclideanSpace ℝ (Fin n)) :
    inner ℂ (ofRealVec q) (ofRealVec k) = ((inner ℝ q k : ℝ) : ℂ) := by sorry

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