`BookProof.ChapterB4.pure_state_satisfies_P1` : ∃ ρ, IsPureState ρ ∧ Matrix.trace (ρ * P1) = 1 / 2

Proved

BookProof.ChapterB4.pure_state_satisfies_P1

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterB4.

BookProof.ChapterB4.pure_state_satisfies_P1 : ∃ ρ, IsPureState ρ ∧ Matrix.trace (ρ * P1) = 1 / 2

Formalization note: Lean 4 identifier BookProof.ChapterB4.pure_state_satisfies_P1.

Preamble

-- Generated from ChapterB4.lean — theorem BookProof.ChapterB4.pure_state_satisfies_P1
import Mathlib
import Definitions.Def_ChapterB4
open BookProof.ChapterB4



open Matrix

noncomputable section

Formal statement

theorem BookProof.ChapterB4.pure_state_satisfies_P1 :
    ∃ ρ, IsPureState ρ ∧ Matrix.trace (ρ * P1) = 1 / 2 := by sorry

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