`BookProof.ChapterF3.diagGen_eigenstate` (a : ℂ) (n : ℕ) : (a • ChapterF1.numberOp) (X ^ n) = (a * n) • X ^ n

Proved

BookProof.ChapterF3.diagGen_eigenstate

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF3.

BookProof.ChapterF3.diagGen_eigenstate (a : ℂ) (n : ℕ) : (a • ChapterF1.numberOp) (X ^ n) = (a * n) • X ^ n

Formalization note: Lean 4 identifier BookProof.ChapterF3.diagGen_eigenstate.

Preamble

-- Generated from ChapterF3.lean — theorem BookProof.ChapterF3.diagGen_eigenstate
import Mathlib
import Definitions.Def_ChapterF3
import Definitions.Def_ChapterGhostField
open BookProof.GhostField
open BookProof.ChapterF3


open scoped BigOperators
open Polynomial


noncomputable section

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E]

Formal statement

theorem BookProof.ChapterF3.diagGen_eigenstate (a : ℂ) (n : ℕ) :
    (a • ChapterF1.numberOp) (X ^ n) = (a * n) • X ^ n := by sorry

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