`BookProof.SmHamiltonian.realCoeff_C_real` {d : ℕ} (t : ℝ) : RealCoeff (C ((t : ℝ) : ℂ) : MvPolynomial (Fin d) ℂ)

Proved

BookProof.SmHamiltonian.realCoeff_C_real

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmHamiltonian.

BookProof.SmHamiltonian.realCoeff_C_real {d : ℕ} (t : ℝ) : RealCoeff (C ((t : ℝ) : ℂ) : MvPolynomial (Fin d) ℂ)

Formalization note: Lean 4 identifier BookProof.SmHamiltonian.realCoeff_C_real.

Preamble

-- Generated from ChapterSmHamiltonian.lean — theorem BookProof.SmHamiltonian.realCoeff_C_real
import Definitions.Def_ChapterSmOneParticle
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterFriedrichsExtension
import Mathlib
import Definitions.Def_ChapterSmHamiltonian
import Definitions.Def_ChapterYangMillsHermite
open BookProof.YangMillsHermite
open BookProof.SmHamiltonian



open MvPolynomial
open BookProof.SmOneParticle
open BookProof.YangMillsHermite BookProof.YangMillsFriedrichs
open BookProof.HermiteProductCore BookProof.FarisLavine
open BookProof.FriedrichsExtension

noncomputable section

Formal statement

theorem BookProof.SmHamiltonian.realCoeff_C_real {d : ℕ} (t : ℝ) :
    RealCoeff (C ((t : ℝ) : ℂ) : MvPolynomial (Fin d) ℂ) := by sorry

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