`BookProof.ChapterGaugeIncompleteFixing.remnant_faithful` [Nonempty X] (h : MovesEveryPointOfSpectrum G X) {g : G} (hg : ∀ x : X, g • x = x) : g = 1

Proved

BookProof.ChapterGaugeIncompleteFixing.remnant_faithful

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeIncompleteFixing.

BookProof.ChapterGaugeIncompleteFixing.remnant_faithful [Nonempty X] (h : MovesEveryPointOfSpectrum G X) {g : G} (hg : ∀ x : X, g • x = x) : g = 1

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

Preamble

-- Generated from ChapterGaugeIncompleteFixing.lean — theorem BookProof.ChapterGaugeIncompleteFixing.remnant_faithful
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.remnant_faithful [Nonempty X] (h : MovesEveryPointOfSpectrum G X)
    {g : G} (hg : ∀ x : X, g • x = x) : g = 1 := by sorry

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