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`BookProof.ChapterGaugeUnconstrainedSpectrum.constrainedSpectrum_eq_univ_of_isUnconstrained` {U : G → Op X} (hU : IsUnconstrainedGaugeFixing U) (hU1 : U 1 = LinearMap.id) : constra

Proved
BookProof.ChapterGaugeUnconstrainedSpectrum.constrainedSpectrum_eq_univ_of_isUnconstrained

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeUnconstrainedSpectrum.

BookProof.ChapterGaugeUnconstrainedSpectrum.constrainedSpectrum_eq_univ_of_isUnconstrained {U : G → Op X} (hU : IsUnconstrainedGaugeFixing U) (hU1 : U 1 = LinearMap.id) : constrainedSpectrum U = Set.univ

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

Preamble
-- Generated from ChapterGaugeUnconstrainedSpectrum.lean — theorem BookProof.ChapterGaugeUnconstrainedSpectrum.constrainedSpectrum_eq_univ_of_isUnconstrained
import Mathlib
import Definitions.Def_ChapterGaugeUnconstrainedSpectrum
import Definitions.Def_ChapterAbelianDiagonalCountable
open BookProof.ChapterAbelianDiagonalCountable
open BookProof.ChapterGaugeUnconstrainedSpectrum



variable {X : Type*}

variable {G : Type*} [Group G]
Formal statement
theorem BookProof.ChapterGaugeUnconstrainedSpectrum.constrainedSpectrum_eq_univ_of_isUnconstrained {U : G → Op X}
    (hU : IsUnconstrainedGaugeFixing U) (hU1 : U 1 = LinearMap.id) :
    constrainedSpectrum U = Set.univ := by sorry

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