Prove2Me

`BookProof.ChapterGaugeComprehensiveFixing.exists_not_extendable_of_not_complete` (hS : ¬ IsCompleteGaugeFixing' G S) : ∃ h : X → ℝ, ¬ ∃ f : X → ℝ, IsPhysicalObservable G f ∧ ∀ s ∈

Proved
BookProof.ChapterGaugeComprehensiveFixing.exists_not_extendable_of_not_complete

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeComprehensiveFixing.

BookProof.ChapterGaugeComprehensiveFixing.exists_not_extendable_of_not_complete (hS : ¬ IsCompleteGaugeFixing' G S) : ∃ h : X → ℝ, ¬ ∃ f : X → ℝ, IsPhysicalObservable G f ∧ ∀ s ∈ S, f s = h s

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

Preamble
-- Generated from ChapterGaugeComprehensiveFixing.lean — theorem BookProof.ChapterGaugeComprehensiveFixing.exists_not_extendable_of_not_complete
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.exists_not_extendable_of_not_complete (hS : ¬ IsCompleteGaugeFixing' G S) :
    ∃ h : X → ℝ, ¬ ∃ f : X → ℝ, IsPhysicalObservable G f ∧ ∀ s ∈ S, f s = h s := by sorry

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