`BookProof.ChapterGaugeUnconstrainedSpectrum.isUnconstrained_of_movesEveryPoint` [Nonempty X] {ρ : G →* Equiv.Perm X} (hmoves : ∀ g : G, g ≠ 1 → ∀ x : X, ρ g x ≠ x) : IsUnconstrain

Proved

BookProof.ChapterGaugeUnconstrainedSpectrum.isUnconstrained_of_movesEveryPoint

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeUnconstrainedSpectrum.

BookProof.ChapterGaugeUnconstrainedSpectrum.isUnconstrained_of_movesEveryPoint [Nonempty X] {ρ : G →* Equiv.Perm X} (hmoves : ∀ g : G, g ≠ 1 → ∀ x : X, ρ g x ≠ x) : IsUnconstrainedGaugeFixing (fun g => permOp (ρ g))

Formalization note: Lean 4 identifier BookProof.ChapterGaugeUnconstrainedSpectrum.isUnconstrained_of_movesEveryPoint.

Preamble

-- Generated from ChapterGaugeUnconstrainedSpectrum.lean — theorem BookProof.ChapterGaugeUnconstrainedSpectrum.isUnconstrained_of_movesEveryPoint
import Mathlib
import Definitions.Def_ChapterGaugeUnconstrainedSpectrum
open BookProof.ChapterGaugeUnconstrainedSpectrum



variable {X : Type*}

variable {G : Type*} [Group G]

Formal statement

theorem BookProof.ChapterGaugeUnconstrainedSpectrum.isUnconstrained_of_movesEveryPoint [Nonempty X]
    {ρ : G →* Equiv.Perm X} (hmoves : ∀ g : G, g ≠ 1 → ∀ x : X, ρ g x ≠ x) :
    IsUnconstrainedGaugeFixing (fun g => permOp (ρ g)) := by sorry

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