`BookProof.SqueezedGaussStates.op_squeezeState` (i : Fin d) (α γ v : ℝ) (M : ℕ) : ((α : ℝ) : ℂ) • (X i * squeezeState i v M) + ((γ : ℝ) : ℂ) • pderiv i (squeezeState i v M) = coord

Proved

BookProof.SqueezedGaussStates.op_squeezeState

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSqueezedGaussStates.

BookProof.SqueezedGaussStates.op_squeezeState (i : Fin d) (α γ v : ℝ) (M : ℕ) : ((α : ℝ) : ℂ) • (X i * squeezeState i v M) + ((γ : ℝ) : ℂ) • pderiv i (squeezeState i v M) = coordCombo i (opCoef α γ v M) 1 M

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

Preamble

-- Generated from ChapterSqueezedGaussStates.lean — theorem BookProof.SqueezedGaussStates.op_squeezeState
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.op_squeezeState (i : Fin d) (α γ v : ℝ) (M : ℕ) :
    ((α : ℝ) : ℂ) • (X i * squeezeState i v M)
        + ((γ : ℝ) : ℂ) • pderiv i (squeezeState i v M)
      = coordCombo i (opCoef α γ v M) 1 M := by sorry

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