`BookProof.ChapterGaugeIncompleteFixing.physical_ext_of_comprehensive` {S : Set X} (hS : IsComprehensiveGaugeFixing G S) {f f' : X → ℝ} (hf : IsPhysicalObservable G f) (hf' : IsPhy

Proved

BookProof.ChapterGaugeIncompleteFixing.physical_ext_of_comprehensive

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeIncompleteFixing.

BookProof.ChapterGaugeIncompleteFixing.physical_ext_of_comprehensive {S : Set X} (hS : IsComprehensiveGaugeFixing G S) {f f' : X → ℝ} (hf : IsPhysicalObservable G f) (hf' : IsPhysicalObservable G f') (hagree : ∀ s ∈ S, f s = f' s) : f = f'

Formalization note: Lean 4 identifier BookProof.ChapterGaugeIncompleteFixing.physical_ext_of_comprehensive.

Preamble

-- Generated from ChapterGaugeIncompleteFixing.lean — theorem BookProof.ChapterGaugeIncompleteFixing.physical_ext_of_comprehensive
import Mathlib
import Definitions.Def_ChapterGaugeIncompleteFixing
open BookProof.ChapterGaugeIncompleteFixing


open scoped InnerProductSpace

variable {X : Type*}
variable (G : Type*) [Group G] [MulAction G X]

Formal statement

theorem BookProof.ChapterGaugeIncompleteFixing.physical_ext_of_comprehensive {S : Set X}
    (hS : IsComprehensiveGaugeFixing G S) {f f' : X → ℝ}
    (hf : IsPhysicalObservable G f) (hf_prime : IsPhysicalObservable G f')
    (hagree : ∀ s ∈ S, f s = f' s) : f = f' := by sorry

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