`BookProof.ChapterGaugeUnconstrainedSpectrum.permOp_isFunctionOfSpectrum_iff` (σ : Equiv.Perm X) : IsFunctionOfSpectrum (permOp σ) ↔ σ = 1

Proved

BookProof.ChapterGaugeUnconstrainedSpectrum.permOp_isFunctionOfSpectrum_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeUnconstrainedSpectrum.

BookProof.ChapterGaugeUnconstrainedSpectrum.permOp_isFunctionOfSpectrum_iff (σ : Equiv.Perm X) : IsFunctionOfSpectrum (permOp σ) ↔ σ = 1

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

Preamble

-- Generated from ChapterGaugeUnconstrainedSpectrum.lean — theorem BookProof.ChapterGaugeUnconstrainedSpectrum.permOp_isFunctionOfSpectrum_iff
import Mathlib
import Definitions.Def_ChapterGaugeUnconstrainedSpectrum
import Definitions.Def_ChapterAbelianDiagonalCountable
import Definitions.Def_ChapterE4
open BookProof.ChapterAbelianDiagonalCountable
open BookProof.ChapterE4
open BookProof.ChapterGaugeUnconstrainedSpectrum



variable {X : Type*}

Formal statement

theorem BookProof.ChapterGaugeUnconstrainedSpectrum.permOp_isFunctionOfSpectrum_iff (σ : Equiv.Perm X) :
    IsFunctionOfSpectrum (permOp σ) ↔ σ = 1 := by sorry

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