`BookProof.SqueezedGaussStates.Acoef_rec` (v : ℝ) (m : ℕ) : (2 * (m : ℝ) + 2) * Acoef v (m + 1) = 4 * v ^ 2 * (2 * (m : ℝ) + 1) * Acoef v m

Proved

BookProof.SqueezedGaussStates.Acoef_rec

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSqueezedGaussStates.

BookProof.SqueezedGaussStates.Acoef_rec (v : ℝ) (m : ℕ) : (2 * (m : ℝ) + 2) * Acoef v (m + 1) = 4 * v ^ 2 * (2 * (m : ℝ) + 1) * Acoef v m

Formalization note: Lean 4 identifier BookProof.SqueezedGaussStates.Acoef_rec.

Preamble

-- Generated from ChapterSqueezedGaussStates.lean — theorem BookProof.SqueezedGaussStates.Acoef_rec
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterGaussCoordCombo
import Mathlib
import Definitions.Def_ChapterSqueezedGaussStates
open BookProof.SqueezedGaussStates



open MvPolynomial BookProof.HermiteProductCore BookProof.GaussCoordCombo

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.SqueezedGaussStates.Acoef_rec (v : ℝ) (m : ℕ) :
    (2 * (m : ℝ) + 2) * Acoef v (m + 1) = 4 * v ^ 2 * (2 * (m : ℝ) + 1) * Acoef v m := by sorry

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