`BookProof.ChapterF2.massGap_smallest_excited` (n : ℕ) (hn : n ≠ 0) : hamiltonian (X ^ n) = (n : ℂ) • X ^ n ∧ (1 : ℕ) ≤ n

Proved

BookProof.ChapterF2.massGap_smallest_excited

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF2.

BookProof.ChapterF2.massGap_smallest_excited (n : ℕ) (hn : n ≠ 0) : hamiltonian (X ^ n) = (n : ℂ) • X ^ n ∧ (1 : ℕ) ≤ n

Formalization note: Lean 4 identifier BookProof.ChapterF2.massGap_smallest_excited.

Preamble

-- Generated from ChapterF2.lean — theorem BookProof.ChapterF2.massGap_smallest_excited
import Definitions.Def_ChapterF1
import Mathlib
import Definitions.Def_ChapterF2
import Definitions.Def_ChapterNavierStokesFullEsa
open BookProof.NavierStokesFlow.FullEsa
open BookProof.NavierStokesFlow.FullEsa.NSFullData
open BookProof.ChapterF2


open Polynomial Finset
open scoped BigOperators


open BookProof.ChapterF1

noncomputable section

Formal statement

theorem BookProof.ChapterF2.massGap_smallest_excited (n : ℕ) (hn : n ≠ 0) :
    hamiltonian (X ^ n) = (n : ℂ) • X ^ n ∧ (1 : ℕ) ≤ n := by sorry

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