`BookProof.SqueezedGaussStates.exists_momentum_small` {ε : ℝ} (hε : 0 < ε) : ∃ (v : ℝ) (M : ℕ), 4 * v ^ 2 < 1 ∧ coordComboSum (opCoef (-(1 / 2)) 1 v M) 1 M ≤ ε * coordComboSum (sqC

Proved

BookProof.SqueezedGaussStates.exists_momentum_small

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSqueezedGaussStates.

BookProof.SqueezedGaussStates.exists_momentum_small {ε : ℝ} (hε : 0 < ε) : ∃ (v : ℝ) (M : ℕ), 4 * v ^ 2 < 1 ∧ coordComboSum (opCoef (-(1 / 2)) 1 v M) 1 M ≤ ε * coordComboSum (sqCoef v M) 0 M

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

Preamble

-- Generated from ChapterSqueezedGaussStates.lean — theorem BookProof.SqueezedGaussStates.exists_momentum_small
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.exists_momentum_small {ε : ℝ} (hε : 0 < ε) :
    ∃ (v : ℝ) (M : ℕ), 4 * v ^ 2 < 1 ∧
      coordComboSum (opCoef (-(1 / 2)) 1 v M) 1 M ≤ ε * coordComboSum (sqCoef v M) 0 M := by sorry

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