`BookProof.ChapterEulerDensityMatrix.density_euler` (t : ℝ) : densityMatrix t = (1 / 2 : ℝ) • (1 : Matrix (Fin 2) (Fin 2) ℝ) + Zdiag * ((Real.cos (2 * t)) • (1 : Matrix (Fin 2) (Fi

Proved

BookProof.ChapterEulerDensityMatrix.density_euler

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerDensityMatrix.

BookProof.ChapterEulerDensityMatrix.density_euler (t : ℝ) : densityMatrix t = (1 / 2 : ℝ) • (1 : Matrix (Fin 2) (Fin 2) ℝ) + Zdiag * ((Real.cos (2 * t)) • (1 : Matrix (Fin 2) (Fin 2) ℝ) + (Real.sin (2 * t)) • Jdens)

Formalization note: Lean 4 identifier BookProof.ChapterEulerDensityMatrix.density_euler.

Preamble

-- Generated from ChapterEulerDensityMatrix.lean — theorem BookProof.ChapterEulerDensityMatrix.density_euler
import Mathlib
import Definitions.Def_ChapterEulerDensityMatrix
open BookProof.ChapterEulerDensityMatrix


open scoped Matrix

Formal statement

theorem BookProof.ChapterEulerDensityMatrix.density_euler (t : ℝ) :
    densityMatrix t =
      (1 / 2 : ℝ) • (1 : Matrix (Fin 2) (Fin 2) ℝ)
        + Zdiag * ((Real.cos (2 * t)) • (1 : Matrix (Fin 2) (Fin 2) ℝ)
            + (Real.sin (2 * t)) • Jdens) := by sorry

View graph