`BookProof.ChapterGaugeCasimirAverage.finiteGaugeAverage_of_isPhysicalObservable` {f : X → ℝ} (hf : IsPhysicalObservable G f) : finiteGaugeAverage (X := X) G f = f

Proved

BookProof.ChapterGaugeCasimirAverage.finiteGaugeAverage_of_isPhysicalObservable

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeCasimirAverage.

BookProof.ChapterGaugeCasimirAverage.finiteGaugeAverage_of_isPhysicalObservable {f : X → ℝ} (hf : IsPhysicalObservable G f) : finiteGaugeAverage (X := X) G f = f

Formalization note: Lean 4 identifier BookProof.ChapterGaugeCasimirAverage.finiteGaugeAverage_of_isPhysicalObservable.

Preamble

-- Generated from ChapterGaugeCasimirAverage.lean — theorem BookProof.ChapterGaugeCasimirAverage.finiteGaugeAverage_of_isPhysicalObservable
import Mathlib
import Definitions.Def_ChapterGaugeCasimirAverage
import Definitions.Def_ChapterGaugeIncompleteFixing
open BookProof.ChapterGaugeIncompleteFixing
open BookProof.ChapterGaugeCasimirAverage



open BookProof.ChapterGaugeIncompleteFixing
open MeasureTheory
open scoped InnerProductSpace

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
variable {ι : Type*} [Fintype ι]
variable {X : Type*}
variable {G : Type*} [Group G] [MeasurableSpace G] [MeasurableMul G] [MulAction G X]
variable {X : Type*} {G : Type*} [Group G] [Fintype G] [MulAction G X]

Formal statement

theorem BookProof.ChapterGaugeCasimirAverage.finiteGaugeAverage_of_isPhysicalObservable {f : X → ℝ}
    (hf : IsPhysicalObservable G f) :
    finiteGaugeAverage (X := X) G f = f := by sorry

View graph