`BookProof.ChapterGaugeUnconstrainedSpectrum.exists_isUnconstrainedGaugeFixing` : ∃ (G : Type) (_ : Group G) (X : Type) (U : G → Op X), Nontrivial G ∧ IsUnconstrainedGaugeFixing U

Proved

BookProof.ChapterGaugeUnconstrainedSpectrum.exists_isUnconstrainedGaugeFixing

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeUnconstrainedSpectrum.

BookProof.ChapterGaugeUnconstrainedSpectrum.exists_isUnconstrainedGaugeFixing : ∃ (G : Type) (_ : Group G) (X : Type) (U : G → Op X), Nontrivial G ∧ IsUnconstrainedGaugeFixing U ∧ constrainedSpectrum U = Set.univ

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

Preamble

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



variable {X : Type*}

variable {G : Type*} [Group G]

Formal statement

theorem BookProof.ChapterGaugeUnconstrainedSpectrum.exists_isUnconstrainedGaugeFixing :
    ∃ (G : Type) (_ : Group G) (X : Type) (U : G → Op X),
      Nontrivial G ∧ IsUnconstrainedGaugeFixing U ∧
        constrainedSpectrum U = Set.univ := by sorry

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