`BookProof.ChapterB4.no_pure_state_satisfies_both` : ¬ ∃ ρ, IsPureState ρ ∧ Matrix.trace (ρ * P1) = 1 / 2 ∧ Matrix.trace (ρ * P2) = 1 / 2

Proved

BookProof.ChapterB4.no_pure_state_satisfies_both

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterB4.

BookProof.ChapterB4.no_pure_state_satisfies_both : ¬ ∃ ρ, IsPureState ρ ∧ Matrix.trace (ρ * P1) = 1 / 2 ∧ Matrix.trace (ρ * P2) = 1 / 2

Formalization note: Lean 4 identifier BookProof.ChapterB4.no_pure_state_satisfies_both.

Preamble

-- Generated from ChapterB4.lean — theorem BookProof.ChapterB4.no_pure_state_satisfies_both
import Mathlib
import Definitions.Def_ChapterB4
open BookProof.ChapterB4



open Matrix

noncomputable section

Formal statement

theorem BookProof.ChapterB4.no_pure_state_satisfies_both :
    ¬ ∃ ρ, IsPureState ρ ∧ Matrix.trace (ρ * P1) = 1 / 2 ∧
      Matrix.trace (ρ * P2) = 1 / 2 := by sorry

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