`BookProof.SqueezedGaussStates.X_mul_coordCombo_even` (i : Fin d) (a : ℕ → ℝ) (M : ℕ) (ha : a (M + 1) = 0) : X i * coordCombo i a 0 M = coordCombo i (fun k => a k + 2 * (k + 1) * a

Proved

BookProof.SqueezedGaussStates.X_mul_coordCombo_even

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSqueezedGaussStates.

BookProof.SqueezedGaussStates.X_mul_coordCombo_even (i : Fin d) (a : ℕ → ℝ) (M : ℕ) (ha : a (M + 1) = 0) : X i * coordCombo i a 0 M = coordCombo i (fun k => a k + 2 * (k + 1) * a (k + 1)) 1 M

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

Preamble

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



open MvPolynomial BookProof.HermiteProductCore BookProof.GaussCoordCombo

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.SqueezedGaussStates.X_mul_coordCombo_even (i : Fin d) (a : ℕ → ℝ) (M : ℕ) (ha : a (M + 1) = 0) :
    X i * coordCombo i a 0 M = coordCombo i (fun k => a k + 2 * (k + 1) * a (k + 1)) 1 M := by sorry

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