`BookProof.ChapterEulerGenericDensity.density_symm` (θ : ℝ) (l w : Fin d → ℝ) : (Matrix.vecMulVec (eulerVec θ l w) (eulerVec θ l w))ᵀ = Matrix.vecMulVec (eulerVec θ l w) (eulerVec

Proved

BookProof.ChapterEulerGenericDensity.density_symm

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerGenericDensity.

BookProof.ChapterEulerGenericDensity.density_symm (θ : ℝ) (l w : Fin d → ℝ) : (Matrix.vecMulVec (eulerVec θ l w) (eulerVec θ l w))ᵀ = Matrix.vecMulVec (eulerVec θ l w) (eulerVec θ l w)

Formalization note: Lean 4 identifier BookProof.ChapterEulerGenericDensity.density_symm.

Preamble

-- Generated from ChapterEulerGenericDensity.lean — theorem BookProof.ChapterEulerGenericDensity.density_symm
import Mathlib
import Definitions.Def_ChapterEulerGenericDensity
open BookProof.ChapterEulerGenericDensity


open scoped Matrix
open Matrix


variable {d : ℕ}

Formal statement

theorem BookProof.ChapterEulerGenericDensity.density_symm (θ : ℝ) (l w : Fin d → ℝ) :
    (Matrix.vecMulVec (eulerVec θ l w) (eulerVec θ l w))ᵀ
      = Matrix.vecMulVec (eulerVec θ l w) (eulerVec θ l w) := by sorry

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