`BookProof.ChapterGaugeUnconstrainedSpectrum.exists_eigenvalue_of_isFunctionOfSpectrum` [DecidableEq X] {T : Op X} (hT : IsFunctionOfSpectrum T) (y : X) : ∃ c : ℂ, T (basisVec y) =

Proved

BookProof.ChapterGaugeUnconstrainedSpectrum.exists_eigenvalue_of_isFunctionOfSpectrum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeUnconstrainedSpectrum.

BookProof.ChapterGaugeUnconstrainedSpectrum.exists_eigenvalue_of_isFunctionOfSpectrum [DecidableEq X] {T : Op X} (hT : IsFunctionOfSpectrum T) (y : X) : ∃ c : ℂ, T (basisVec y) = c • basisVec y

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

Preamble

-- Generated from ChapterGaugeUnconstrainedSpectrum.lean — theorem BookProof.ChapterGaugeUnconstrainedSpectrum.exists_eigenvalue_of_isFunctionOfSpectrum
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.exists_eigenvalue_of_isFunctionOfSpectrum [DecidableEq X] {T : Op X}
    (hT : IsFunctionOfSpectrum T) (y : X) :
    ∃ c : ℂ, T (basisVec y) = c • basisVec y := by sorry

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