`BookProof.SqueezedGaussStates.Usum_identity` (v : ℝ) (M : ℕ) : (1 - 4 * v ^ 2) * Usum v M = Vsum v M - 4 * v ^ 2 * (2 * (M : ℝ) + 1) * Acoef v M

Proved

BookProof.SqueezedGaussStates.Usum_identity

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSqueezedGaussStates.

BookProof.SqueezedGaussStates.Usum_identity (v : ℝ) (M : ℕ) : (1 - 4 * v ^ 2) * Usum v M = Vsum v M - 4 * v ^ 2 * (2 * (M : ℝ) + 1) * Acoef v M

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

Preamble

-- Generated from ChapterSqueezedGaussStates.lean — theorem BookProof.SqueezedGaussStates.Usum_identity
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.Usum_identity (v : ℝ) (M : ℕ) :
    (1 - 4 * v ^ 2) * Usum v M = Vsum v M - 4 * v ^ 2 * (2 * (M : ℝ) + 1) * Acoef v M := by sorry

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