`BookProof.SqueezedGaussStates.coordComboSum_opCoef_le` (α γ v : ℝ) (M : ℕ) (hv : 4 * v ^ 2 < 1) : coordComboSum (opCoef α γ v M) 1 M ≤ ((kappa α γ v) ^ 2 / (1 - 4 * v ^ 2) + α ^ 2

Proved

BookProof.SqueezedGaussStates.coordComboSum_opCoef_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSqueezedGaussStates.

BookProof.SqueezedGaussStates.coordComboSum_opCoef_le (α γ v : ℝ) (M : ℕ) (hv : 4 * v ^ 2 < 1) : coordComboSum (opCoef α γ v M) 1 M ≤ ((kappa α γ v) ^ 2 / (1 - 4 * v ^ 2) + α ^ 2 * (2 * (M : ℝ) + 1) * (4 * v ^ 2) ^ M) * coordComboSum (sqCoef v M) 0 M

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

Preamble

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



open MvPolynomial BookProof.HermiteProductCore BookProof.GaussCoordCombo

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.SqueezedGaussStates.coordComboSum_opCoef_le (α γ v : ℝ) (M : ℕ) (hv : 4 * v ^ 2 < 1) :
    coordComboSum (opCoef α γ v M) 1 M
      ≤ ((kappa α γ v) ^ 2 / (1 - 4 * v ^ 2) + α ^ 2 * (2 * (M : ℝ) + 1) * (4 * v ^ 2) ^ M)
        * coordComboSum (sqCoef v M) 0 M := by sorry

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