`BookProof.ChapterGleasonPureMixed.halfI_not_pure` : ¬ IsPureState ((1/2 : ℝ) • (1 : Matrix (Fin 2) (Fin 2) ℝ))

Proved

BookProof.ChapterGleasonPureMixed.halfI_not_pure

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGleasonPureMixed.

BookProof.ChapterGleasonPureMixed.halfI_not_pure : ¬ IsPureState ((1/2 : ℝ) • (1 : Matrix (Fin 2) (Fin 2) ℝ))

Formalization note: Lean 4 identifier BookProof.ChapterGleasonPureMixed.halfI_not_pure.

Preamble

-- Generated from ChapterGleasonPureMixed.lean — theorem BookProof.ChapterGleasonPureMixed.halfI_not_pure
import Mathlib
import Definitions.Def_ChapterGleasonPureMixed
import Definitions.Def_ChapterB4
open BookProof.ChapterB4
open BookProof.ChapterGleasonPureMixed


open scoped BigOperators
open Matrix

Formal statement

theorem BookProof.ChapterGleasonPureMixed.halfI_not_pure :
    ¬ IsPureState ((1/2 : ℝ) • (1 : Matrix (Fin 2) (Fin 2) ℝ)) := by sorry

View graph