`BookProof.ChapterG.ghost_car` : ghostAnnih * ghostCreat + ghostCreat * ghostAnnih = (1 : Matrix (Fin 2) (Fin 2) A)

Proved

BookProof.ChapterG.ghost_car

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterG.

BookProof.ChapterG.ghost_car : ghostAnnih * ghostCreat + ghostCreat * ghostAnnih = (1 : Matrix (Fin 2) (Fin 2) A)

Formalization note: Lean 4 identifier BookProof.ChapterG.ghost_car.

Preamble

-- Generated from ChapterG.lean — theorem BookProof.ChapterG.ghost_car
import Mathlib
import Definitions.Def_ChapterG
import Definitions.Def_ChapterNavierStokes
open BookProof.NavierStokes
open BookProof.ChapterG


open scoped ComplexConjugate InnerProductSpace Matrix
open MeasureTheory

variable {G : Type*} [Group G] [MeasurableSpace G]
variable {μG : Measure G} [IsProbabilityMeasure μG] [μG.IsMulLeftInvariant]
variable {X : Type*} [MulAction G X]
variable {A : Type*} [Ring A]

Formal statement

theorem BookProof.ChapterG.ghost_car :
    ghostAnnih * ghostCreat + ghostCreat * ghostAnnih = (1 : Matrix (Fin 2) (Fin 2) A) := by sorry

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