`BookProof.ChapterGaugeComprehensiveFixing.physical_ext_iff_comprehensive` : (∀ f f' : X → ℝ, IsPhysicalObservable G f → IsPhysicalObservable G f' → (∀ s ∈ S, f s = f' s) → f = f')

Proved

BookProof.ChapterGaugeComprehensiveFixing.physical_ext_iff_comprehensive

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeComprehensiveFixing.

BookProof.ChapterGaugeComprehensiveFixing.physical_ext_iff_comprehensive : (∀ f f' : X → ℝ, IsPhysicalObservable G f → IsPhysicalObservable G f' → (∀ s ∈ S, f s = f' s) → f = f') ↔ IsComprehensiveGaugeFixing G S

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

Preamble

-- Generated from ChapterGaugeComprehensiveFixing.lean — theorem BookProof.ChapterGaugeComprehensiveFixing.physical_ext_iff_comprehensive
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] {S : Set X}

Formal statement

theorem BookProof.ChapterGaugeComprehensiveFixing.physical_ext_iff_comprehensive :
    (∀ f f' : X → ℝ, IsPhysicalObservable G f → IsPhysicalObservable G f' →
        (∀ s ∈ S, f s = f' s) → f = f') ↔ IsComprehensiveGaugeFixing G S := by sorry

View graph