`BookProof.ChapterEulerDensityMatrix.euler_rhs` (t : ℝ) : (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

Proved

BookProof.ChapterEulerDensityMatrix.euler_rhs

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerDensityMatrix.

BookProof.ChapterEulerDensityMatrix.euler_rhs (t : ℝ) : (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) = !![1 / 2 + Real.cos (2 * t) / 2, Real.sin (2 * t) / 2; Real.sin (2 * t) / 2, 1 / 2 - Real.cos (2 * t) / 2]

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

Preamble

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


open scoped Matrix

Formal statement

theorem BookProof.ChapterEulerDensityMatrix.euler_rhs (t : ℝ) :
    (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)
      = !![1 / 2 + Real.cos (2 * t) / 2, Real.sin (2 * t) / 2;
           Real.sin (2 * t) / 2, 1 / 2 - Real.cos (2 * t) / 2] := by sorry

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