`BookProof.ChapterCoherentOverlapComplex.coherentOverlapC_ofReal` (q k : EuclideanSpace ℝ (Fin n)) : coherentOverlapC (ofRealVec q) (ofRealVec k) = ((BookProof.ChapterCoherentOverl

Proved

BookProof.ChapterCoherentOverlapComplex.coherentOverlapC_ofReal

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCoherentOverlapComplex.

BookProof.ChapterCoherentOverlapComplex.coherentOverlapC_ofReal (q k : EuclideanSpace ℝ (Fin n)) : coherentOverlapC (ofRealVec q) (ofRealVec k) = ((BookProof.ChapterCoherentOverlap.coherentOverlap q k : ℝ) : ℂ)

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

Preamble

-- Generated from ChapterCoherentOverlapComplex.lean — theorem BookProof.ChapterCoherentOverlapComplex.coherentOverlapC_ofReal
import Mathlib
import Definitions.Def_ChapterCoherentOverlapComplex
import Definitions.Def_ChapterCoherentOverlap
open BookProof.ChapterCoherentOverlap
open BookProof.ChapterCoherentOverlapComplex


open scoped BigOperators

noncomputable section


variable {n m : ℕ}

Formal statement

theorem BookProof.ChapterCoherentOverlapComplex.coherentOverlapC_ofReal (q k : EuclideanSpace ℝ (Fin n)) :
    coherentOverlapC (ofRealVec q) (ofRealVec k)
      = ((BookProof.ChapterCoherentOverlap.coherentOverlap q k : ℝ) : ℂ) := by sorry

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