`BookProof.ChapterEulerDensityMatrix.density_collapse` (t : ℝ) : densityMatrix t - (Real.sin (2 * t)) • (Zdiag * Jdens) = !![Real.cos t ^ 2, 0; 0, Real.sin t ^ 2]

Proved

BookProof.ChapterEulerDensityMatrix.density_collapse

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerDensityMatrix.

BookProof.ChapterEulerDensityMatrix.density_collapse (t : ℝ) : densityMatrix t - (Real.sin (2 * t)) • (Zdiag * Jdens) = !![Real.cos t ^ 2, 0; 0, Real.sin t ^ 2]

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

Preamble

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


open scoped Matrix

Formal statement

theorem BookProof.ChapterEulerDensityMatrix.density_collapse (t : ℝ) :
    densityMatrix t - (Real.sin (2 * t)) • (Zdiag * Jdens)
      = !![Real.cos t ^ 2, 0; 0, Real.sin t ^ 2] := by sorry

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