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`BookProof.ChapterEulerDensityMatrix.densityMatrix_idempotent` (t : ℝ) : densityMatrix t * densityMatrix t = densityMatrix t

Proved
BookProof.ChapterEulerDensityMatrix.densityMatrix_idempotent

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerDensityMatrix.

BookProof.ChapterEulerDensityMatrix.densityMatrix_idempotent (t : ℝ) : densityMatrix t * densityMatrix t = densityMatrix t

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

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


open scoped Matrix
Formal statement
theorem BookProof.ChapterEulerDensityMatrix.densityMatrix_idempotent (t : ℝ) :
    densityMatrix t * densityMatrix t = densityMatrix t := by sorry

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