Prove2Me

`BookProof.ChapterGaugeComprehensiveFixing.not_isPhysicalObservable_indicator` [Nontrivial G] [Nonempty X] (hcomp : IsComprehensiveGaugeFixing G S) (hcompl : IsCompleteGaugeFixing'

Proved
BookProof.ChapterGaugeComprehensiveFixing.not_isPhysicalObservable_indicator

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeComprehensiveFixing.

BookProof.ChapterGaugeComprehensiveFixing.not_isPhysicalObservable_indicator [Nontrivial G] [Nonempty X] (hcomp : IsComprehensiveGaugeFixing G S) (hcompl : IsCompleteGaugeFixing' G S) (hfree : MovesEveryPointOfSpectrum G X) : ¬ IsPhysicalObservable G (S.indicator (fun _ => (1 : ℝ)))

Formalization note: Lean 4 identifier BookProof.ChapterGaugeComprehensiveFixing.not_isPhysicalObservable_indicator.

Preamble
-- Generated from ChapterGaugeComprehensiveFixing.lean — theorem BookProof.ChapterGaugeComprehensiveFixing.not_isPhysicalObservable_indicator
import Mathlib
import Definitions.Def_ChapterGaugeComprehensiveFixing
import Definitions.Def_ChapterGaugeIncompleteFixing
open BookProof.ChapterGaugeIncompleteFixing
open BookProof.ChapterGaugeComprehensiveFixing



open BookProof.ChapterGaugeIncompleteFixing

variable {X : Type*} (G : Type*) [Group G] [MulAction G X]
variable {X : Type*} {G : Type*} [Group G] [MulAction G X] {S : Set X}
Formal statement
theorem BookProof.ChapterGaugeComprehensiveFixing.not_isPhysicalObservable_indicator [Nontrivial G] [Nonempty X]
    (hcomp : IsComprehensiveGaugeFixing G S) (hcompl : IsCompleteGaugeFixing' G S)
    (hfree : MovesEveryPointOfSpectrum G X) :
    ¬ IsPhysicalObservable G (S.indicator (fun _ => (1 : ℝ))) := by sorry

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